Historic, Archive Document
Do not assume content reflects current scientific knowledge, policies, or practices.
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United States Department of ' Agriculture |
^^A Programmer's Guide |
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Forest Service Intermountain |
to the Prognosis |
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Research Station General Technical Report INT-269 |
Optimization l\/lodel |
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June 1990 |
Robert A. [\/lonserud ^ . Robert G. Height |
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)u4s( |
1
934920
at the University of California in Berkeley. In 1 985 he earned a Ph.D. degree in forest management at Oregon State
Support for this research came from the following University. After spending 2 years as Ciriacy-Wantrup
branches of the Forest Service: Intermountain Research Postdoctoral Fellow at the University of California, Berkeley,
Station, Northern Region of the National Forest System, Dr. Haight joined the Southeastern Forest Experiment
and the Timber Management Research Staff from the Station in 1987. He has authored several important
Washington Office. We are indebted to Bill Wykoff and publications on optimal management of both even-aged and
Nick Crookston for invaluable programming assistance. uneven-aged forest stands, as well as a book on population
harvesting coauthored with Wayne Getz.
THE AUTHORS
CONTENTS
ROBERT A. MONSERUD is principal mensurationist,
Intermountain Research Station, at the Forestry Sciences 1 Introduction 1
Laboratory in Moscow, ID. After earning a B.A. degree in 2 The Prognosis Optimization Model 1
mathematics at the University of Iowa in 1968 and teaching 3 '"PUt Requirements and Output Produced 2
high school math for 3 years, Monserud switched to forestry. 3-1 Optimizer Input File 2
He earned an M.S. degree in forest management in 1973 3.2 Prognosis Input Files 4
and a Ph.D. degree in forest biometrics and mensuration in 3.3 Output File 4
1975, both at the University of Wisconsin, Madison. Since 4 Three Examples 4
joining the Intermountain Research Station in 1975, 4.1 Example 1 4
Monserud has worked on a variety of problems centered 4.2 Example 2 7
on modeling stand dynamics and site productivity for 4.3 Example 3 1 0
uneven-aged mixed-species forests. For the past 6 years, 5 Program Execution and Size Limits 14
Monserud has served as associate editor of Forest Science. 6 Program Installation 14
He has also served as invited visiting professor at University 7 Program Structure 1 5
of California, Berkeley, and as invited visiting scientist at the 7.1 Initialization 15
International Institute for Applied Systems Analysis in 7-2 Search Process 16
Laxenburg, Austria. Current projects include problems in 8 Creating an Executable Program 1 6
optimal stand management (conducted with Haight), model- 8.1 Compiling Source Code 1 6
ing the components of tree growth, site productivity, and 8.2 Building Object Libraries 1 7
crown backdating, and global vegetation modeling. 8.3 Linking the Object Code 1 7
8.4 Modifying the Program 1 8
ROBERT G. HAIGHT is principal economist. Southeastern g References 18
Forest Experiment Station at the Forestry Sciences Labora- ^ g Appendix: Optimizer Program Code".'.\'.'L 1 9 tory in Research Triangle Park, NC. Haight earned a B.S. degree in forestry in 1978 and an M.F. degree in 1981, both
The use of trade or firm names in this publication is for reader information and does not imply endorsement by the U.S. Department of Agriculture of any product or service.
A Programmer's Guide to the Prognosis Optimization IVIodei
Robert A. Monserud Robert G. Haight
INTRODUCTION
The Prognosis Optimization Model is designed as a research tool to investigate the effects of changes in economic and biological parameters on optimal harvest regimes for mixed-species stands in the Northern Rocky Mountains. The optimization program involves a coordinate-search process called the Method of Hooke and Jeeves (Hooke and Jeeves 1961), and it incorporates without modification version 5.2 of the Stand Prognosis Model (Wykoffet al. 1982; Ferguson and Crookston 1984; Crookston 1985; Ferguson et al. 1986; Hamilton 1986; WykofF 1986). The optimizer requires the same keyword and treelist input files as the Prognosis Model, as well as an additional input file that defines the size and objective of the harvest problem. The user sets the size of the prob- lem by defining harvest classes that consist of diameter classes, species groups, and periods in which harvesting may take place. The management objective may either be to maximize present value or to maximize volume produc- tion. The program returns optimal harvest intensities for the predefined harvest classes. Because of their compati- bility, results fi-om the Prognosis Optimization Model complement simulation results obtained with the Stand Prognosis Model.
This guide describes how to compile and run the optimi- zation program using a personal computer. In section 2 we describe the kinds of problems that may be solved and some limitations. Section 3 describes the input require- ments and output associated with the optimization model. The input and output for three optimization runs are described in section 4. Section 5 describes how to organ- ize the input files and execute the optimizer. Section 6 describes how to install the optimizer on a personal computer. The file names used in sections 5 and 6 are identical to those contained in the distribution diskette, which may be obtained from the senior author. Readers interested in using the existing executable module for optimization work should read the first six sections. Those interested in changing and compiling the source code should read sections 7 and 8, which describe in detail the source code and compilation instructions.
There are other sources of information related to the Prognosis Optimization Model. We assume that readers are familiar with the operation of the Stand Prognosis Model (see Wykoffet al. 1982; Wykoff 1986; Ferguson and Crookston 1984; Crookston 1985; Ferguson et al. 1986; Hamilton 1986). Those interested in changing the program should also read WykofPs (1988) instructions for compiling the Prognosis Model on a personal computer.
The performance of the Prognosis Optimization Model and its application to various management problems are described by Haight and Monserud (1990a, b).
The following conventions are used to describe pro- grams, variables, and files. Fortran PROGRAM NAMES are written in capital letters; VARIABLES in the pro- grams are written in capital italics. Except where noted, Fortran programs are found in MS-DOS files with the same names. When DOS files are described, they are written in capital italics with a suffix (MAIN. FOR) Prognosis keywords are written in small capitals, and they will always be identified as keywords in the text.
THE PROGNOSIS OPTIMIZATION MODEL
The Stand Prognosis Model is designed to simulate the development of forest stands in the Northern Rocky Mountains. The individual tree is the basic unit of projec- tion, and stands with any combination of species and size classes can be accommodated. We use the Inland Empire version 5.2 of the Prognosis Model, which is calibrated for 11 conifer species on 30 habitat types in northern Idaho and northwestern Montana.
The Prognosis Optimization Model is capable of solving harvesting problems that fit two broad stand- management categories: any-aged management and even-aged management. The any-aged stand manage- ment problem is to determine the best sequence of species and diameter-class harvesting rates and planting intensi- ties for an existing stand over an infinite time horizon. Harvesting and planting may take place simultaneously in any period, and there are no constraints on the stand size or £ige structure. Because the sequence of residual diameter distributions may take on any structure, the optimal management regime is any-aged (see Haight and Monserud 1990a for a mathematical description of the problem). In practical applications, an infinite-time- horizon problem cannot be solved. However, sensitivity analysis can be used to determine the impacts of finite- time-horizon approximations. Haight and Monserud (1990a) formulate any-aged management problems in which the stand is eventually clearcut. They find that, with a maximum present value objective and a 4 percent discount rate, horizons greater than 160 years have little impact on optimal management regimes and present values. Haight and Monserud (1990b) determine the impacts of maximum present value and maximum cubic foot volume objectives on optimal any-aged manaigement regimes.
1
For even-aged management, harvesting problems have two components: the determination of the best thinning regime to employ in an existing stand before it is clearcut (or seedtree harvested), and the determination of the best sequence of thinnings to undertake in the subsequent plantation (or even-aged natural stand). These compo- nents are called the conversion problem and the planta- tion problem, respectively. The optimal plantation regime is found independently of the conversion regime, and it maximizes an infinite series of rents. (Rent is a general term for payoffs that may be measured in present value or volume units depending on the problem objective. Haight and Monserud [1990b] give detailed solutions to even- aged management problems that are formulated with these two objectives.) The best infinite-series plantation is found by comparing the rents from plantations with dif- ferent rotation ages. The optimal conversion regime maximizes the sum of the rents fi*om conversion and plan- tation management. The optimal conversion period is found by comparing the rents fi-om conversion and planta- tion regimes with different conversion ages.
A third category of harvesting problems involves un- even-aged stand management. The goal is to determine the best sequence of selection harvests for a transition regime that terminates with a steady state. The develop- ment of methods for solving these constrained problems is in the planning stage, and they are not included in this version of the optimizer.
The coordinate-search algorithm does not guarantee convergence to a globally optimal solution to a given har- vesting problem. For both even-aged and any-aged man- agement problems, the Prognosis Optimization Model evaluates harvest regimes that are defined by a set of con- trol variables representing the Abactions of trees harvested by diameter class and species group in specified periods. The number of diameter classes and species groups greatly affects convergence. Performance tests show that, for problems with diameter-class and species-class har- vest controls defined in two or more periods, the algorithm converges to solutions that may vary considerably in pres- ent value and harvest pattern depending on the point at which the search starts and how broadly the control vari- ables are defined (Haight and Monserud 1990a).
From our experience, the performance of the optimizer is improved by defining harvest controls for relatively wide diameter classes and broad species groupings. In the examples presented here, we use three submerchantable diameter classes (0-2, 2-4, and 4-7 inches) and five mer- chantable diameter classes (7-10, 10-14, 14-18, 18-22, and 22-40 inches). These groupings have proven efficient and considerably reduce the variability resulting from differ- ent random starts (Haight and Monserud 1990a). We rec- ommend using species groups in addition to diameter classes only when stumpage price varies by species group. For maximum volume production objectives in which stumpage price is not a concern, the optimizer usually converges to solutions with higher objective function val- ues using just one species group.
Because the optimizer does not guarantee the global optimum, we recommend examining a range of local optima before selecting the best solution to a given prob- lem. In our management studies, we solve each harvest- ing problem at least three times (and usually six) using different starting points for the harvest controls. Starting points are determined either randomly or from solutions to problems with shorter time horizons.
While the coordinate-search algorithm concentrates on determining optimal harvest intensities by diameter class and species group, planting and site preparation may also be scheduled in any period. These cultural ac- tivities are defined as fixed rather than variable inputs. The coordinate-search process determines the optimal harvest proportions for a given set of cultural activities. Repeated application of the optimization program allows comparison of the efficiencies of sets of cultural activities. In an example presented in section 4.3, the Prognosis Optimization Model is used to determine the thinning regime that maximizes merchantable cubic foot volume production for a white pine plantation that starts with 600 seedlings per acre and has a rotation age of 120 years. To determine the best planting density, the optimization needs to be repeated for a wide range of planting densities (see, for example, Haight and Monserud 1990b). Perform- ance tests showed that this procedure provides solutions with higher objective function values than does a proce- dure in which cultural activities are treated as control variables in addition to the harvest controls (Haight and Monserud 1990a).
3 INPUT REQUIREMENTS AND OUTPUT PRODUCED
3.1 Optimizer Input File
The input file for the optimizer contains records. Each record is a line containing one or more numerical entries. Unless otherwise specified, each entry is assigned a five- space column. Each entry is either an integer, which is right justified within its column, or a real number, which includes a decimal point and may be placed anywhere within its column. For an example of the optimizer input, see figure la, section 4.1. Those interested in the Fortran code that defines the input format may refer to MAIN.FOR in the appendix. In the following description, variable names are taken directly from the Fortran code.
The first entry in record 1 is an integer (NRUN) repre- senting the number of separate optimizations to be made during the execution of the program. Then, on the same record are NRUN entries representing random number seeds. These are coded as integer-valued real numbers. Each optimization run uses a different seed. If a seed is positive, the optimization will begin by using a set of ran- dom harvest controls generated by that seed. If the seed is negative, the optimization will start by using specified harvest controls (see record type 8, below). This conven- tion allows for combining optimizations that begin with
2
different random seeds along with an optimization that begins with specific harvest controls, all in the same batch job.
Record 2 has five real-number entries that define the discount rate and parameters for the search procedure (see Haight and Monserud 1990a):
1. R is the decimal-valued discount rate (between 0.0 and 1.0).
2. ALPHA is the acceleration step used in the pattern search.
3. DELTA is the beginning step size for the coordinate search.
4. EPS is the minimum step size allowed in the coordi- nate search before termination.
5. EPSl is the minimum improvement in present value resulting from successive coordinate seiches allowed before termination.
The discount rate is used to evaluate harvest revenues. When 0.0 < J? < 1.0, the objective is to maximize present value. When R = 0.0, a maximum volume yield objective is implied. Based on our experience, we suggest using the following values for ALPHA, DELTA, EPS, and EPSl. Setting ALPHA = 0.1 allows for a moderate change in the harvest control values each time a pattern search is per- formed. Setting DELTA =1.0 tests the boundary of each control during the first coordinate search. Setting EPS = 0.2 and EPSl = 999.0 allows five coordinate-search iterations before termination.
Record 3 contains seven integer entries that define the size of the optimization problem and the features of the output:
1. NUMCYC is the number of growth periods in the planning horizon. (This has the same value as the NUMCYCLE keyword in Prognosis.)
2. MERCH is the index of the minimum merchantable diameter class (for example, if the first three diameter classes contain unmerchantable trees, MERCH = 4).
3. NGROUP is the number of species groups used to classify trees.
4. MVOL is an index for the unit of volume measure- ment used in evaluating management regimes. When MVOL > 0, merchantable board foot volume is used. When MVOL < 0, merchantable cubic foot volume is used.
5. LENGTH is the length of the growth period (usually 10 years).
6. NTH specifies that output be printed every NTH growth period.
7. NOKEY is zero if the thindbh keywords describing the optimal regime are not to be written on the optimizer output file.
All entries on record 4 are integers. The first entry is the number of harvest periods NCUTS. The remaining entries are the periods (vector ICUT) in which harvests are scheduled. Note that the start of period 1 in the op- timizer corresponds to year 0 in Prognosis and therefore denotes an immediate harvest. Also note that a clearcut in the final period always takes place and thus is not a variable in the optimization.
The first entry on record 5 is an integer representing the number of diameter-class boundaries (NCLASS + 1). Following this entry are NCLASS + 1 real numbers repre- senting the boundaries. The first boundary is 0.0, and the last should be larger than any tree you expect the optimizer to see. The optimizer then calculates class midpoints, which are used in the output routine to sum- marize the diameter distribution. The diameter classes defined by these boundaries classify tree records in Prog- nosis for the purpose of harvesting. A harvest control variable is defined for each diameter class.
The next set of records (call these record type 6) enters the species codes for the species groups. There is one record for each of the NGROUP species groups. The first entry is an integer representing the number of species. The following entries are real numbers representing spe- cies identification codes that Prognosis uses (see WykofT 1986). As a shortcut when all species are assigned to one group (NGROUP = 1), simply enter 1 for the number of species in the group and 0.0 as the species code (see fig. la, section 4.1).
Prices for each species group are entered with the next set of records (record type 7). Again, there is one record for each species group, and these records are in the same order as the species-group records written above. The en- tries on each record are real numbers representing prices by diameter class. The prices for unmerchantable diame- ter classes are negative and represent the cost per tree for precommercial thinning. The prices for merchantable diameter classes represent stumpage prices per thousand board feet or thousand cubic feet, depending on the value of MVOL. If merchantable volume maximization is the objective, the prices for the unmerchantable and mer- chantable classes should be 0.0 and 1.0, respectively (the discount rate R should also be 0.0).
The final sets of records (record type 8) enter the initial values for the harvest control array Ul. First of all, there is one set of records for each species group. The record sets are in the same order as the species-group records written above. There are NUMCYC records for each spe- cies group. Each of these records contain the harvest con- trol values by diameter class for each period, beginning in the first period. Note that harvests occur at the start of a period and that all optimizations end with a clearcut that capitalizes the growing stock. The entries in each record are real numbers between 0.0 and 1.0 that represent the harvest proportions for the smallest to the largest diame- ter class. In contrast to previous records, each entry is contained in a seven-space column. If a particular period is not scheduled for cut, the harvest controls are 0.0 for that period. With a positive random number seed, ran- dom values between 0.0 and 1.0 are subsequently as- signed to the harvest controls in each of the cutting periods specified on record 4.
In summary, the first five records are one line each. The next two sets of records each have NGROUP lines. The last set of records has NGROUP • NUMCYC lines. Thus, the input file should contain 5 + 2 • NGROUP + NGROUP • NUMCYC lines.
3
3.2 Prognosis Input Files
In addition to the input file for the optimizer, there are two input files required to run the Prognosis Model: a treelist file and a keyword file (see Wykoff'et al. 1982 and Wykoff" 1986 for a detailed description of the format for these input files). The treelist file contains a list of tree records that describe attributes of the trees in the initial stand. The keyword file (see fig. lb, section 4.1, for example) contains all the commands that are required to run Prognosis except for the harvest controls, which are read directly into Prognosis during the optimization. In addition, a response file is also utilized. It simply con- tains the names of the treelist file and the keyword file, thus telling the Prognosis Model where to find its input data.
3.3 Output File
The output file from the optimization program has four parts (see fig. Ic, section 4.1, for example). Part 1 lists input data including the discount rate, the parameters for the coordinate-search process, the random number seed, the thinning periods, and the species numbers for each species group.
Part 2 lists the present value and step size associated with each coordinate search and pattern search. The first present value represents the evaluation of the initial management regime. When the algorithm terminates, the program writes the present value of the final manage- ment regime and the number of calls to Prognosis. The initial value of the stand is calculated, printed, and subtracted from the present value of the regime. This optimal net value is then printed. Note that using net rather than total value in an analysis eliminates problems that might arise if several stands (with different initial volumes) are to be examined. It is clearly necessary to work with net value to avoid double counting if sequential optimizations on the same stand over time are concate- nated. (Haight and Monserud [1990b] concatenated three successive 160-year optimizations on the same stand in an attempt to examine the steady-state properties of the optimal any-aged regime.) If volume rather than present value is being optimized, the program also prints average annual production (AAP), which is optimal net volume divided by the length of the regime. Note that AAP equals mean annual increment for an even-aged plantation or stand.
In the third part of the output, the optimal harvest re- gime is described in three tables (for each species group) that describe various diameter distributions over time: the residual stand, the harvested stand, and the percent- age of trees harvested. Four stand averages are written aft;er each diameter distribution: trees per acre, basal area per acre, merchantable volume per acre, and value (dollars per acre). Merchantable volume is either in units of 1,000 board feet or 1,000 cubic feet, whichever was specified on input. Note that the estimate of basal area is biased because it is calculated using the midpoint of the
associated diameter class (Prognosis does not use a basal area vector); this estimate is used only for display pur- poses, however.
In part 4 of the output, the program writes the optimal harvest control variables in exactly the format used for input. This allows for efficiently restarting an optimiza- tion from the output of a shorter optimization problem. Part 4 also contains a list of thindbh keywords specifying the appropriate year, diameter class, species, and harvest proportions for use in the Prognosis model. There is no Prognosis output associated with the optimization. To obtain Prognosis output, these thindbh keywords must be added to the keyword file for a separate Prognosis simula- tion. The THINDBH keywords will be written in the op- timizer output file if NOKEY is not zero (see the seventh entry on record 3 of the optimizer input file described in section 3.1).
4 THREE EXAMPLES
This section gives examples of conversion and plantation management problems that can be solved by the Prognosis Optimization Model. The first two examples assume that we start with a mixed-conifer stand in the Tsuga hetero- phylla I Clintonia uniflora habitat type and seek the best thinning regime for the stand before it is clearcut. Ex- ample 1 uses a maximum present value objective and a 20-year horizon. Example 2 uses a maximum cubic foot volume objective and a 40-year horizon. Example 3 as- sumes that we start with bare ground and plant 600 white pine seedlings per acre and seek the best thinning regime for a 120-year plantation.
4.1 Example 1
Suppose we start with the mixed conifer stand described in the Prognosis User's Guide (WykoflFet al. 1982). The problem is to determine the best thinning in period 1 (year 0) assuming that the stand is clearcut at the begin- ning of period 3 (year 20). Recall that thinnings take place at the start of a period. The objective is to maximize the present value of the stand over the 20-year horizon using a 4 percent discount rate. Trees less than 6 inches are not merchantable and cost $0.10 per tree to cut. Trees greater than 6 inches are worth $100.00 per Mbf independent of species and diameter. Harvest controls are defined for diameter classes, and all species are included in one species group.
The optimizer input file for this problem is listed in figure la; here we highlight some of the entries. Because the random number seed (record 1, entry 2) is positive, random proportions will be given to the starting values for the harvest controls. Because NUMCYC = 2 (record 3, entry 1), there are two growth periods in the planning horizon. Because MERCH = 4 (record 3, entry 2), there are three unmerchantable diameter classes. There is one species group (record 3, entry 3), and merchantable board foot volume is used to value harvested trees (record 3, entry 4). The length of the growth period is 10 years
4
(record 3, entry 5). There is one cutting period (record 4, entry 1), which is the first period (record 4, entry 2). Record 5 gives the diameter class bounds; note that there are eight diameter classes. Record 6 indicates one species in the group, and its species code is the shortcut 0 (all spe- cies are lumped into one group). Record 7 gives the tree prices (unmerchantable diameter classes) and stumpage prices (merchantable diameter classes). Records 8 and 9 list the initial values for the harvest controls for periods 1 and 2. Note that period 2 harvest controls equal zero be- cause no harvest is scheduled. Although harvest controls for period 1 equal 0, they are subsequently assigned ran- dom proportions between 0.0 and 1.0 because harvesting was specified for the first period.
The keyword file used to address Prognosis during the optimization run is listed in figure lb. The first four lines are based on the stand information given in the Prognosis User's Guide. The numtrip command specifies record tripling in the first two periods.* There are two growth
projection periods (>aJMcycLE is 2). The regeneration es- tablishment routine is called in the first period (estab is 0). Within this routine, the number of plot replications is 10, and no output is requested. The treedata ke)rword indicates that Prognosis should look for a treelist file for the description of the initial stand. The last two keywords are required to end the file.
This optimization run takes about 160 seconds on an IBM PS/2 Model 80 with a 20-Mhz processor. During the optimization, there are 31 calls to the Prognosis Model for projection. Output fi*om this example is listed in figure Ic. The optimal strategy for maximizing present value is simple: remove all merchantable trees immediately. The regime produces $216.53 after subtracting the initial value of the stand. Because the optimizer seeks diameter-class harvest controls in only one species group and period, the solution is obtained with a relatively short execution time. Beginning this problem with random harvest controls gen- erated by any integer seed between 1 and 6 results in the same solution.
Prognosis is well-behaved if it has approximately 500-600 tree records to project (W. Wykoff, personal commiuiication). Normal use of the NUMTRIP keyword (tripling twice) is intended to generate adequate variation from stand inventories that contain fewer tree records. We strongly recommend against using the optimizer with the NUMTRIP keyword disabled. If few records are projected, the optimizer may devise an anomalous management regime that favors the few fast growing tree records — which will unrealistically represent a large niimber of trees per acre. We also reconmiend using 5-year projection periods until version 6 of the Prognosis Model is released. This modification is necessary to elimi- nate a height-growth bias on small trees.
Figure 1a — Optimizer input file FIG1.INP \or example 1.
|
1 |
1. |
2. |
||
|
.OA |
.1 |
1.0 |
0.2 999. |
|
|
2 |
4 |
1 |
1 10 1 |
1 |
|
1 |
1 |
|||
|
9 |
0. |
2. |
A. 7. 10. |
1A. 18. 22. AO. |
|
1 |
0. |
|||
|
-.1 - |
1 |
-.1 |
100. 100. 100. |
100. 100. |
|
0.0000 |
0. |
0000 0.0000 0.0000 0 |
.0000 0.0000 0.0000 0.0000 |
|
|
0.0000 |
0. |
0000 0 |
.0000 0.0000 0 |
.0000 0.0000 0.0000 0.0000 |
Figure 1b — Prognosis keyword file FIGI.KEYfor example 1. STDIDENT
S2A8112 HOOKE AND JEEVES DISCRETE STEP; FIGURE 1
DESIGN 11.0 1,0
STOINFO 18.0 570.0 0.00 8.0 3.0 3A.0
NUMTRIP 2.
NUMCYCLE 2.
ESTAB 0.
HINREP 10.
OUTPUT 0.
END
TREEDATA
PROCESS
STOP
5
Figure 1c — Optimizer output file FIGI.OUTfor example 1.
B0BS2: PROGNOSIS OPTIMIZATION BY THE BOBS
OPTIMIZATION NUMBER 1 INTEREST RATE = 0.040 ACCELERATION STEP = 0.100 BEGINNING STEP SIZE = 1.000 MINIMUM STEP SIZE = 0.200 MINIMUM GAIN = 999.000 RANDOM NUMBER SEED = 1.000
THE OPTIMIZER WILL DETERMINE 1 HARVEST, OCCURRING IN PERIOD
SPECIES COOES FOR GROUP 1 ARE 0.
HOOKE & JEEVES COORDINATE SEARCH PROCESS:
PRESENT VALUE = 386.84
PERFORMED STEP SEARCH WITH DELTA = 1.000 PRESENT VALUE = 588.74
ACCELERATION STEP NOT SUCCESSFUL PERFORMED STEP SEARCH WITH DELTA = 0.500 PRESENT VALUE = 588.74
ACCELERATION STEP NOT SUCCESSFUL PERFORMED STEP SEARCH WITH DELTA = 0.250 PRESENT VALUE = 588.74
ACCELERATION STEP NOT SUCCESSFUL PERFORMED STEP SEARCH WITH DELTA = 0.125 PRESENT VALUE = 588.74
NUMBER OF PROGNOSIS SIMULATIONS = 31
INITIAL VALUE = 372.21 DOLLARS/ AC
OPTIMAL PRESENT NET VALUE (PNV) = 216.53 DOLLARS/AC
RESIDUAL TREES PER ACRE FOR SPECIES GROUP 1 DBH YEAR >
|
CLASS |
0 |
10 |
20 |
|
1. |
245.5 |
929.8 |
0.0 |
|
3. |
54.5 |
10.9 |
0.0 |
|
5. |
136.6 |
132.6 |
0.0 |
|
8. |
0.0 |
85.1 |
0.0 |
|
12. |
0.0 |
8.7 |
0.0 |
|
16. |
0.0 |
0.0 |
0.0 |
|
20. |
0.0 |
0.0 |
0.0 |
|
31. |
0.0 |
0.0 |
0.0 |
|
TOTAL |
437. |
1167. |
0. |
|
BA/AC |
27. |
68. |
0. |
|
VO/AC |
0.00 |
1.87 |
0.00 |
|
$$/AC |
-43.7 |
79.8 |
0.0 |
HARVESTED TREES PER ACRE FOR SPECIES GROUP 1:
|
DBH |
••-YEAR |
||
|
CLASS |
0 |
10 |
|
|
1 . |
0.0 |
n n |
CUUO. o |
|
3. |
0.0 |
7 L |
|
|
5. |
0.0 |
n n |
JO . C |
|
8. |
78.5 |
U.U |
in ^ |
|
12. |
21.0 |
0.0 |
60.7 |
|
16. |
0.0 |
0.0 |
2.2 |
|
20. |
0.0 |
0.0 |
0.0 |
|
31. |
0.0 |
0.0 |
0.0 |
|
TOTAL |
99. |
0. |
2246. |
|
BA/AC |
47. |
0. |
116. |
|
VO/AC |
4.16 |
0.00 |
5.86 |
|
S$/AC |
415.9 |
0.0 |
378.8 |
PERCENTAGE TREES PER ACRE CUT FOR SPECIES GROUP 1:
|
DBH |
YEAR-- |
|||
|
CLASS |
0 |
10 |
20 |
|
|
1- |
0.00 |
0.00 |
100 |
.00 |
|
3. |
0.00 |
0.00 |
100 |
.00 |
|
5. |
0.00 |
0.00 |
100 |
.00 |
|
8. |
100.00 |
0.00 |
100 |
.00 |
|
12. |
100.00 |
0.00 |
100 |
.00 |
|
16. |
0.00 |
0.00 |
100 |
.00 |
|
20. |
0.00 |
0.00 |
0 |
.00 |
|
31. |
0.00 |
0.00 |
0 |
.00 |
OPTIMAL HARVEST CONTROL PARAMETERS FOR SPECIES GROUP 1: 0.0000 0.0000 0.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
OPTIMAL HARVEST KEYWORDS FOR PROGNOSIS
(INSERT IN THE KEYWORD FILE)
THINOBH 1. 7. 10, 1.0000
THINDBH 1. 10. 14. 1.0000
6
4.2 Example 2
In this case we start with the same stand, but the prob- lem is to determine the best thinnings in period 1 (year 0) and 3 (year 20) assuming that the stand is clearcut at the beginning of period 5 (year 40). The initial stand is ap- proximately 50 years old. The objective is to maximize the merchantable cubic foot volume produced in the stand over the 40-year horizon. Trees less than 6 inches in diameter are not merchantable. Harvest controls are defined for diameter classes in two species groups. Group 1 includes the two intolerant species, western larch (Larix occidentalis Nutt.) and lodgepole pine (Pinus contorta Dougl. ex Loud.), and group 2 includes all other species. (Note that we use two species groups for illustration. Because there are no stumpage price differences by species group, superior solu- tions may be obtained with only one group.)
The input file for the optimizer is listed in figure 2a; note the differences from the input listed in figure la. Because we are maximizing merchantable cubic foot volume, the discount rate is 0.0 (record 2, entry 1). With a 10-year projection interval and a 40-year horizon, NUMCYC = 4 (record 3, entry 1). There are two species groups (record 3, entry 3), and the volume code (record 3, entry 4) is less than zero to indicate a cubic foot volume measure. Record 4 indicates that there are two harvests, in periods 1 and 3. Records 6 and 7 give the number of species and species code for each of the two species groups. Note that there are two lines of prices (records 8 and 9), one for each species group. Unmerchantable tree classes have no value; mer- chantable tree prices equal 1, so that value is measured in thousand cubic foot units. Finally, note that initial harvest control variable values are entered as a block for each spe- cies group. The zeros in periods 1 and 3 will be replaced with random harvest proportions because the random seed is positive.
The Prognosis keyword file for the optimization run is listed in figure 2b. In this case there are four growth
projection periods (>aiMCYCLE is 4). The regeneration es- tablishment routine is called at the start of periods 1 (year 0) and 3 (year 20).
The optimization run requires about 30 minutes on an IBM PS/2 Model 80 with a 20-Mhz processor. During the optimization, there are 119 calls to the Prognosis Model for stand projection. The output is listed in figure 2c. The optimal regime calls for removing almost all of the merchantable intolerants immediately. The second har- vest (year 20) includes a precommercial thinning and the removal of a few of the largest trees in both species groups. In the clearcut in year 40, just over 200 merchant- able trees per acre are harvested. After subtracting the initial volume, the stand produces 116 ft^ per acre per year. As we are about to see in the next example, the stand is obviously understocked.
Figure 2a — Optimizer input file FIG2.INP \or example 2.
|
1 |
5. 6. |
7. |
8. 9. |
10. |
||||||
|
.0 |
.1 1.0 |
.2 999. |
||||||||
|
4 |
4 2 |
-1 |
10 1 |
1 |
||||||
|
2 |
1 3 |
|||||||||
|
9 |
0. 2. |
4. |
7. 10. |
14. |
18. 22 |
40 |
||||
|
2 |
2. 7. |
|||||||||
|
5 |
1. 3. |
4. |
5. 6. |
|||||||
|
0. |
0. 0. |
1. |
1. 1. |
1. |
1. |
|||||
|
0. |
0. 0. |
1. |
1. 1. |
1. |
1. |
|||||
|
0 |
0000 |
0.0000 0. |
0000 |
0.0000 0. |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0.0000 0. |
0000 |
0.0000 0. |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0.0000 0. |
0000 |
0.0000 0. |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0.0000 0. |
0000 |
0.0000 0. |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0.0000 0. |
0000 |
0.0000 0. |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0.0000 0. |
0000 |
0.0000 0. |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0.0000 0. |
0000 |
0.0000 0. |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0.0000 0. |
0000 |
0.0000 0. |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
Figure 2b — Prognosis keyword file FIG2.KEY\or example 2. STOIDENT
S248112 HOOKE AND JEEVES DISCRETE STEP: FIGURE 2
DESIGN 11.0 1.0
STDINFO 18.0 570.0 0.00 8.0 3.0 34.0
NUMTRIP 2.
NUMCYCLE 4.
ESTAB 0.
MINREP 10.
OUTPUT 0,
END
ESTAB 20. END
TREEDATA
PROCESS
STOP
7
Figure 2c— Optimizer output file FIG2.0UTfor example 2.
|
B0BS2: PROGNOSIS OPTIMIZATIOM BY THE BOBS |
RESIDUAL TREES |
PER ACRE FOR |
SPECIES GROUP |
2 |
|||||
|
DBH |
---YEAR |
-> |
|||||||
|
OPTIMIZATION NUMBER 1 |
CLASS |
0 |
10 |
20 |
30 |
40 |
|||
|
INTEREST RATE = 0.000 |
1. |
245.5 |
863.9 |
1800.9 |
1415.1 |
0.0 |
|||
|
ACCELERATION STEP = 0.100 |
3. |
54.5 |
42.0 |
5.4 |
39.6 |
0.0 |
|||
|
BEGINNING STEP SIZE = 1.000 |
5. |
120.8 |
107.0 |
79.0 |
33.5 |
0.0 |
|||
|
MINIMUM STEP SIZE = 0.200 |
8. |
11.2 |
71.3 |
98.5 |
81.4 |
0.0 |
|||
|
MINIMUM GAIN = 999.000 |
12. |
15.9 |
21.2 |
40.7 |
74.4 |
0.0 |
|||
|
RANDOM NUMBER SEED = 5.000 |
16. |
0.0 |
4.9 |
7.1 |
28.9 |
0.0 |
|||
|
20. |
0.0 |
0.0 |
0.0 |
1.8 |
0.0 |
||||
|
THE OPTIMIZER WILL DETERMINE |
2 HARVESTS. |
31. |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
||
|
THEY OCCUR IN PERIODS: 1 |
3 |
TOTAL |
448. |
1110. |
2032. |
1675. |
0. |
||
|
BA/AC |
41. |
76. |
104. |
150. |
0. |
||||
|
SPECIES COOES FOR GROUP 1 ARE 2. 7. |
VO/AC |
0.39 |
0.99 |
1.61 |
2.82 |
0.00 |
|||
|
SPECIES COOES FOR GROUP 2 ARE 1. 3. 4. |
5. 6. |
t$/AC |
0.4 |
1.0 |
1.6 |
2.8 |
0.0 |
||
|
HOOKE & JEEVES COORDINATE SEARCH PROCESS: |
HARVESTED TREES PER |
ACRE FOR SPECIES GROUP |
1: |
||||||
|
PRESENT VALUE = 3.57 |
DBH |
---YEAR |
-> |
||||||
|
PERFORMED STEP SEARCH WITH |
DELTA = 1.000 |
CLASS |
0 |
10 |
20 |
30 |
40 |
||
|
PRESENT VALUE = 5.57 |
1. |
0.0 |
0.0 |
33.2 |
0.0 |
13.7 |
|||
|
ACCELERATION STEP NOT SUCCESSFUL |
3. |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
|||
|
PERFORMED STEP SEARCH WITH |
DELTA = 0.500 |
5. |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
||
|
PRESENT VALUE = 5.57 |
8. |
64.3 |
0.0 |
0.0 |
0.0 |
0.0 |
|||
|
ACCELERATION STEP SUCCESSFUL |
12. |
0.6 |
0.0 |
1.1 |
0.0 |
3.5 |
|||
|
PRESENT VALUE = 5.57 |
16. |
0.0 |
0.0 |
1.4 |
0.0 |
10.7 |
|||
|
PERFORMED STEP SEARCH WITH |
DELTA = 0.250 |
20. |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
||
|
PRESENT VALUE = 5.57 |
31. |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
|||
|
ACCELERATION STEP NOT SUCCESSFUL |
TOTAL |
65. |
0. |
36. |
0. |
28. |
|||
|
PERFORMED STEP SEARCH WITH |
DELTA = 0.125 |
BA/AC |
26. |
0. |
3. |
0. |
18. |
||
|
PRESENT VALUE = 5.66 |
VO/AC |
0.49 |
0.00 |
0.09 |
0.00 |
0.43 |
|||
|
$S/AC |
0.5 |
0.0 |
0.1 |
0.0 |
0.4 |
||||
|
NUMBER OF PROGNOSIS SIMULATIONS = 119 |
|||||||||
|
HARVESTED TREES PER |
ACRE FOR SPECIES GROUP |
2: |
|||||||
|
INITIAL VOLUME = |
1019.8 CUFT/AC |
||||||||
|
DBH |
YEAR |
||||||||
|
NET OPTIMAL VOLUME = |
4635.5 CUFT/AC |
CLASS |
0 |
10 |
20 |
30 |
40 |
||
|
1. |
0.0 |
0.0 |
213.2 |
0.0 |
1568.0 |
||||
|
AVERAGE ANNUAL PRODUCTION = |
115.9 CUFT/AC/ YR |
3. |
0.0 |
0.0 |
0.8 |
0.0 |
84.5 |
||
|
5. |
0.0 |
0.0 |
0.0 |
0.0 |
8.7 |
||||
|
8. |
3.0 |
0.0 |
0.0 |
0.0 |
73.8 |
||||
|
RESIDUAL TREES PER ACRE FOR |
SPECIES GROUP |
1 |
12. |
0.0 |
0.0 |
0.0 |
0.0 |
71.5 |
|
|
16. |
0.0 |
0.0 |
7.3 |
0.0 |
41.7 |
||||
|
OBH YEAR |
-> |
20. |
0.0 |
0.0 |
0.6 |
0.0 |
9.9 |
||
|
CLASS 0 10 20 |
30 40 |
31. |
0.0 |
0.0 |
0.0 |
0.0 |
0.4 |
||
|
1. 0.0 30.5 1.9 |
0.9 0.0 |
TOTAL |
3. |
0. |
222. |
0. |
1859. |
||
|
3. 0.0 0.0 0.0 |
0.0 0.0 |
BA/AC |
1. |
0. |
13. |
0, |
181. |
||
|
5. 15.8 0.0 0.0 |
0.0 0.0 |
VO/AC |
0.03 |
0.00 |
0.32 |
0.00 |
4.30 |
||
|
8. 0.0 15.4 8.2 |
1.5 0.0 |
$$/AC |
0.0 |
0.0 |
0.3 |
0.0 |
4.3 |
||
|
12. 4.4 4.1 7.8 |
8.9 0.0 |
||||||||
|
16. 0.0 0.0 0.0 |
4.8 0.0 |
PERCENTAGE TREES PER ACRE CUT FOR |
SPECIES |
GROUP 1 : |
|||||
|
20. 0.0 0.0 0.0 |
0.0 0.0 |
||||||||
|
31. 0.0 0.0 0.0 |
0.0 0.0 |
DBH |
YEAR |
- - > |
|||||
|
TOTAL 20. 50. 18. |
16. 0. |
CLASS |
0 |
10 |
20 |
30 |
40 |
||
|
BA/AC 6. 9. 9. |
14. 0. |
1. |
0.00 |
0.00 |
94.65 |
0.00 |
100.00 |
||
|
0.34 0.00 |
3. |
0.00 |
0.00 |
0.00 |
0.00 |
100.00 |
|||
|
VO/AC 0.11 0.21 0.22 |
|||||||||
|
$$/AC 0.1 0.2 0.2 |
5. |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
|||
|
0.3 0.0 |
|||||||||
|
8. |
100.00 |
0.00 |
0.00 |
0.00 |
0.00 |
||||
|
12. |
12.50 |
0.00 |
12.50 |
0.00 |
100.00 |
||||
|
16. |
0.00 |
0.00 |
100.00 |
0.00 |
100.00 |
||||
|
20. |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
||||
|
31. |
0.00 |
0.00 |
0.00 |
0.00 |
0.00 |
8
Figure 2c (Con.)
PERCENTAGE TREES PER ACRE CUT FOR SPECIES GROUP 2:
|
DBH |
|
|
CLASS |
0 |
|
1. |
0.00 |
|
3. |
0.00 |
|
5. |
0.00 |
|
8. |
20.92 |
|
12. |
0.00 |
|
16. |
0.00 |
|
20. |
0.00 |
|
31. |
0.00 |
YEAR
|
10 |
20 |
|
0.00 |
10.58 |
|
0.00 |
12.50 |
|
0.00 |
0.00 |
|
0.00 |
0.00 |
|
0.00 |
0.00 |
|
0.00 |
50.60 |
|
0.00 |
100.00 |
|
0.00 |
0.00 |
30 40 0.00 100.00 0.00 100.00 0.00 100.00 0.00 100.00 0.00 100.00 0.00 100.00 0.00 100.00 0.00 100.00
OPTIMAL HARVEST CONTROL PARAMETERS FOR SPECIES GROUP 1: 0.0000 0.0000 0.0000 1.0000 0.1250 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.9465 0.0000 0.0000 0.0000 0.1250 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
OPTIMAL HARVEST CONTROL PARAMETERS FOR SPECIES GROUP 2: 0.0000 0.0000 0.0000 0.2092 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1058 0.1250 0.0000 0.0000 0.0000 0.5060 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
|
OPTIMAL HARVEST |
KEYWORDS |
FOR PROGNOSIS |
|||
|
(INSERT IN THE |
KEYWORD |
FILE) |
|||
|
THINDBH |
1. |
7. |
10. |
1.0000 |
2. |
|
THINDBH |
1. |
7. |
10. |
1.0000 |
7. |
|
THINDBH |
1. |
7. |
10. |
0.2092 |
1. |
|
THINDBH |
1. |
7. |
10. |
0.2092 |
3. |
|
THINDBH |
1. |
7. |
10. |
0.2092 |
4. |
|
THINDBH |
1. |
7. |
10. |
0.2092 |
5. |
|
THINDBH |
1. |
7- |
10. |
0.2092 |
6. |
|
THINDBH |
1. |
10. |
14. |
0.1250 |
2. |
|
THINDBH |
1. |
10. |
14. |
0.1250 |
7. |
|
THINDBH |
21. |
0. |
2. |
0.9465 |
2. |
|
THINDBH |
21. |
0. |
2. |
0.9465 |
7. |
|
THINDBH |
21. |
0. |
2. |
0.1058 |
1. |
|
THINDBH |
21. |
0. |
2. |
0.1058 |
3. |
|
THINDBH |
21. |
0. |
2. |
0.1058 |
4. |
|
THINDBH |
21. |
0. |
2. |
0.1058 |
5. |
|
THINDBH |
21. |
0. |
2. |
0.1058 |
6. |
|
THINDBH |
21. |
2. |
4. |
0.1250 |
1. |
|
THINDBH |
21. |
2. |
4. |
0.1250 |
3. |
|
THINDBH |
21. |
2. |
4. |
0.1250 |
4. |
|
THINDBH |
21. |
2. |
4. |
0.1250 |
5. |
|
THINDBH |
21. |
2. |
4. |
0.1250 |
6. |
|
THINDBH |
21. |
10. |
14. |
0.1250 |
2. |
|
THINDBH |
21. |
10. |
14. |
0.1250 |
7. |
|
THINDBH |
21. |
u. |
18. |
1.0000 |
2. |
|
THINDBH |
21. |
u. |
18. |
1.0000 |
7. |
|
THINDBH |
21. |
u. |
18. |
0.5060 |
1. |
|
THINDBH |
21. |
14. |
18. |
0.5060 |
3. |
|
THINDBH |
21. |
14. |
18. |
0.5060 |
4. |
|
THINDBH |
21. |
14. |
18. |
0.5060 |
5. |
|
THINDBH |
21. |
14. |
18. |
0.5060 |
6. |
|
THINDBH |
21. |
18. |
22. |
1,0000 |
1. |
|
THINDBH |
21. |
18. |
22. |
1.0000 |
3. |
|
THINDBH |
21. |
18. |
22. |
1.0000 |
4. |
|
THINDBH |
21. |
18. |
22. |
1.0000 |
5. |
|
THINDBH |
21. |
18. |
22. |
1.0000 |
6. |
9
4.3 Example 3
The following example is used by Haight and Monserud (1990b) to develop optimal white pine plantation manage- ment regimes. The objective is to maximize cubic foot volume production over a 120-year horizon in which thin- nings may take place every 20 years beginning in year 20. The fixed silvicultural inputs are defined in the Prognosis keyword file (fig. 3b). Using the same stand and site parameters as in the previous example (see the stdinfo keyword), this run begins with bare ground and plants 600 white pine seedlings per acre after site preparation is completed. During the 120-year projection (24 cycles of 5 years), the regeneration establishment model is called if thinning removes at least 20 ft^ per acre. If the thinning leaves less than 80 per acre then a regeneration cut is assumed to have occurred; site preparation is performed, and the establishment and development of both advanced and subsequent regeneration are simulated. If the
thinning leaves at least 80 ft^ per acre then site prepara- tion is not done, aind only advanced regeneration is simulated. Because we start with bare ground (note the NOTREES keyword), we have taken out the treedata kejrword.
The optimizer input file is listed in figure 3a. Unlike the previous examples, this optimization does not start with random harvest controls (on record 1, entry 2 is nega- tive). Instead, the run begins with the optimal 100-year regime specified in the block of harvest controls at the end of the file. When the optimization problem is complicated, this sequential strategy for specifying initial conditions is far more efficient than beginning with many random starts.
This optimization problem requires 177 calls to Prognosis and takes 112 minutes on a 20-Mhz personal computer. Output describing the optimal plantation management is listed in figure 3c. The optimal regime, which produces 163 ft^ per acre per year, is discussed in detail by Haight and Monserud (1990b).
Figure 3a— Optimizer input file FIG3.INPfor example 3.
|
1 |
-1 |
||||||||||||||
|
.0 |
.1 1.0 |
.2 999. |
|||||||||||||
|
24 |
t, |
1 |
-1 |
5 |
2 |
1 |
|||||||||
|
5 |
5 9 |
13 |
17 21 |
||||||||||||
|
9 1 |
0 |
. 2 D. |
i>. |
7. 10. |
14. |
18. 22 |
40 |
||||||||
|
0. |
0 |
0 |
1. |
1. 1. |
1. |
1. |
|||||||||
|
0 |
0000 |
0 |
.0000 |
0 |
.0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
.0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0.0000 |
0 |
0000 |
0 |
0000 |
|
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
1 |
0000 |
0 |
.5262 |
0 |
.0224 |
0 |
.8346 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
1250 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
1250 |
0. |
5000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
1 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.7500 |
0 |
0000 |
0. |
0000 |
0 |
3750 |
0 |
0000 |
|
0 |
.0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
.0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.8750 |
1 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
|
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0 |
.0000 |
0 |
0000 |
0. |
0000 |
0 |
0000 |
0 |
0000 |
10
Figure 3b — Prognosis keyword file F/G3.KEV for example 3.
|
STDIDENT |
||
|
S248112 |
HOOKE AND JEEVES; PLANT 600 UUP & GROU 120 YEARS |
|
|
STDIMFO |
18.0 570-0 0.00 8.0 3.0 34.0 |
|
|
NUMTRIP |
5. |
|
|
NOTREES |
||
|
TIMEINT |
5. |
|
|
NUMCYCLE |
24. |
|
|
ESTAB |
0. |
|
|
PLANT |
2. 1. 600. |
|
|
HECHPREP |
1. 50. |
|
|
BURNPREP |
1. 30. |
|
|
HINREP |
10. |
|
|
OUTPUT |
0. |
|
|
END |
||
|
COMMENT |
||
|
Schedule |
a normal call to ESTAB whenever a regeneration cut occurs: |
|
|
END |
||
|
IF |
||
|
(FRAC((CYCLE- |
1)/4 ) EQ 0) AND (CYCLE NE 1 ) & |
|
|
AND ( |
((BBA- |
ABA) GT 20) AND (ABA LT 80) ) |
|
THEN |
||
|
ESTAB |
||
|
MECHPREP |
0. 20. |
|
|
END |
||
|
END IF |
||
|
COMMENT |
||
|
Otherwise pump in advary:ed regeneration every 20 years: |
||
|
END |
||
|
IF |
||
|
(FRAC((CYCLE- |
1)/4 ) EQ 0) AND (CYCLE NE 1) & |
|
|
ANO ( |
((BBA-ABA) LE 20) OR (ABA GE 80) ) |
|
|
THEN |
||
|
ESTAB |
||
|
MECHPREP |
0. 0. |
|
|
TALLYONE |
3. |
|
|
END |
||
|
END IF |
||
|
PROCESS |
||
|
STOP |
11
Figure 3c — Optimizer output file FIG3.0UT\qx example 3.
B0BS2: PROGNOSIS OPTIMIZATION BY THE BOBS
OPTIMIZATION NUMBER 1
INTEREST RATE = 0.000
ACCELERATION STEP = 0.100
BEGINNING STEP SIZE = 1.000
MINIMUM STEP SIZE - 0.200
MINIMUM GAIN = 999.000
RANDOM NUMBER SEED - -1.000
THE OPTIMIZER WILL DETERMINE 5 HARVESTS. THEY OCCUR IN PERIODS: 5 9 13 17 21
SPECIES COOES FOR GROUP 1 ARE 0.
HOOKE & JEEVES COORDINATE SEARCH PROCESS:
PRESENT VALUE = 19.10
PERFORMED STEP SEARCH WITH DELTA = 1.000 PRESENT VALUE = 19.47
ACCELERATION STEP NOT SUCCESSFUL PERFORMED STEP SEARCH WITH DELTA = 0.500 PRESENT VALUE = 19.53
ACCELERATION STEP SUCCESSFUL PRESENT VALUE = 19.53
PERFORMED STEP SEARCH WITH DELTA = 0.250 PRESENT VALUE = 19.53
ACCELERATION STEP MOT SUCCESSFUL PERFORMED STEP SEARCH WITH DELTA = 0.125 PRESENT VALUE » 19.53
NUMBER OF PROGNOSIS SIMULATIONS = 177
INITIAL VOLUME = 0.0 CUFT/AC
NET OPTIMAL VOLUME = 19531.1 CUFT/AC
AVERAGE ANNUAL PRODUCT lOH = 162.8 CUFT/AC/YR
RESIDUAL TREES PER ACRE FOR SPECIES GROUP 1
|
DBH |
YEAR |
|||||
|
CLASS |
0 |
10 |
20 |
30 |
40 |
50 |
|
1. |
0.0 |
1976.8 |
0.0 |
1950.2 |
2871.6 |
2441.1 |
|
3. |
0.0 |
0.0 |
156.1 |
22.3 |
0.0 |
0.0 |
|
5. |
0.0 |
0.0 |
249.9 |
197.9 |
92.3 |
33.8 |
|
8. |
0.0 |
0.0 |
1.1 |
155.8 |
198.3 |
135.5 |
|
12. |
0.0 |
0.0 |
0.0 |
11.9 |
69,3 |
143.1 |
|
16. |
0.0 |
0.0 |
0.0 |
0.0 |
2.6 |
22.2 |
|
20. |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
1.0 |
|
31. |
0.0 |
0.0 |
0,0 |
0.0 |
0.0 |
0.0 |
|
TOTAL |
0. |
1977. |
407. |
2338. |
3234. |
2777. |
|
BA/AC |
0. |
11. |
49. |
115. |
167. |
218. |
|
VO/AC |
0.00 |
0.00 |
0.00 |
1.18 |
3.21 |
5.44 |
|
$J/AC |
0.0 |
0.0 |
0.0 |
1.2 |
3.2 |
5.4 |
HARVESTED TREES PER ACRE FOR SPECIES GROUP 1:
DBH YEAR >
CLASS 0 10 20 30 40 1. 0.0 0.0 3221.8 0.0 0.0
|
60 |
70 |
80 |
90 |
100 |
110 |
120 |
|
0.0 |
686.6 |
609.2 |
866.3 |
725.0 |
730.5 |
0.0 |
|
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
11.9 |
0.0 |
|
2.1 |
0.6 |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
|
21.9 |
14.5 |
6.0 |
2.3 |
0.0 |
0.0 |
0.0 |
|
155.9 |
105.3 |
0.0 |
2.9 |
1.8 |
1.4 |
0.0 |
|
53.6 |
65.8 |
65.0 |
45.1 |
23.7 |
12.0 |
0.0 |
|
2.7 |
20.9 |
40.7 |
41.8 |
46.5 |
36.4 |
0.0 |
|
0.0 |
0.8 |
1.4 |
14.3 |
25.7 |
41.7 |
0.0 |
|
236. |
894. |
722. |
973. |
823. |
834. |
0. |
|
212. |
234. |
193. |
237. |
275. |
321 . |
0. |
|
7.02 |
9.03 |
8.33 |
10.49 |
12.35 |
14.34 |
0.00 |
|
7.0 |
9.0 |
8.3 |
10.5 |
12.4 |
14.3 |
0.0 |
50
60
0.0 1986.5
70 0.0
80 0.0
90 0.0
100 0.0
110 0.0
120 485.6
12
Figure 3c (Con.)
|
u.u |
1 r J |
u.u |
n fl u.u |
fl n u.u |
n n |
u.u |
n n u.u |
fl fl u.u |
0.0 |
0.0 |
111.2 |
||
|
c !>• |
U.U |
n n U.U |
J ,( |
u.u |
fl fl u.u |
fl fl u.u |
u.u |
fl fl u.u |
u.u |
n n |
0.0 |
0.0 |
|
|
D o. |
U.u |
u.u |
ft n u.u |
fl fl u.u |
fl fl u.u |
fSk ft |
n n u.u |
n 0 U . T |
fl f) u.u |
u . o |
0.0 |
0.0 |
|
|
1 y |
U . V |
u.u |
fl fl u.u |
fl fl u.u |
fl fl u.u |
0 n |
0.0 |
0.0 |
2.2 |
0.0 |
1 . 1 |
||
|
1 A |
n fl u.u |
u.u |
fl n u.u |
fl fl u.u |
£. . D |
fl fl u.u |
u.u |
0.0 |
0.0 |
0.0 |
0.0 |
0.0 |
3.1 |
|
^u. |
u.u |
u.u |
n n u.u |
n fl u.u |
fl fl u.u |
fl fl u.u |
1 A 1 .o |
fl fl u.u |
0.0 |
0.0 |
0.0 |
0.0 |
29.9 |
|
^1 • |
u.u |
u.u |
u.u |
fl fl u.u |
fl fl u.u |
fl fl u.u |
fl fl u.u |
fl n u.u |
fl fl u.u |
fl n u.u |
u.u |
0.0 |
52.0 |
|
TOTAL |
0, |
0. |
3407. |
0. |
3. |
0. |
2054. |
0. |
75. |
0. |
3. |
0. |
683. |
|
BA/AC |
0. |
0. |
29. |
0. |
4. |
0. |
40. |
0. |
59. |
0. |
2. |
0. |
351. |
|
VO/AC |
0.00 |
0.00 |
0.02 |
0.00 |
0.10 |
0.00 |
0.74 |
0.00 |
2.62 |
0.00 |
0.07 |
0.00 |
15.99 |
|
$S/AC |
0.0 |
0.0 |
0.0 |
0.0 |
0.1 |
0.0 |
0.7 |
0.0 |
2.6 |
0.0 |
0.1 |
0.0 |
16.0 |
PERCENTAGE TREES PER ACRE CUT FOR SPECIES GROUP 1:
|
DBH |
|
|
CLASS |
0 |
|
1, |
0.00 |
|
3. |
0.00 |
|
5. |
0.00 |
|
8. |
0.00 |
|
12. |
0.00 |
|
16. |
0.00 |
|
20. |
0.00 |
|
31. |
0.00 |
--YEAR â–
10 20 0.00 100.00 0.00 52.62 0.00 2.24 0.00 83.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
|
30 |
40 |
|
|
0.00 |
0. |
00 |
|
0.00 |
0. |
00 |
|
0.00 |
0. |
00 |
|
0.00 |
0 |
00 |
|
0.00 |
0 |
00 |
|
0.00 |
50 |
00 |
|
0.00 |
0 |
00 |
|
0.00 |
0 |
00 |
so 60
0.00 100.00
0.00 0.00
0.00 0.00
0.00 75.00
0.00 0.00
0.00 0.00
0.00 37.50
0.00 0.00
|
70 |
80 |
|
|
0. |
00 |
0.00 |
|
0. |
00 |
0.00 |
|
0. |
00 |
0.00 |
|
0 |
00 |
12.50 |
|
0 |
00 |
100.00 |
|
0 |
00 |
0.00 |
|
0 |
00 |
0.00 |
|
0 |
00 |
0.00 |
90 100
0.00 0.00
0.00 0.00
0.00 0.00
0.00 100.00
0.00 55.00
0.00 0.00
0.00 0.00
0.00 0.00
110 120 0.00 100.00 0.00 100.00 0.00 0.00 0.00 0.00 0.00 100.00 0.00 100.00 0.00 100.00 0.00 100.00
OPTIMAL HARVEST CONTROL PARAMETERS FOR SPECIES GROUP 1: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.5262 0.0224 0.8346 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.7500 0.0000 0.0000 0.3750 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0,0000 0.0000 0.0000 0,0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1250 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 t.OOOO 0.5500 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 o.oooo
|
OPTIMAL |
HARVEST |
KEYWORDS |
FOR PROGNOSIS |
||
|
(INSERT |
IN THE |
KEYWORD |
FILE} |
||
|
THINOBH |
21. |
0, |
2, |
1.0000 |
|
|
THINOBK |
21, |
2. |
4. |
0.5262 |
|
|
THINOBH |
21. |
4. |
7. |
0.0224 |
|
|
THINDBH |
21. |
7. |
10. |
0.8346 |
|
|
THINOBH |
41. |
14. |
18. |
0.5000 |
|
|
THINDBH |
61. |
0. |
2, |
1.0000 |
|
|
THINOBH |
61. |
7. |
10. |
0.7500 |
|
|
THINOBH |
61, |
18, |
22. |
0.3750 |
|
|
THINOBH |
81. |
7, |
10. |
0.1250 |
|
|
THINDBH |
81. |
10. |
14. |
1.0000 |
|
|
THINDBH |
101, |
7, |
10. |
1,0000 |
|
|
THINDBH |
101. |
10. |
14. |
0.5500 |
13
5 PROGRAM EXECUTION AND SIZE LIMITS
As we described in sections 3.1 and 3.2, there are sev- eral files required to run the Prognosis Optimization Model. Here we describe how to organize these files and execute the optimizer. File names correspond to those contained in the distribution diskette. Installing the pro- gram is the subject of section 6.
We recommend executing the Prognosis Optimization Model with a DOS batch file such as FIGl. BAT with the following commands:
DT
COPY FIGl.INP BOBS.INP COPY FIGl.KEY TEST.KEY OPTGROW < TEST.RSP COPY BOBS.OUT FIGl.OUT DT
F1G1.BAT contains the set of commands needed to solve the harvest problem discussed in example 1 above. The DT execute commands print the date and time at the start and end of the optimization. File FIGl.INP contains the input data for the optimizer (fig. la). It is copied to file BOBS.INP, which the optimizer will read for input para- meters. File FIGl.KEJY contains the Prognosis keywords (fig. lb), and it is copied to file TEST.KEY, which Progno- sis will read for keywords. The command OPTGROW executes the optimizer. This command points to response file TEST.RSP, which contains file names for the Progno- sis treelist file TEST.TRE and keyword file TEST.KEY. After executing the OPTGROW command, the output file BOBS.OUT is copied to FIGl.OUT (Qg. Ic), which will not be v*Titten over by a subsequent execution of the op- timizer (as BOBS.OUT will be).
Now that we know what is contained in the input files, it is time to make the optimization run. To do this, simply type the command:
FIGl
which initiates execution of the batch file that contains the commands for running the program.
Limits to the size of the optimization problem that can be solved are affected by the size of the arrays declared in the optimization program (see the appendix; Haight and Monserud [1990a] also discuss practical limits on the com- plexity of optimization problems that can be solved). Cur- rently the maximum numbers of periods, diameter classes, and species groups are 33, 8, and 3, respectively. If these are changed, be sure to modify array size declara- tions in each of the following optimization routines: MAIN and subroutines CONTROL, OUT, STATE, VALUE, and GKEY (all of which are in OPT.FOR), and PMAIN2 (which is in PMAIN.FOR).
Limits to the size of the problem are also affected by the maximum number of keywords (1,200) and keyword para- meters (6,000) that may be processed by the Prognosis Model. In a keyword file for a thinning regime, thindbh keywords take up the most space. Whenever harvesting takes place by species group, a THINDBH keyword is created for each diameter class, tree species, and period in which harvesting may occur. Further, there are five
parameters on each thindbh keyword. To see how rap- idly these accumulate, suppose we define an optimization problem with 10 tree species among three groups, eight diameter classes, and 15 cutting periods. Then, there are 10 X 8 X 15 = 1,200 keywords and 1,200 x 5 = 6,000 para- meters. Because there are several other keywords that define the harvest regime (estab, for example), this key- word file is too large for the Prognosis Model, with uncer- tain consequences. The Prognosis Model may either ter- minate prematurely or not process keywords beyond the upper limit. Thus, it is important to make sure the prob- lem size is within these boundaries.
Execution time depends on the size of the problem. Ex- ample 1, which includes one thinning period, eight diame- ter classes, one species group, and a 20-year horizon, re- quires about 3 minutes on a 386 personal computer (an IBM PS/2 Model 80) with a 20-Mhz processor. Problems with thinnings every 20 years and 40-, 60-, and 160-year time horizons require around 25, 50, and 240 minutes, respectively. For more than one species group, multiply these times by the number of groups. Execution times on other personal computers should be approximately pro- portional to the ratio of the processor ft-equencies. For ex- ample, the 3-minute run discussed above took 3.8 minutes on a Compaq 386 with a 16-Mhz clock.
6 PROGRAM INSTALLATION
There are two ways to get an executable version of the optimizer on your system. The first — and by far the simplest — is to extract it fi-om the archived executable code stored on the distribution diskette. This approach is fine if you simply want to run the optimizer and do not need to modify anything in the program. This section explains this choice. The second way to get an executable program is to build it from the source code contained on the distribution diskette. This procedure is explained in section 8.
For openers, we assume that MS-DOS is the operating system on your personal computer (we will occasionally use the DOS wildcard character *). Begin by copying OPTGROW.ARC, ARC.DOC, and ARC.EXE files from the program diskette onto a directory dedicated to running the optimizer. The Prognosis Optimization Model and input files for three examples are compactly written onto OPTGROW.ARC using a public domain archiving utility called ARC that is distributed by Systems Enhancement Associates, Wayne, NJ. This utility is stored in file ARC.EXE with documentation given in ARC.DOC. The SOURCE*.ARC files on the distribution diskette contain the source code for the Prognosis optimizer and are needed only if you plan to create a new executable pro- gram. Unload all files fi-om OPTGROW.ARC with the ARC extraction command:
ARC X OPTGROW
The extracted executable module, OPTGROW.EXE, will require about 529K. The three overlays are ESESTAB.OVL, ESGROWTH.OVL, and ESINPUT.OVL. You will find that the following input and batch files also have been extracted: TEST.RSP, TEST.TRE, FIG*.KEY, FIG*.INP, FIG*.BAT, DT.EXE, and UNLOAD.BAT.
14
These are all the files needed to run the example problems. (Note that the last file is used only if you are going to ex- tract the source code as discussed in section 8.)
7 PROGRAM STRUCTURE
This section describes the structure of the source code for the Prognosis Optimization Model, which is listed in the appendix. The driver program for stand optimization (program MAIN) contains a coordinate-search process that repeatedly evaluates and attempts to improve the value of the harvest regime for a given stand. The harvest regime specifies the proportions (fi-actions between 0.0 and 1.0) of trees cut by size class, species group, and period. These proportions are called "harvest controls." During the course of an optimization the Prognosis Model is called as a subroutine to project the stand as a function of the har- vest controls. Except where noted, no changes have been made in the Prognosis code. The variables in MAIN are independent of those in Prognosis and are defined in the program listing. The MAIN program contains three blocks: initialization, search process, and writing the re- sults. The first two blocks are described here, and the output block is described in section 3.3. When reading the descriptions of these blocks, make sure to look at the source code and comments listed in the appendix.
7.1 Initialization
The initialization phase involves reading input parame- ters that control the optimization, opening the Prognosis files, initializing the harvest controls, and evaluating the harvest regime.
The optimization begins by reading control parameters for the optimizer (see fig. la) on unit 25. These parame- ters are discussed in detail in section 3.1. Among other things, they include the diameter classes, species groups, and periods in which harvesting may take place, the stumpage prices used to value harvests, and the initial values given to the harvest controls. After optimizer ini- tialization, an outer loop is entered that repeats the opti- mization run with different seeds for generating random starting points for the harvest controls.
The next step involves opening the Prognosis files. Be- fore we describe this step, a little background information is needed. During the course of the optimization, the Prog- nosis Model is repeatedly called as a subroutine to project candidate management regimes. These simulations are controlled by the keyword file (unit 5) and the treelist file (unit 2), which must be present in addition to the input file for the optimizer (see section 5). The keyword file contains all the controls for the Prognosis Model except for the har- vest controls. These are not specified as keywords but instead are copied directly into Prognosis by using the OPADD routine described below. The treelist file contains the initial stand inventory. Because MAIN contains a loop that allows more than one optimization to be done in a given run, units 2 and 5 must be rewound for each optimization.
The driver program for the Prognosis Model is split into three subprograms: PMAINl, PMAIN2, and PMAIN3. The first subprogram contains the Prognosis initialization
routines, including file-open statements, and it is called first. The file-open routines are near the top of PMAINl, and they are called only once (when ISKIP=0) during the program execution. The file-open routines are skipped for each subsequent call to PMAINl {ISKIP=1).
After calling PMAINl and when test variable JSET<0, all the Prognosis variables necessary to restart the simula- tion from that point are stored on a scratch file (unit 50) by calling BHPUT. This is done so that subsequent Prognosis calls during the coordinate search do not have to repeat PMAINl. When JSET>0, JSET is the number of periods before the first harvest. In this case, the stand is grown JSET periods by calling PMAIN2. The resulting Prognosis variables are stored on the scratch file by calling BHPUT in PMAIN2. Again, this avoids repeating the initial pro- jection before harvests can take place during the coordi- nate search. Think of the optimization as a search of a multibranched decision tree. The optimizer uses BHPUT (and BHGET, which reverses the process) to back down the decision tree only as far as necessary to reach another node or branch in its search for the highest point. (Our implementation of BHPUT and BHGET is high-graded fi-om the Parallel Processing Extension of Crookston and Stage [1988].) Note that the optimizer would execute faster if we used BHPUT to store the status of Prognosis in dynamic memory rather than in a scratch file. Unfortu- nately, there is not enough memory available within the 640K limitation of MS-DOS to do this.
The third section of the original Prognosis driver, PMAIN3, contains calls to output routines. These are not called by the optimization program because they are not needed and would seriously slow down execution of the optimizer. If Prognosis output is desired for a particular optimal policy, the user simply runs the normal Prognosis program (rather than the optimizer) after inserting the appropriate thindbh keywords (fi-om the optimizer's out- put file) into the keyword file for Prognosis. This proce- dure is useful for another reason: if the yields from Prog- nosis match the yields found by the optimizer (as they well should), then everything is working properly, both with the programs and the user.
Following the segment of code that opens the Prognosis files, there is a small block of code that echoes the optimi- zation control information to the output file. This is de- scribed in section 3.3.
Harvest controls are initialized in two steps. First, the harvest control for each diameter class, period, and species group is assigned the value that was previously read from the input file. Second, if random harvest controls are de- sired to begin the optimization, random numbers between 0 and 1 are computed for controls in periods when harvests are scheduled. The user chooses the random number seed in this process. The controls are stored in two arrays, Ul and U2, which are identical at the start. Harvest controls with a value of 0.0 indicate that no harvesting will take place. During the optimization, Ul is the current optimal regime, and U2 is a candidate regime obtained with a coordinate search and passed to Prognosis for evaluation.
The present value of the initial regime Ul is computed with four subroutine calls. First, the Prognosis variables stored on the scratch file are obtained with BHGET. Second, the harvest controls in Ul are copied onto the
15
proper Prognosis variables using the OP ADD routines contained in GKEY. The OPADD routines do the same thing as thindbh keywords in the keyword file, except that they are dynamic and therefore eliminate the need to pre- determine the thinning levels. This feature is clearly the key that allows the optimizer to unlock Prognosis. The arguments for OPADD include the period, the diameter class limits, the harvest control, and the species number. Third, PMAIN2 is called with JSET<0 so that the stand is projected for the full number of cycles (numcycle is speci- fied in the keyword file). When a thinning is implemented in Prognosis, all tree records that fall into the specified di- ameter and species class have their tree factor (the num- ber of trees per acre represented by the tree record) re- duced by the proportion represented by the harvest con- trol. Within PMAIN2, a subroutine called STATE is called in each period. This classifies tree records by diameter class and species group. Before-harvest trees per acre and volume per acre by diameter and species class are stored in arrays X and V, respectively. Finally, after the stand projection, present value is calculated by calling VALUE. For each merchantable diameter and species class, value is the product of total volume before cut V, discounted price per unit volume P, and the proportion of trees cut U. For each unmerchantable class, value is the product of total number of trees before cutX, discounted price per tree P, and the proportion of trees cut U.
7.2 Search Process
Each iteration of the Method of Hooke Eind Jeeves in- volves a set of coordinate searches followed by an evalu- ation of the termination criteria and one pattern search. A coordinate search involves varying one control variable by a small amount and evaluating the new management regime. If the new management regime has a higher pres- ent value, the changed control variable is accepted and the next control variable is varied. The sequence of searches starts with the first cutting period and the smallest diame- ter class. Note that if the class does not contain trees, no search and evaluation takes place. Searches may go in both positive and negative directions, depending on the initial value of the harvest control. The present value of a candidate regime is computed using the same sequence of subroutine calls (BHGET, GKEY, PMAIN2, and VALUE), with JSET<0.
After coordinate searches have been performed for the control variables in the first harvest period, the state variables X must be restored to the values associated with the current optimum U2. This is done using BHGET, GKEY, and PMAIN2 with JSET<0. In addition, the stand is grown to the beginning of the next cutting period and saved. In this block, JSET is the number of periods before the second cut. In GKEY, only the harvest controls associ- ated with the current cut are copied to Prognosis variables. PMAIN2 is called to grow the stand, and JSET is reset to -1 (in PMAIN2). The Prognosis variables are saved on the scratch file using BHPUT. The coordinate searches for the second growth period now proceed. Note that the evalu- ation of a control variable change in the second harvest
period involves a Prognosis projection that starts with the updated stand at the beginning of that period. This avoids redundant growth projection in periods before the control variable takes effect.
After coordinate searches have been performed for all control variables, the termination criteria are evaluated. If the difference DIF in present value between two subse- quent management regimes is less than a tolerance EPSl, and if the search distance DELTA is less than a tolerance EPS, then the search process stops and the current re- gime is printed. Otherwise, a pattern search is conducted.
The first step in the pattern search is to compute the search direction. The direction is U2-U1, which is the difference between management regimes before and afi;er the most recent set of coordinate searches. Next, the status of relevant variables in Prognosis must be stored and then reinitialized because we want to start the projec- tion from year 0. (Recall that after the last coordinate search, the stored stand equals the stand just prior to the last cut.) Then, the new management regime is computed by calling CONTROL. The pattern search changes the current regime by moving in the pattern search direction DIR by a distance ALPHA. The present value of this new regime is computed using BHGET, GKEY, PMAIN2, and VALUE, with JSET<0. If the new regime is an improve- ment, it is saved, the step size for the coordinate search DELTA is reduced, and the next set of coordinate searches is started. If the new regime is not better, the old regime is restored, the step size reduced, and the next set of searches started.
8 CREATING AN EXECUTABLE PROGRAM
To give users the option to change the Prognosis Optimization Program to suit their purposes, we have enclosed its source code on the distribution diskette. The source code is long and contains over a hundred subpro- grams, including all those for the Prognosis Model. Thus, it takes between 1 and 2 hours to create the executable program (most of this time is required to compile the source code). As Wykoff (1988) describes in the appendix of the Prognosis Model Update, there are three steps in- volved in creating an executable version of the Prognosis Model: (1) compiling the Fortran files, (2) creating object libraries, and (3) linking the object libraries and files. We use the same steps to create the executable version of the Prognosis Optimization Model.
8.1 Compiling Source Code
To compile the Prognosis code, begin by copying files SOURCELARC, S0URCE2.ARC, and S0URCE3.ARC fi-om the program diskette into the directory reserved for the optimizer. SOURCELARC and S0URCE2.ARC con- tain the source code for version 5.2 of the Prognosis Model. S0URCE3.ARC contains the source code for the optimizer and several utility files for building the execut- able program. S0URCE3.ARC also contains four files that intentionally have the same names as files in
16
S0URCE1.ARC and S0URCE2.ARC: MAIN.FOR, BLKDAT.FOR, OPFIND.FOR, and OPCOM.F77. These files replace certain common blocks, arrays, and variable declarations that determine the number of key- words that may be used in Prognosis. These limits have been increased to accommodate the large number of THINDBH ke)rwords necessary for optimization. When you extract each of these four files fi-om S0URCE3.ARC, the ARC utility will stop and ask if you really want to write over a file that already exists; the correct answer is "yes". To extract all the remaining files, simply execute the UNLOAD.BAT me:
UNLOAD
MAIN.FOR contains the MAIN program for the op- timizer and replaces the Prognosis main driver MAIN.FOR extracted above. The PMAIN.FOR file con- tains subroutines PMAINl, PMAIN2, and PMAIN3, which together form the Prognosis main driver used in the optimization. Note that almost all of the calls to Prog- nosis output routines have been disabled in PMAIN3. File OPT.FOR contains optimizer subroutines OUT, GKEY, CONTROL, STATE, VALUE, and DRAND. The BHSTAR.FOR file contains 12 subroutines adapted from Crookston and Stage (1988) that allow for storing and retrieving the complete status of Prognosis variables and arrays during the course of a projection.
Your optimization directory now contains several hundred Fortran source files i*.FOR) and common blocks {*.F77), in addition to the utilities. That number is about to double because compilation will create an *.OBJ file for each *.FOR file. We have compiled successfully using Ryan-McFarland version 2.40 (RMFORT). (WykofF [per- sonal communication 1990] has also produced a working executable module of Prognosis using Lahey F77L version 4.01.) Note that changes in array dimensions contained in BLKDAT.FOR, OPFIND.FOR, and OPCOM.F77 necessi- tate recompiling the Prognosis routines even if you al- ready have a compiled version of Prognosis. Compile the source code by executing the COMPILE.BAT batch file and specifying the appropriate compiler as an argument (we use RMFORT):
COMPILE RMFORT
A relatively long time is needed to compile such a large number of subprograms (approximately 45 minutes on a 20-Mhz personal computer). Note that these programs are all compiled with the /IZ option, which is necessary to make the executable program small enough to run on a microcomputer under the 640K limit imposed by MS- DOS. Also note that the batch commands intentionally do not compile subprograms associated with the COVER ex- tension (Moeur 1985) because they are not needed for un- constrained value optimization. However, an optimiza- tion problem that includes constraints on hiding cover for big game, for example, would require them. In that case the only alternatives would be either to recompile Progno- sis with smaller dimensions for the tree vectors or to use an operating system such as UNIX that does not have the 640K restriction.
8.2 Building Object Libraries
If you now look at a directory listing, you run the risk of being overwhelmed by the sheer number of files that have been created. Clearly, some sort of file reduction is needed. Object libraries are the answer. By using the Phoenix PLINK86 overlay linker and associated libraries (supplied with the Ryan-McFarland RMFORT compiler), all of the object files needed for the optimizer are loaded into six object libraries: MAIN.LIB, BASE.LIB, GROWTH.LIB, INPUT.LIB, INPUT2.LIB, and ESTAB.LIB. Execute LOADPLIB.BAT to create these libraries:
LOADPLIBALL
Note that you can also use LOADPLIB.BAT to build these libraries one at a time if you replace ALL with the appro- priate library name in the preceding statement.
All of the source and object files can now be erased. Al- though this step may seem scary, all of the object files are conveniently stored in one of the six object libraries and all of the source code is still abstracted in the ARC files. Thus, the following commands should considerably reduce bookkeeping problems in your optimization directory:
ERASE *.OBJ ERASE *.FOR ERASE *.F77
As strange as it may seem, all of these erased files are still cluttering up your subdirectory, even though they do not appear to be in your directory. They have been marked as deleted in the file allocation table, but the file contents are untouched. The optimizer can be seriously slowed down in such a cluttered directory because it must repeatedly swap overlay segments when it is executed. The simplest solution is to create a new optimization directory, copy everything into it, and delete the old direc- tory. Alternately, you could create a separate run direc- tory containing only the executable optimizer code (in- cluding overlays), input and output files, response files, and any batch files that will simplify the submission of runs.
8.3 Linking the Object Code
The size of the optimization code requires the use of program overlays in the executable module. To link the object code and create the overlays, the Phoenix PLINK86 overiay linker is used. Batch file OPTPLK.BAT and re- sponse file OPTPLK.RSP contain the instructions for cre- ating the overlaid version of the executable module. Exe- cute the batch file with the command:
OPTPLK
The resulting executable module, OPTGROW.EXE, should require about 529K. The three overlays are ESESTAB.OVL, ESGROWTH.OVL, and ESINPUT.OVL.
17
8.4 Modifying the Program
If it is necessary to modify the optimizer code for some reason (such as increasing variable dimensions), then only a few steps are required to produce an executable module. After revising the appropriate source code, compile by specifying the program name and the /IZ option as argu- ments to the compiler. For example, assume that the subprogram STATE has been changed. Create a new OPT. OBJ file (where STATE is stored) by executing the Ryan-McFarland compiler:
RMFORT OPT/IZ
Next, update the appropriate object library (MAIN.LIB in this case) by using the MODLOAD.BAT hatch file:
MODLOAD MAIN OPT
Finally, update the executable module OPTGROW.EXE by relinking:
OPTPLK
You will also need to update the ARC source file if you plan to work fi"om the archive in the future:
ARC U SOURCES STATE.FOR
The other useful ARC options are D to delete a file and V to get a verbose listing of the contents of the archive file. The syntax is the same as for the X and U options that have been illustrated.
9 REFERENCES
Crookston, N. L. 1985. User's guide to the Event Monitor: an addition to the Prognosis Model. Gen. Tech. Rep. INT-196. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Research Station. 36 p.
Crookston, N. L.; Stage, A. R. 1988. User's guide to the Parallel Processing Extension of the Prognosis Model. Review draft on file at the Intermountain Research Station, 1221 S. Main, Moscow, ID 83843.
Ferguson, D. E.; Crookston, N. L. 1984. User's guide to the Regeneration Establishment Model — a Prognosis Model extension. Gen. Tech. Rep. INT-161. Ogden, UT: U.S. Department of Agriculture, Forest Service, Inter- mountain Forest and Range Experiment Station. 23 p.
Ferguson, D. E.; Stage, A. R.; Boyd, R. J. 1986. Predicting regeneration in the grand fir-cedar-hemlock ecosystem of the Northern Rocky Mountains. Forest Science Monograph 26. 41 p.
Haight, R. G.; Monserud, R. A. 1990a. Optimizing any- aged management of mixed-species stands: I. Perform- ance of a coordinate-search process. Canadian Journal of Forest Research. 20: 15-25.
Haight, R. G.; Monserud, R. A. 1990b. Optimizing any- aged management of mixed-species stands: II. Effects of decision criteria. Forest Science. 36(1): 125-144.
Hamilton, D. A., Jr. 1986. A logistic model of mortality in thinned and unthinned mixed conifer stands of north- em Idaho. Forest Science. 32: 989-1000.
Hooke, R.; Jeeves, T. A. 1961. Direct search solution of numerical and statistical problems. Journal of the Association for Computing Machinery. 8: 212-221.
Moeur, M. 1985. COVER: a user's guide to the CANOPY and SHRUBS extension of the Stand Prognosis Model. Gen. Tech. Rep. INT-190. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Research Station. 49 p.
Wykoff, W. R.; Crookston, N. L.; Stage, A. R. 1982. User's guide to the Stand Prognosis Model. CJen. Tech. Rep. INT-133. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Forest and Range Experiment Station. 112 p.
Wykoff, W. R. 1986. Supplement to the user's guide for the Stand Prognosis Model-Version 5.0. Gen. Tech. Rep. INT-208. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Research Station. 36 p.
Wykoff, W. R. 1988. Prognosis Model update version 5.2 (Fortran 77). Review drafi; on file at the Intermountain Research Station, 1221 S. Main, Moscow, ID 83843.
18
10 APPENDIX: OPTIMIZER PROGRAM CODE
PROGRAM MAIN
C OPTIMIZE PROCHOSIS USING THE COORDIUATE GRID SEARCH METHOD C OF HOOK AMD JEEVES.
C WRITTEN BY ROBERT G. HAIGHT 1988 AND MODIFIED IN 1989 BY C ROBERT A. MONSERUO (PROGRAMMING DIVISION OF "THE BOBS")
C OPTIMIZATION PROBLEM BOUNDS:
C MAXIMUM NUMBER OF PROGNOSIS GROWTH PERIODS = 33
C MAXIMUM NUMBER OF DIAMETER CLASSED = 8
C MAXIMUM NUMBER OF SPECIES GROUPS ' 3
C IF THESE DIMENSIONS ARE CHANGED, BE SURE TO MODIFY AND RECOMPILE
C SUBROUTINES CONTROL, OUT, STATE, VALUE, GICEY, AND PMAIN2.
CQMHON/BEST/0CL(8,2),0(8),U1(33,8,3),UZ(33,8,3).0IR(33,8,3), >IYEAR(33>.X(33,8,3),V(33,8,3),P(33,8,3),BF(33),VA(33).NS<3), >SPC3,10),ICUT(33),NCYCLE,NCLASS,NGROUP,MVOL
DIMENSION C(33,8,3),DCB(9},ISP(10) DOUBLE PRECISION DRANO,SEED(20),RAND
OPEH(25,F I LE='B0BS2. I NP',STATUS= 'UNKNOWN ',ACCESS= 'SEQUENTIAL') OPEN(26,F I LE='B0BS2. OUT ',STATUS= 'UNKNOWN ',ACCESS='SEOUEHTIAL') OPENCUNIT=50,STATUS=' SCRATCH ',FORM= 'UNFORMATTED')
ISKIP = 0
C*****REAO THE HCLAS$*1 DIAMETER CLASS BOUNOARYS
REAI)(2S,2SS) NCP1,(DCB(K).K = 1,NCP1) 255 FOIiHAT<l5,20f5.0)
C NCLASS = NUMBER OF DIAMETER CLASSES NCLASS = NCP1 - 1 00 15 K = 1, NCLASS DCL(K,1) = DCB(K) DCL(K,2) = 0CB(K+1) D(IC) ' (OCB(K) * DCB<K«1)) /2. 15 CONTINUE
(SIZE)
C*****FOIt THE NGRCUP SPECIES GROUPS READ THE SPECIES ID NUMBERS DO 13 L > 1,NGR0UP
REAO<2S,25S) NSP, (SP(L,L1),L1=1,NSP)
NS(L) « NSP 13 CONTINUE
C*"**READ AND COMPUTE DISCOUNTED STUMPAGE PRICES DO 12 L > 1,NGR0UP
READ(25,257> <P(1,J,L),J - 1, NCLASS) DO 10 I = 1,NCYCLE
DIS = (1.+R> *• ({I - 1)*LENGTH)
DO 11 J = 1, NCLASS
P(l,J,L) = P(1,J,L)/DIS
11 CONTINUE 10 CONTINUE
12 CONTINUE
************************** ****************** C BEGIN INPUT AND INITIALIZATION PHASE
C*****.****.**.*******..*.***.****************************************
C*»***KU> NUMBER OF RUNS AND RANDOM # SEEDS
READ(25,259) NRUN, (SEED(NR),NR - I.NRUN) 259 FORMAT( 15,2005.0)
C*****READ OPTIMIZER CONTROL PARAMETERS
REA0(25,257) R, ALPHA, DELTA1, EPS, EPS1 257 fORMAT(20F5.0)
MAXVOL=0
IF(R.LT. 0.0001) MAXV0L»1
C*****READ THINNING CONTROL VARIABLES (PERCENTAGE OF TREES REMOVED) C OUTER LOOP FOR SPP GROUPS, C INNER LOOP FOR TIME (DOWN). C IMPLIED LOOP FOR DIA CLASSES (ACROSS) DO 39 L = 1,NGR0UP DO 36 I - 1,NUMCYC
READ (25,256) (C(I,K,L).K = 1, NCLASS) 256 FORMAT(10F7.4) 36 CONTINUE
DO 38 K = 1, NCLASS
C(NCTCLE,K,L) = 1.0
38 CONTINUE
39 CONTINUE
C"***READ INTERNAL PARAMETERS
C NCYCLE = 1 + NUMBER OF PROGNOSIS CYCLES (TIME)
C MERCK = INDEX FOR THE FIRST MERCHANTABLE DIAMETER CLASS
C NCROUP = NUMBER OF SPECIES GROUPS FOR VALUE CLASSIFICATION (SPP)
C MVOL > 0 IF BOARD FT VOL; MVOL < 0 IF MERCH CUFT VOL
C LENGTH = LENGTH OF THE GROWTH PERIOD (TIMEINT)
C NTH = PRINT EVERT NTH PROGNOSIS CYCLES
C NOKEYU = 0 IF YOU WANT NO THINDBH KEYWORD OUTPUT WRITTEN
READ(25,258) NUMCYC, MERCH, NCROUP, MVOL, LENGTH, NTH, NOKEY 258 FORMATdOlS)
NCTCLE = NUMCYC ♦ 1
MERCHI • MERCH - 1
YEARS = FLOAT( NUMCYC * LENGTH )
IF(NTH.EQ.O) NTH = 1
C*"**READ CUTTING PERIODS
C NCUTS = NUMBER OF CUTTING PERIODS
READ(25.Z58) NCUTS. (ICUT( I ), I = 1, NCUTS) C JS = NUMBER OF PERIODS BEFORE THE FIRST CUTTING
JS * ICUT(I) - 1
IF(JS.EQ.O) JS » -1
JSET X JS
^***** ********************************* *******************************
C OUTER LOOP FOR SEPERATE OPTIMIZATIONS WITH DIFFERENT SEEDS
Q********************* ***************************************** *******
DO 999 NR > l.NRUN
NCALLS = 0 DELTA ' DELTA1
C**"*CALL PROCHOSIS TO OPEN TREELIST FILE 2 AND KEYWORD FILE 5 REWIND 2 REWIND 5
CALL PMAINl(ISKIP) IF (JSET.LT.O) THEN
CALL BHPUT ELSE
CALL PMAIN2(JSET) END IF
C**"*PRINT INPUT
WRITE (26.648)
MS F0RHAT(///'B06S2: PROGNOSIS OPTIMIZATION BY THE BOBS') SEED1 > SNGL(SEED(NR))
19
URITE(26,649) NR,R, ALPHA, DELTA. EPS,EPS1,SEED1 U9 FORMAK/,
>'0PTIMIZAT10N NUHBER ',14/, >'INTEREST RATE = ',F8.3/, >' ACCELERATION STEP = ',F8.3/, ><BEG1NNING STEP SIZE =',F8.3/, >'MIHIHUH STEP SIZE " ',F8.3/, >'MIHIHUM GAIN = ',F8.3/, >' RANDOM NUMBER SEED = •,F8.3/)
IF<NCUTS.CT.l) URITE(26,65B) NCUTS,{ICUT(K>,IC = 1,NCUTS)
658 rORHATCTHE OPTIMIZER WILL DETERMINE' , 13, • HARVESTS.'/ >'THEY OCCUR IN PERIODS: ' .2014
>/22X,13l4) IF(NCUTS.EO.I) URITE(26,659) ICUT(I)
659 FORMATCTHE OPTIMIZER UILL DETERMINE 1 HARVEST,*, >' OCCURRING IN PERIOD', 13)
URITE(26,651)
651 FORHATC ')
DO 30 L » 1,NGR0UP
URITE(26,650) 1,(SP<L,L1),L1 = I.NSCD) 650 FORMAT( 'SPECIES COOES FOR GROUP', 12,' ARE',10F4.0} 30 CONTINUE
WRITE (26, 652)
652 FORMAT (/'HOOKE t JEEVES COORDINATE SEARCH PROCESS: •/)
C BEGIN SEARCH PROCESS
C*"**FOR EACH SPECIES CROUP 00 31 L = I.NGROUP
NCALIS " NCALLS * 1 URnE(26,635) Z1 635 FORMAT ('PRESENT VALUE =>,F10.2)
C*****FOS EACH CUTTING PCRI(» I 49 CONTINUE
DO 46 II â– 1,NCUTS I = ICUT(Il)
C*****FOR EACH DIAMETER AND SPECIES CLASS J AND L DO 47 J = 1,HCLASS DO 48 L « I.NGROUP
C**"*ADO DELTA TO TEST CONTROL U2(I,J,L) IF(1((I.J.L).IT..01) GOTO 48 IF(U1(I,J,L).EQ.1.) GOTO 43 U2(I.J,L) = UUl.J.L) ♦ DELTA IF(U2(I,J,L).GT.1.) U2(I,J,L) = 1.
C**«**GET THE INITIAL STAND AND COMPUTE PV OF CHANGED CONTROL CALL BHGET
CALL GKEY(DCL.U2,NCLASS.N6ROUP.NS,SP,ICUT,NCUTS, II, LENGTH) CALL PMAIH2(JSET)
CAL L VALUE ( Z , P , V , X , U2 , NCYCLE . NCLASS. MERCH , MGROUP ) HCALIS = NCALLS * 1 IF(Z.GT.Z2) GOTO 40
C*****IF PLUS DELTA DOES NOT IMPROVE PV. SUBTRACT DELTA TO TEST CONTROL
1F(U1(I,J.L).EQ.0.) GOTO 42 43 CONTINUE
U2(I,J.L) = UI(I.J.L) - DELTA
IF(U2(I.J.L).LT.O.) U2(I,J,L) = 0.
C*****SET CONTROL VARIABLES 00 33 I = 1, NCYCLE DO 32 K = 1, NCLASS UKI.K.L) = Cd.K.L)
32 CONTINUE
33 CONTINUE
C*****SET RANDOM STARTING VALUES IF(SEE0(NR).GE.0.D0) THEN DO 26 II = I.NCUTS I « ICUT(II) DO 27 K = 1, NCLASS
RAND = DRAND(SEE0(NR)) U1(I,IC,L) = SNGL(RAND)
27 CONTINUE 26 CONTINUE
END IF
C*****SET U2(I,K,L) = UKI.K.L) DO 28 I = 1, NCYCLE DO 29 K = 1, NCLASS U2(I.K.L) = U1<I.IC,L) Xd.K.L) = 0. 29 CONT I HUE
28 CONTINUE 31 CONTINUE
C***»*COMPUTE PRESENT VALUE OF U1
CALL BHGET
CALL CKEY(DCL, U1, NCLASS, NGR0UP,NS,SP,ICUT,NCUTS,1, LENGTH) CALL PHAIN2(JSET)
CALL VALUE(21,P,V,X,U1, NCYCLE, NCLASS, MERCH, NGROUP) 22 * Z1
C*****GET THE INITIAL STAND AND COMPUTE PV OF CHANCED CONTROL CALL BHGET
CALL GKE Y (DCL , U2 . NCLASS , NGROUP. HS . SP, I CUT , NCUTS , 1 1 , LENGTH) CALL PMAIN2(JSET)
CALL VALUE(Z,P,V,X,U2, NCYCLE, NCLASS. MERCH, NGROUP)
NCALLS « NCALLS * 1
IF <Z.GT.Z2) GOTO 40 42 CONTINUE
U2(I,J,L> c U1(I,J,L)
Z = Z2 40 CONTINUE
Z2 > Z 48 CONTINUE 47 CONTINUE
C*»*"RECOMPUTE STATE USING BEST CONTROL SEQUENCE CALL BHGET
CALL GKEY(DCL,U2, NCLASS, NGROUP, NS.SP,ICUT, NCUTS, II, LENGTH) CALL PMA1N2(JSET) NCALLS « NCALLS * 1
C*****PARK THE STAND AFTER II CUTS IFdI.LT. NCUTS) THEN JSET = ICUTdl + 1) - 1 CALL BHGET
CALL CKEY(DCL,U2, NCLASS, NGROUP, NS.SP.ICUT, 1 1,11, LENGTH) CALL PMAIN2(JSET) NCALLS < NCALLS ♦ 1 END IF 46 CONTINUE
C*****NOTE TERMINATION OF STEP SEARCH LOOP WRITE{26,637) DELTA
20
637 FORMATC PERFORMED STEP SEARCH UITH DELTA â– ',F5.3) WRITE(26.635) Z2
C*****1F DIF .LT. EPS1 .AND. DELTA. .LT. EPS, GO TO PRINT DIF = Z2 - Z1
IF(DIF. LT.EPS1.AN0.DELTA.lt. EPS) GOTO 90
C***«*PERFORM ACCELERATION STEP: FIRST DETERMINE SEARCH DIRECTION DO 50 II = I.NCUTS I » ICUT(ll) 00 52 L = I.NGROUP
00 51 J = I.NCLASS
DIRd.J.L) = U2(I,J,L> - UUI.J.L) UKI.J.L) = U2(I,J.L)
51 CONTINUE
52 CONTINUE 50 CONTINUE
C*****NEXT, REINITIALIZE AND PUT THE STAND REWIND 2 REWIND 5 JSET = JS
CALL PHAINUISKIP) IF(JSET.LT.O) THEN
CALL BHPUT ELSE
CALL PHAIN2(JSET) END IF
C*****NEXT. COMPUTE PRESENT VALUE Z1 = Z2
CALL C0NTR0L(ALPHA,U2,DIR,HCLASS,NGR0UP, ICUT.NCUTS) CALL BHGET
CALL GICEY(DCL,U2,NCLASS,NGR0UP,NS,SP,ICUT,NCUTS,1, LENGTH) CALL PHAIN2(JSET)
CALL VALUE(Z2,P,V,X,U2,NCYCLE,NCLASS,MERCH,NGR0UP) NCALLS = NCALLS ♦ 1
C*****IF IMPROVEMENT, SAVE AND RETURN TO COORDINATE SEARCH
IF(Z2.GT.Z1) THEN
URITE(26,636) 636 FORMATC ACCELERATION STEP SUCCESSFUL')
URITE(26.635) Z2
DO 54 11 = 1,NCUTS
1 = ICUT(II)
DO 57 L » 1,NGR0UP DO 55 J ■I.NCLASS UUI.J.L) = U2(I,J,L) 55 CONTINUE 57 CONTINUE 54 CONTINUE Z1 . 22
IF(DELTA.GT.EPS) DELTA = DELTA/2. GOTO 49
^0 IMPROVEMENT, REDUCE STEP SIZE AND RETURN TO COORDINATE ELSE
WRITE(26,656)
656 FORMATC ACCELERATION STEP NOT SUCCESSFUL') DO 70 11 = I.NCUTS I = ICUT(II) DO 72 L = 1,NGR0UP DO 71 J = I.NCLASS U2(],J,L) » UUI.J.L)
71 CONTINUE
72 CONTINUE
70 CONTINUE 22 = Z1
IF(DELTA.GT.EPS) DELTA = DELTA/2. GOTO 49 END IF
90 CONTINUE
C SEARCH PROCESS COMPLETE; PRINT RESULTS
C***«*COMPUTE AND SUBTRACT INITIAL VALUE (OR VOLUME)
VAINIT > 0. DO SO L > I.NGROUP DO 86 J = 1.MERCH1
VAINIT = VAINIT ♦ P(I.J.L) * X(1,J,L) 86 CONTINUE
DO 89 J = MERCH.NCLASS
VAINIT = VAINIT ♦ P(I.J.L) * Vd.J.L) 89 CONTINUE 80 CONTINUE
Z2NET « Z2 - VAINIT
C*****PRINT OPTIMAL VALUE
IF(MAXVOL.EQ.O) URITE(26.626) NCALLS. VAINIT, Z2NET
626 FORMATC/ "NUMBER OF PROGNOSIS SIMULATIONS ='.I5// >'INITIAL VALUE « ',F10.2,' DOLLARS/AC'//
>'0PT1MAL PRESENT NET VALUE (PNV) ='.F10.2.' DOLLARS/AC'/ )
VAINIT = VAINIT * 1000. 22NET = Z2NET * 1000. AAP = Z2NET / YEARS
I F (MAXVOL . EQ . 1 . AND . HVOL . GT . 0)WR I TE ( 26, 627) NCALLS, VA I N I T , Z2NE T , AAP
627 FORHAT(/ 'NUMBER OF PROGNOSIS SIMULATIONS =>,I5// >'IHITIAL VOLUME = '.FK.I,' 80FT/AC'//
>'NET OPTIMAL VOLUME =',F14.1,' BDFT/AC'// >'AVERAGE ANNUAL PRODUCTION =',F7.1,' BOFT/AC/YR'/)
IF(MAXVOL.E0.1.AND.MVOL.LE.0)URITE(26,628) NCALLS, VAI NIT, 22NET, AAP
628 FORMAT(/ 'NUMBER OF PROGNOSIS SIMULATIONS s'.lS// >'INITIAL VOLUME = '.FU.I.' CUFT/AC'//
>'NET OPTIMAL VOLUME «',F14.1,' CUFT/AC'//
>' AVERAGE ANNUAL PRODUCTION =',F7.1,' CUFT/AC/YR'/)
C*****COMPUTE OUTPUT YEAR ARRAY DO 66 I > 1,NCYCLE
lYEAR(I) = (I - 1) * LENGTH 66 CONTINUE
C*****WRITE RESIDUAL STATE SEQUENCE DO 60 L = 1,NCR0UP DO 58 I « 1,NCYCLE VA(I) = 0. BF(I) = 0. 00 56 J * 1,HERCH1
UKI.J.L) = X(I.J.L) * (1. - U2(I.J.L)) VA(I) ' VA(I) ♦ Pd.J.l) * UKI.J.L) 56 CONTINUE
DO 59 J = MERCH.NCLASS
UKI.J.L) = Xd.J.L) * (1. - U2d.J,L))
VAd) = VAd) + Pd.J.L) • Vd.J.L) • d. - UZd.J.D)
BFd) = BFCI) ♦ Vd.J.L) • (1, - U2d,J.L))
21
59 CONTINUE 58 CONTINUE
UR1TE(26,657) L
657 FQRMAT(/, 'RESIDUAL TREES PER ACRE FOR SPECIES GROUP', 13) CALL OUT(IYEAB,D,U1,BF,VA,NCYCLE,MCLASS,L,0,MTH)
60 CONTINUE
C*****UIRITE HARVEST SEQUENCE DO 68 L > I.NGROUP DO 61 I - I.NCYCLE
VA(I) = 0.
Bf(I) = 0.
00 67 J = I.MERCHI
UKI.J.L) " X(I,J,L) * U2(1,J,L) VA(I) = VA(I) + Pd.J.L) * UKI.J.L)
67 CONTINUE
DO 62 J = KERCH. NCLASS
UKI.J.L) = Xd.J.L) • U2(I.J.L)
VA(I) » VA(I) + Pd.J.L) * V(I.J.L) • U2(I.J.L)
BF(I) M BF(I) ♦ V(I.J.L) * UZd.J.L)
62 CONTINUE
61 CONTINUE WRITE(26.660) L
660 fOftHAT{/, 'HARVESTED TREES PER ACRE FOR SPECIES GROUP' , 13, ':' ) CALL OUTd YEAR, D.U1,BF,VA,NCYCLE,NCLASS.L,0, NTH)
68 CONTINUE
C*****URITE CONTROL SEQUENCE DO 69 L = I.NGROUP DO 63 I = I.NCYCLE DO 64 J = I.NCLASS
IF(UKI,J,L).GT.0.001) UKI.J.L) = U2d.J.L) • 100. 64 CONTINUE
63 CONTINUE URITEC26.633) L
633 FORMAT(/, 'PERCENTAGE TREES PER ACRE CUT FOR SPECIES GROUP' >.I3.':')
CALL OUTdYEAR.D.UI.BF.VA.NCYCLE.NCLASS.L.I.NTH)
69 CONTINUE
C*****REURITE CONTROL SEQUENCE IN THE INPUT FORMAT C (DIAMETER CLASSES ACROSS. TIME PERIODS DOWN) DO 85 L = I.NGROUP DO 83 I « I.NCYCLE DO 84 J = I.NCLASS
UKI.J.L) = UKI.J.L) / ICQ.
84 CONTINUE 83 CONTINUE
URITE(26.67a) L
670 FORMATC/. 'OPTIMAL HARVEST CONTROL PARAMETERS FOR SPECIES GROUP' >.I3.':')
DO 87 1 = I.NUMCYC
WR1TE(26,256) (UKI.J.L). J = I.NCLASS) 87 CONTINUE
85 CONTINUE
IF(NOICEY.EQ.O) GOTO 990 C*****URITE CONTROL SEQUENCE AS THINDBH KEYWORDS FOR PROGNOSIS WRITE(26.690)
690 FORMAT(/. 'OPTIMAL HARVEST KEYWORDS FOR PROGNOSIS'/ >' (INSERT IN THE KEYWORD FILE)' )
00 94 I = I.NCUTS
IC = ICUT(I)
YEAR ' (LENGTH * (K - 1)) ♦ 1 DO 93 J = I.NCLASS J1 = J + 1 DO 92 L = I.NGROUP IF(U1(K, J, D.LT. 0.0001) GOTO 92 NSP= NS(L) DO 91 L1=1,NSP SPECIE = SP{L,L1) IF(NGROUP.GT.I) THEM
WRITE(26.696) YEAR,DCB(J).DCB(J1 ),U1(K, J, D.SPECIE 696 FORMATC THINDBH ' ,3F10.0. F10.4, F 10 .0 )
ELSE
URITE<26,696) YEAR,DCB(J).DCB(J1).U1(K,J.L) ENDIF
91 CONTINUE
92 CONTINUE
93 CONTINUE
94 CONTINUE
990 CONTINUE 999 CONTINUE
END FILE 26
END
SUBROUTINE OUT( I YEAR.D.U, BF, VA, NCYCLE . NCLASS, L , L3, NTH ) DIMENSION IYEAR(33),D(8),U{33,8.3).BF{33).VA(33).TR(33).BA(33)
C*****CO«PUTE STAND AVERAGES C = 0.00545415 00 10 I « I.NCYCLE TR(I) = 0. BA(I) = 0. DO 11 J = I.NCLASS
TRd) « TR(I) ♦ Ud.J.L) BAd) = BAd) + Ud.J.L) • C * D(J)**2 11 CONTINUE 10 CONTINUE
C*"**WRITE STAND STATISTICS
N1 = 1
N2 < NCYCLE
NPAGE = 1
N3=(NCYCLE-1)/NTH + 1 IF(N3.GT.17) NPAGE « 2 IF(NPAGE.CT.I) N2 = 17 * NTH
DO 100 I PAGE = 1, NPAGE IF(IPAGE.EQ.2) N1 » N2 ♦ 1 IFdPACE.EQ.2) N2 = NCYCLE
URITE(26,401>
401 FORMAT(/,' DBH YEAR >•)
URITE(26.402) (lYEARd).I = N1,N2.NTH )
402 FORMAT('CLASS'.1X,17(2X.I3.2X)) IF(L3.GT.O) GOTO 80
DO 40 J = I.NCLASS
URITE(26.403) 0(J). (Ud.J.L), I = N1.N2.NTH)
403 FOfiHAT(F4.0.1X.17F7.1) 40 CONTINUE
22
WRITE(26,A12) (TR(I),I = M1.M2,NTH)
412 FORHATC 'TOTAL ',17F7.0) URITE(26,413) (BA(I),1 = N1,N2,NTH)
413 FORMAT ( 'BA/ AC, 17F7.0) WRITE<26,407) (BF(I),I = N1,M2,NTH)
407 FORHAT('VO/AC',17F7.2)
WRITE(26,4U) (VA(I),I = N1,N2,NTH) 4U F0RMAT('»$/AC',17F7.1)
GOTO 100
80 CONTINUE
DO 90 J = I.NCLASS
URITE(26,A04) D<J), (U( I , J.L), I = N1,N2,NTH) 404 FORHAT(F4.0,1X,17F7.2) 90 CONTINUE
100 CONTINUE RETURN END
Q* ********************************************************************* ^******«**************** A* *********************************************
SUBROUTINE CONTROL(THETA,U2,OIR,NCLASS,NGR0UP, ICUT.NCUTS) DIHENSIOH U2(33,8,3),DIR<33,8.3).ICUT(33)
DO 15 II = I.NCUTS I = ICUT(II) DO U L = 1,NGRCUP DO 16 K = I.NCLASS
U2<I,K,L) » U2(I.K,L) * THETA * DIRd.tC.L) IF(U2(I,K,L).LT.O.) U2(I.IC.L) = 0. IF(U2<I,IC,L).GT.1.) U2(I,IC,L) = 1. 16 CONTINUE
14 CONTINUE
15 CONTINUE RETURN END
^************************* ******************************************** (^* ************************************************* *******************
SUBROUTINE VALUE(Z,P,V,X,U,NCYCLE,NCLASS,MERCH,NGROUP) DIMENSION P(33,8,3),V(33,8,3),X(33,8,3),U(33,8,3)
C*****COHPUTE PRECOHMERCIAL AND COMMERCIAL THINNING REVENUES C*****FOft EACH TIME PERIOD
HERCH1=MERCH-1 Z=0.
DO 21 I=1,NCYCLE DO 24 Lx1,NGR0UP DO 22 J=1,HERCH1
Z=2*P<I,J,L)*X(I,J,L)*U(I,J,L)
22 CONTINUE
DO 23 J^ERCH.NCLASS
2=2*P(I,J,L)*V(I,J,L)*U(I,J,L)
23 CONTINUE
24 CONT I NUE 21 CONTINUE
RETURN END
Q*********************************************************** *********** £**********************************************************************
SUBROUTINE GKEY(DCL,U,NCLASS,NGROUP,NS,SP, ICUTS.NCUTS, NCI .LENGTH) DIHENSIOH DCL(8,2),U<33,8,3),NS(3),SP(3.10),ICUTS(33), >WIC6(4}
C*****REUINO PROGNOSIS INPUT AND OUTPUT FILES C***.*xREE DATA FILE
REWIND 2 C*****TREE LIST OUTPUT FILE
REWIND 3 C*****StJHHARY OUTPUT FILE
REWIND 4 C*****OUTPUT FILE
REWIND 6
C*****FOR EACH CUT CYCLE WRITE THINOBH KEYWORDS USING OPADD ROUTINE DO 40 I1=NC1.NCUTS I=ICUTS{I1) IYRi(I-1)*LENGTH+l DO 30 L>1.NGR0UP NSP<NS(L> 00 20 L1=1,NSP DO 10 K=1.NCLASS WIC6(1)=DCL(r,1) WI(6(2)=DCL(K,2) Wi:6(3)=U(I,K,L) WIC6(4)=SP(L,L1)
CALL OPAODdYR, 228,4, WK6,K0OE)
IF(ICOOE.GT.O) STOP 'OPTION PROCESSING ERROR IN GKEY' 10 CONTINUE 20 CONTINUE 30 CONTINUE 40 CONTINUE
RETURN END
C**********************************************************************
Q********************* ******************************************* ******
SUBROUTINE STATE
C0MMON/BEST/DCL<8,2),D{8),U1{33,8,3),U2(33,8,3),DIR(33,8,3), >IYEAR(33),X(33,8,3>,V<33,8,3).P(33,8,3),HF(33),VA(33),NS(3), >SP(3,10),ICUT(33),HCYCLE,NCLASS,NGROUP,MVOL
INCLUDE 'ARRAYS. F77' INCLUDE 'C0NTRL.F77' INCLUDE 'PL0T.F77'
I=ICYC*1
C*.***SET X(I,J,L)=0. DO 10 L>1,NGR0UP DO 5 J>1,NCLASS X{1,J,L)»0. V(l,J,L)=0. 5 CONTINUE 10 CONTINUE
23
C**'**FOR EACH RECORD READ SPECIES, TPA, DBH AND VOLUME 00 40 J1=1,1TRN SP1=ISP(J1) TPA=PR0B(J1 )/GROSPC BDBH=DBH(J1) If<HVOL.CT.O) THEN
TV0L=BFV(J1) ELSE
TV0L=UK1(J1) EMDIF
IF<SP{1,1).EO.O.) SP1=0.
C*****DETERMIHE DIAMETER CLASS DO 30 J=1,NCLASS 1F(B0BH.LT.0CL(J,2)) THEN
C*****DETERMINE SPECIES CLASS AND UPDATE TPA AND VOLUME DO 22 L=1,NGR0UP NSPB=NS(L) 00 20 L1«1,NSPB 1F(SP1.E0.SP{L,L1)) THEN X(I,J,L)»X(I,J,L)+TPA Vd.J.D'Vd.J.D+TVOL'TPA/IOOO. GOTO 40 ENDIF
20 CONTINUE 22 CONTINUE
ENDIF 30 CONTINUE <0 CONTINUE
RETURN
END
(;.....•«••••••••••*••*..*..........*****....««*...........****.,«......*
DOUBLE PftECISIOM FUNCTION DRANO(IX)
DOUBLE PRECISION A, P, IX, B15, B16, XHI ,XALO, LEFTLO, FHI , K
DATA A/16807. DO/, B15/32768. DO/, 816/65536. DO/, P/2H7483647. DO/
XHI < 1X/B16
XHI = XHI - DMOO(XHI,1.00} XALO » (IX - XHI*B16)*A
LEFTLO = XAL0/B16
LEFTLO * LEFTLO - DHO0(LEFTL0, 1 .00)
FHI = XHI*A ♦ LEFTLO
K ' FHI/B15
K = K - DHOO(IC,1.D0)
IX = (((XALO - LEFTL0*B16) - P) + (FHI - IC*B15)*B16) ♦ X
IF(IX.LT.O.DO) IX = IX ♦ P
DRANO * IX*4.656612875D - 10
RETURN
END
24
Monserud, Robert A.; Haight, Robert G. 1990. A programmer's guide to the Progno Optimization Model. Gen. Tech. Rep. INT-269. Ogden, UT: U.S. Department of Agriculture, Forest Service, Intermountain Research Station. 24 p.
The Prognosis Optimization Model is used to compute optimal harvest regimes for mixed-conifer stands in the Northern Rocky Mountains. The optimizer is capable of determining optimal regimes (termed any-aged) without any constraints on the age structure or species composition of the stand. It also may be used to determine optimal thinning regimes for plantations or natural stands that are eventually clearcut. The input requirements and output for the optimization model are described in detail. Input and output for three optimization runs for maximizing the present value and merchantable cubic foot volume of a stand are described. Instructions for installing and running the pro- gram on a personal computer are provided. For those interested in changing the source code for the optimizer, the structure of the optimization code is described, and detailed instructions for compiling the program are provided.
1022245349
KEYWORDS: optimal harvesting, any-aged management, single-tree simulator
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