# AN OPTIMAL SILVICULTURAL REGIME MODEL USING COMPETITIVE CO-EVOLUTIONARY GENETIC ALGORITHMS

### Oliver Chikumbo

#### 2009

#### Abstract

A competitive co-evolutionary genetic algorithm was successfully employed to determine an optimal silvicultural regime for the South African Pinus patula Schl. Et Cham. The solution to the silvicultural regime included: initial planting density; frequency, timing and intensity of thinnings; final crop number; and rotation length. The growth dynamics for P.patula were estimated using dynamical models, the building blocks of the combined optimal control and parameter selection formulation, with a single objective function that was maximised for value production. The results were compared against a silvicultural regime determined using Pontryagin’s Maximum Principle. Both the regimes were then compared against the recommended silvicultural regime determined from years of experimental trials. The genetic algorithms regime was superior to the other two.

#### References

- Anderson, B.D.O., and Moore, J.B. (1989), Optimal Control: Linear Quadratic Methods, prentice-Hall International Editions, Engelwood Cliffs, NJ 07632.
- Arthaud, G.J., and Pelkki, M.H. (1997), Exploring enhancements to dynamic programming, Seventh Symposium on Systems Analysis in Forest Resources, USDA For. Serv. North Central Research Station, General Technical Rpt. NC-205, ed. Sessions, J., pp. 337-342.
- Arthaud, G.J., and Warnell, D.B. (1994), A comparison of forward-recursion dynamic programming and A* in forest stand optimisation, Management Systems for a Global Economy with Global Resource Concerns, eds. Sessions, J. & Brodie, J.D., Pacific Grove, California.
- Bellman, R.E. (1957), Dynamic Programming, NJ, Princeton University Press.
- Brooke, A., Kendrick, D., and Meeraus, A. (1988), GAMS: A User's Guide, The Scientific Press.
- Chen, C.M., Rose, D.W., and Leary, R.A. (1980), How to formulate and solve optimal stand density over time problem for even-aged stands using dynamic programming, General Technical NC-56, St. Paul, MN:USDA Forest Service, North Central Forest Experiment Station.
- Chikumbo, O. (1996), Applicability of dynamical modeling and theoretical control methods in tree growth prediction and planning, PhD thesis, The Australian National University, Canberra, ACT, Australia.
- Chikumbo, O., and Mareels, I. M. Y. (2003), Predicting terminal time and final crop number for a forest plantation stand: Pontryagin's Maximum Principle, Ecosystems and Sustainable Development, eds. Tiezzi, E., Brebbia, C.A., and Uso, J.L., WIT Press, ISBN 1- 85312-834-X, 2:1227-1237.
- Chikumbo, O., and Mareels, I. M. Y. (2002), Impact of tree mortality in optimal control and parameter selection problems in forest stand management, Development and Application of Computer Techniques to Environmental Studies IX, eds. Brebbia, C.A., and Zannetti, P., WIT Press, ISBN 1- 85312-909-7, pp 309-317.
- Chikumbo, O., and Mareels, I. M. Y. (1995), Optimal thinning strategies based on dynamical models and the maximum principle, Application of the New Technologies in Forestry, eds., Bren, L. and Greenwood, C., Ballarat, Victoria, Institute of Foresters of Australia, 1:239-245.
- Chikumbo, O., Mareels, I. M. Y., and Turner, B.J. (1999), Predicting stand basal area in thinned stands using a dynamical model, Forest Ecology and Management, 116(1999): 175-187.
- Chikumbo, O., Mareels, I. M. Y., and Turner, B.J. (1997), A stand optimization model developed from dynamical models for determining thinning strategies, Seventh Symposium on Systems Analysis in Forest Resources, eds. Vasievich, J.M., Fried, J.S. and Leefers, L.A., Traverse City, MI. Gen. Tech. Rep. NC205. St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Research Station, pp. 355-360.
- Chikumbo, O., Mareels, I. M. Y., and Turner, B.J. (1992), Integrating the Weibull into a dynamical model to predict future diameter distributions, Integrating Forest Information over Space and Time, eds., Wood, G.B., and Turner, B.J., The Australian National University, ANUTECH Pty Ltd., pp 94-102.
- Dixon, L.C.W. (1972), Nonlinear Optimisation, The English Universities Press Ltd., Bell & Ban Limited, Glasgow, UK.
- Fan, L.T., and Wang, C.S. (1964), The Discrete Maximum Principle, A Study of Multistage Systems Optimisation, New York, John Wiley & Sons.
- Filius, A.M., & Dul, M.T. (1992), Dependence of rotation and thinning strategy on economic factors and silvicultural constraints: results of an application of dynamic programming, Forest Ecology and Management, 48:345-356.
- Goldberg, D. E. (1989), Genetic Algorithms in Search, Optimisation and Machine Learning, Addison Wesley Longman, Inc., University of Alabama
- Goldberg, D.E., Deb, K., Kargupta, H., and Harik, G. (1993), Rapid, Accurate Optimization of Difficult Problems Using Fast Messy Genetic Algorithms, Proceedings of the Fifth International Conference on Genetic Algorithms, Morgan Kaufmann, pp 56-64.
- Horn, J. (1997), Evolutionary computation applications: Multicriterion decision making, Handbook on Evolutionary Computation, eds., Back, T., Fogel, D.B. and Michalewicz, Z., Bristol, Institute of Physics Publishing and Oxford, New York: Oxford University Press, pp 9-15.
- Kassier, H.W. (1991), Revised thinning policy for softwood sawlog production, Unpublished addendum to Forest Management Instruction No 1/3/1, Department of Water Affairs and Forestry, South Africa pp. 18.
- Kuboyama, H., and Oka, H. (2000), Climate risks and agerelated damage probabilities - effects on the economically optimal rotation length for forest stand management in Japan, Silva Fennica, 34(2):155-166.
- Levine, D. (1994), A parallel genetic algorithm for the set partitioning problem, PhD thesis, Mathematics and Computer Science Division, Argonne National Library, Argonne, IL 60439.
- Ljung, L. (1987), System Identification: Theory for the User, Prentice-Hall Inc., Englewood Cliffs, NJ.
- Mesterton-Gibbons, M. (1995), A Concrete Approach to mathematical Modelling, Wiley-Interscience Publication, John Wiley & Sons, Inc., 597p.
- Michalewicz, Z. (1999), Genetic Algorithms + Data Structures = Evolution Programs, 3rd Edn., SpringerVerlag Berlin Heidelberg, New York.
- Michalewicz, Z., Janikow, C., and Krawczyk, J. (1992), A Modified Genetic Algorithm for Optimal Control Problems, Computers & Mathematics with Applications, 23(12): 83-94.
- Oliver, C.D., and Larson, B.C. (1990), Forest Stand Dynamics, Biological Resource Management Series, McGraw-Hills Inc., USA.
- Pelkki, M.H. (1994), Exploring the effects of aggregation in dynamic programming,
- Pelkki, M.H. & Arthaud, G.J. (1997), Exploring enhancements to dynamic programming, Seventh Symposium on Systems Analysis in Forest Resources, eds. Fried, J., Leefers, L., and & Vasievich, M., General Technical NC-205, St. Paul, MN:USDA Forest Service, North Central Forest Experiment Station, pp. 337-342.
- Pohlheim, H. (2006), Evolutionary Algorithms: Overview, Methods and Operators, GEATbx: Introduction, www.geatbx.com.
- Schittkowski, K. (1985), NLPQL: A FORTRAN subroutine for solving constrained nonlinear programming problems, Annals of Operations Research, 5:485-500.
- Teo, K.L., Wong, K.H., and Goh, C.J. (1989), Optimal maintenance of a system of machines with the weakest link dependence performance, Optimal Control Methods and Application, 10:113-127.
- Yin, R. and Newman, D.H. (1995), Optimal timber rotations with evolving prices and costs revisited, Forest Science, 41:477-490.
- Zitzler, E., Deb, K., and Thiele, L. (2000), Comparison of multi-objective evolutionary algorithms: empirical results, Evolutionary Computation 8(2): 173-195.

#### Paper Citation

#### in Harvard Style

Chikumbo O. (2009). **AN OPTIMAL SILVICULTURAL REGIME MODEL USING COMPETITIVE CO-EVOLUTIONARY GENETIC ALGORITHMS** . In *Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)* ISBN 978-989-674-014-6, pages 209-217. DOI: 10.5220/0002314202090217

#### in Bibtex Style

@conference{icec09,

author={Oliver Chikumbo},

title={AN OPTIMAL SILVICULTURAL REGIME MODEL USING COMPETITIVE CO-EVOLUTIONARY GENETIC ALGORITHMS},

booktitle={Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)},

year={2009},

pages={209-217},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002314202090217},

isbn={978-989-674-014-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Joint Conference on Computational Intelligence - Volume 1: ICEC, (IJCCI 2009)

TI - AN OPTIMAL SILVICULTURAL REGIME MODEL USING COMPETITIVE CO-EVOLUTIONARY GENETIC ALGORITHMS

SN - 978-989-674-014-6

AU - Chikumbo O.

PY - 2009

SP - 209

EP - 217

DO - 10.5220/0002314202090217