Using Different Approaches to Approximate a Pareto Front for a Multiobjective Evolutionary Algorithm: Optimal Thinning Regimes for Eucalyptus fastigata

A stand-level, multiobjective evolutionary algorithm (MOEA) for determining a set of efficient thinning regimes satisfying two objectives, that is, value production for sawlog harvesting and volume production for a pulpwood market, was successfully demonstrated for a Eucalyptus fastigata trial in Kaingaroa Forest, New Zealand. The MOEA approximated the set of efficient thinning regimes (with a discontinuous Pareto front) by employing a ranking scheme developed by Fonseca and Fleming (1993), which was a Pareto-based ranking (a.k.a Multiobjective Genetic Algorithm—MOGA). In this paper we solve the same problem using an improved version of a fitness sharing Pareto ranking algorithm (a.k.a Nondominated Sorting Genetic Algorithm—NSGA II) originally developed by Srinivas and Deb (1994) and examine the results. Our findings indicate that NSGA II approximates the entire Pareto front whereas MOGA only determines a subdomain of the Pareto points.

[1]  C. Coello,et al.  Years of Evolutionary Multi-Objective Optimization : What Has Been Done and What Remains To Be Done , 2006 .

[2]  Carlos A. Coello Coello,et al.  Using the Min-Max Method to Solve Multiobjective Optimization Problems with Genetic Algorithms , 1998, IBERAMIA.

[3]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[4]  Shigeru Obayashi,et al.  Niching and Elitist Models for MOGAs , 1998, PPSN.

[5]  Oliver Chikumbo Exploration and Exploitation in Function Optimisation Using Stochastic Generate-and-Test Algorithms , 2009, GEM.

[6]  Jean Dickinson Gibbons,et al.  Nonparametric Statistical Inference , 1972, International Encyclopedia of Statistical Science.

[7]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

[8]  B. Turner,et al.  Predicting stand basal area in thined stands using a dynamical model , 1999 .

[9]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[10]  Oliver Chikumbo,et al.  An Optimal Silvicultural Regime Model using Competitive Co-evolutionary Genetic Algorithms , 2016, IJCCI.

[11]  Prabhat Hajela,et al.  Genetic search strategies in multicriterion optimal design , 1991 .

[12]  J. Marchal Cours d'economie politique , 1950 .

[13]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[14]  Carlos A. Coello Coello,et al.  A Short Tutorial on Evolutionary Multiobjective Optimization , 2001, EMO.

[15]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[16]  Bernard De Baets,et al.  Bi-objective genetic algorithms for forest management: a comparative study. , 2001 .

[17]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[18]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[19]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[20]  Kalyanmoy Deb,et al.  Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead , 2008, Manag. Sci..

[21]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[22]  J. A. Neldee New Kinds of Systematic Designs for Spacing Experiments , 1962 .

[23]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

[24]  L.J. Fogel,et al.  Intelligent decision-making through a simulation of evolution , 1965 .

[25]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[26]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[27]  Oliver Chikumbo,et al.  Efficient thinning regimes for Eucalyptus fastigata: Multi-objective stand-level optimisation using the island model genetic algorithm , 2011 .

[28]  Mehmet Çunkas,et al.  A tool for multiobjective evolutionary algorithms , 2009, Adv. Eng. Softw..

[29]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[30]  Alan D. Christiansen,et al.  An empirical study of evolutionary techniques for multiobjective optimization in engineering design , 1996 .

[31]  Patrick Siarry,et al.  A multipopulation genetic algorithm aimed at multimodal optimization , 2002 .

[32]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[33]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[34]  I. Mareels,et al.  Predicting Terminal Time And Final Crop Number For A Forest Plantation Stand:Pontryagin's Maximum Principle , 2003 .

[35]  W. Kruskal,et al.  Use of Ranks in One-Criterion Variance Analysis , 1952 .