Evolutionary Computation Techniques for Nonlinear Programming Problems

Abstract This paper presents several evolutionary computation techniques and discusses their applicability to nonlinear programming problems. On the basis of this presentation we discuss also a construction of a new hybrid optimization system, Genocop II, and present its experimental results on a few test cases (nonlinear programming problems).

[1]  T. M. Williams.  Practical Methods of Optimization. Vol. 2 — Constrained Optimization , 1982 .

[2]  Zbigniew Michalewicz,et al.  A Nonstandard Genetic Algorithm for the Nonlinear Transportation Problem , 1991, INFORMS J. Comput..

[3]  David H. Ackley,et al.  An empirical study of bit vector function optimization , 1987 .

[4]  C. G. Shaefer,et al.  The ARGOT Strategy: Adaptive Representation Genetic Optimizer Technique , 1987, ICGA.

[5]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[6]  L. Ingber.  Very fast simulated re-annealing , 1989 .

[7]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[8]  J. David Schaffer,et al.  Proceedings of the third international conference on Genetic algorithms , 1989 .

[9]  Willi Hock,et al.  Lecture Notes in Economics and Mathematical Systems , 1981 .

[10]  Klaus Schittkowski,et al.  Test examples for nonlinear programming codes , 1980 .

[11]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[12]  Garth P. McCormick,et al.  Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems , 1976, Math. Program..

[13]  Zbigniew Michalewicz,et al.  GENOCOP: a genetic algorithm for numerical optimization problems with linear constraints , 1996, CACM.

[14]  L. Darrell Whitley,et al.  The GENITOR Algorithm and Selection Pressure: Why Rank-Based Allocation of Reproductive Trials is Best , 1989, ICGA.

[15]  Lawrence Davis,et al.  Genetic Algorithms and Simulated Annealing , 1987 .

[16]  Rajarshi Das,et al.  A Study of Control Parameters Affecting Online Performance of Genetic Algorithms for Function Optimization , 1989, ICGA.

[17]  Thomas Bäck,et al.  A Survey of Evolution Strategies , 1991, ICGA.

[18]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[19]  Z. Michalewicz,et al.  A genetic algorithm for the linear transportation problem , 1991, IEEE Trans. Syst. Man Cybern..

[20]  John J. Grefenstette,et al.  Proceedings of the 1st International Conference on Genetic Algorithms , 1985 .

[21]  Alden H. Wright,et al.  Genetic Algorithms for Real Parameter Optimization , 1990, FOGA.

[22]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[23]  C. G. Broyden,et al.  A smooth sequential penalty function method for solving nonlinear programming problems , 1984 .

[24]  Kenneth A. De Jong,et al.  Genetic algorithms: A 10 Year Perspective , 1985, ICGA.

[25]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[26]  J. Betts.  An accelerated multiplier method for nonlinear programming , 1977 .

[27]  Z. Michalewicz,et al.  A modified genetic algorithm for optimal control problems , 1992 .

[28]  Lashon B. Booker,et al.  Proceedings of the fourth international conference on Genetic algorithms , 1991 .

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

[30]  Panos M. Pardalos,et al.  A Collection of Test Problems for Constrained Global Optimization Algorithms , 1990, Lecture Notes in Computer Science.

[31]  Zbigniew Michalewicz,et al.  Handling Constraints in Genetic Algorithms , 1991, ICGA.

[32]  Leon Cooper,et al.  Introduction to Methods of Optimization , 1970 .

[33]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[34]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[35]  C. G. Broyden,et al.  Penalty functions, Newton's method, and quadratic programming , 1988 .

[36]  Zbigniew Michalewicz,et al.  A Hierarchy of Evolution Programs: An Experimental Study , 1993, Evolutionary Computation.

[37]  Panos M. Pardalos,et al.  Recent Advances in Global Optimization , 1991 .

[38]  Lawrence Davis,et al.  Adapting Operator Probabilities in Genetic Algorithms , 1989, ICGA.

[39]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

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

[41]  Terence C. Fogarty,et al.  Varying the Probability of Mutation in the Genetic Algorithm , 1989, ICGA.

[42]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[43]  Z. Michalewicz,et al.  Genetic algorithms for numerical optimization , 1991 .

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

[45]  F. Glover.  HEURISTICS FOR INTEGER PROGRAMMING USING SURROGATE CONSTRAINTS , 1977 .

[46]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .