TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION

Abstract This paper presents a new approach to handle constraints using evolutionary algorithms. The new technique treats constraints as objectives, and uses a multiobjective optimization approach to solve the re-stated single-objective optimization problem. The new approach is compared against other numerical and evolutionary optimization techniques in several engineering optimization problems with different kinds of constraints. The results obtained show that the new approach can consistently outperform the other techniques using relatively small sub-populations, and without a significant sacrifice in terms of performance.

[1]  M. Karnaugh.  The map method for synthesis of combinational logic circuits , 1953, Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics.

[2]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[3]  James N. Siddall,et al.  Analytical decision-making in engineering design , 1972 .

[4]  James N. Siddall,et al.  Optimal Engineering Design: Principles and Applications , 1982 .

[5]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

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

[7]  J. D. Schaffer,et al.  Multiple Objective Optimization with Vector Evaluated Genetic Algorithms , 1985, ICGA.

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

[9]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[10]  Gilbert Syswerda,et al.  Uniform Crossover in Genetic Algorithms , 1989, ICGA.

[11]  Jack Sklansky,et al.  Constrained Genetic Optimization via Dynarnic Reward-Penalty Balancing and Its Use in Pattern Recognition , 1989, ICGA.

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

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

[14]  John J. Grefenstette,et al.  Deception Considered Harmful , 1992, FOGA.

[15]  Michael de la Maza,et al.  Book review: Genetic Algorithms + Data Structures = Evolution Programs by Zbigniew Michalewicz (Springer-Verlag, 1992) , 1993 .

[16]  Michael M. Skolnick,et al.  Using Genetic Algorithms in Engineering Design Optimization with Non-Linear Constraints , 1993, ICGA.

[17]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

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

[19]  Atidel B. Hadj-Alouane,et al.  A dual genetic algorithm for bounded integer programs James C. Bean, Atidel Ben Hadj-Alouane. , 1993 .

[20]  Marc Schoenauer,et al.  Constrained GA Optimization , 1993, ICGA.

[21]  Zbigniew Michalewicz,et al.  Evolutionary optimization of constrained problems , 1994 .

[22]  Jan Paredis,et al.  Co-evolutionary Constraint Satisfaction , 1994, PPSN.

[23]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[24]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[25]  Raphael T. Haftka,et al.  A Segregated Genetic Algorithm for Constrained Structural Optimization , 1995, ICGA.

[26]  Z. Michalewicz.  Genetic Algorithms , Numerical Optimization , and Constraints , 1995 .

[27]  Patrick D. Surry,et al.  A Multi-objective Approach to Constrained Optimisation of Gas Supply Networks: the COMOGA Method , 1995, Evolutionary Computing, AISB Workshop.

[28]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[29]  Zbigniew Michalewicz,et al.  Evolutionary algorithms for constrained engineering problems , 1996, Computers & Industrial Engineering.

[30]  Jongsoo Lee,et al.  Constrained genetic search via schema adaptation: An immune network solution , 1996 .

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

[32]  Dorothea Heiss-Czedik,et al.  An Introduction to Genetic Algorithms. , 1997, Artificial Life.

[33]  Carlos A. Coello Coello,et al.  Optimal design of reinforced concrete beams using genetic algorithms , 1997 .

[34]  Zbigniew Michalewicz,et al.  Evolutionary algorithms , 1997, Emerging Evolutionary Algorithms for Antennas and Wireless Communications.

[35]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[36]  Kalyanmoy Deb,et al.  Optimizing Engineering Designs Using a Combined Genetic Search , 1997, ICGA.

[37]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms in Engineering Applications , 1997, Springer Berlin Heidelberg.

[38]  Dae Gyu Kim,et al.  Riemann mapping based constraint handling for evolutionary search , 1998, SAC '98.

[39]  P. Husbands,et al.  Mapping Based Constraint Handling for Evolutionary Search; Thurston’s Circle Packing and Grid Generation , 1998 .

[40]  P. BAiANT.  ANALYSIS OF FRAMED STRUCTURES , .

[41]  A. H. Aguirre,et al.  AUTOMATED DESIGN OF COMBINATIONAL LOGIC CIRCUITS USING GENETIC ALGORITHMS , 2022 .