A New Constrained Multiobjective Optimization Algorithm Based on Artificial Immune Systems

This paper proposes a new constrained multiobjective optimization algorithm based on artificial immune systems (AIS). To deal with constrained multiobjective optimization problems, the constrained AlS-based multiobjective optimization algorithm is developed by integrating a proposed constraint-handling technique with the unconstrained AIS-based multiobjective optimization algorithm named MOAIS (Xiao and Zu, 2006). We propose the constraint-handling technique by extending a single-objective constraint-handling technique called stochastic ranking (Runarsson and Yao, 2000) to multiobjective optimization process. Two scenarios of the multiobjective version of stochastic ranking are suggested. Thereafter, we develop the constrained MOAIS named MOAIS+SR by integrating the two scenarios with MOAIS. A comparative study is performed quantitatively to assess the performance of MOAIS+SR on a constrained test function suite called CTP test problems. In the comparative study, MOAIS+SR is compared against two other constrained multiobjective algorithms. The simulation results show that the proposed multiobjective stochastic ranking outperforms the constrained-dominance principle (Deb et al., 2000) in handling constraints. Furthermore, we show that the proposed MOAIS+SR achieves the best overall performance among the three algorithms under consideration on the CTP test problems. This study demonstrates that the proposed MOAIS+SR is highly competitive with other state-of-the-art algorithms in constrained multiobjective optimization.

[1]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[2]  Jonathan A. Wright,et al.  Self-adaptive fitness formulation for constrained optimization , 2003, IEEE Trans. Evol. Comput..

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

[4]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[5]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[6]  Mitsuo Gen,et al.  An adaptive hyperplane approach for multiple objective optimization problems with complex constraints , 2000 .

[7]  D.A. Van Veldhuizen,et al.  Finding improved wire-antenna geometries with genetic algorithms , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[8]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[9]  Kalyanmoy Deb,et al.  Mechanical Component Design for Multiple Objectives Using Elitist Non-dominated Sorting GA , 2000, PPSN.

[10]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[11]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[12]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[13]  P. Hajela,et al.  Fuzzy multicriterion design using immune network simulation , 2001 .

[14]  Carlos Artemio Coello-Coello,et al.  Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art , 2002 .

[15]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[16]  Kalyanmoy Deb,et al.  Towards a Quick Computation of Well-Spread Pareto-Optimal Solutions , 2003, EMO.

[17]  K. C. Seow,et al.  MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM , 2001 .

[18]  Henrik Esbensen,et al.  Fuzzy/multiobjective genetic systems for intelligent systems design tools and components , 1997 .

[19]  Liang Shi,et al.  Multiobjective GA optimization using reduced models , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).