A new memetic strategy for the numerical treatment of multi-objective optimization problems

In this paper we propose a novel iterative search procedure for multi-objective optimization problems. The iteration process -- though derivative free -- utilizes the geometry of the directional cones of such optimization problems, and is capable both of moving toward and along the (local) Pareto set depending on the distance of the current iterate toward this set. Next, we give one possible way of integrating this local search procedure into a given EMO algorithm resulting in a novel memetic strategy. Finally, we present some numerical results on some well-known benchmark problems indicating the strength of both the local search strategy as well as the new hybrid approach.

[1]  Martin Brown,et al.  Directed Multi-Objective Optimization , 2005, Int. J. Comput. Syst. Signals.

[2]  C. Hillermeier.  Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach , 2001 .

[3]  H. Fawcett.  Manual of Political Economy , 1995 .

[4]  K. Deb,et al.  Hybrid methods for multi-objective evolutionary algorithms , 2002 .

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

[6]  Jörg Fliege,et al.  Steepest descent methods for multicriteria optimization , 2000, Math. Methods Oper. Res..

[7]  Peter A. N. Bosman,et al.  Exploiting gradient information in numerical multi--objective evolutionary optimization , 2005, GECCO '05.

[8]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

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

[10]  Joshua D. Knowles,et al.  M-PAES: a memetic algorithm for multiobjective optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

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

[12]  Kalyanmoy Deb,et al.  Hybridization of SBX based NSGA-II and sequential quadratic programming for solving multi-objective optimization problems , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

[14]  Carlos A. Coello Coello,et al.  A Memetic PSO Algorithm for Scalar Optimization Problems , 2007, 2007 IEEE Swarm Intelligence Symposium.

[15]  Xiaolin Hu,et al.  Hybridization of the multi-objective evolutionary algorithms and the gradient-based algorithms , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[16]  Hisao Ishibuchi,et al.  Multi-objective genetic local search algorithm , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[17]  Pablo Moscato,et al.  On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts : Towards Memetic Algorithms , 1989 .

[18]  Jason R. Schott.  Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. , 1995 .

[19]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[21]  Oliver Schütze,et al.  On Continuation Methods for the Numerical Treatment of Multi-Objective Optimization Problems , 2005, Practical Approaches to Multi-Objective Optimization.

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

[23]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[24]  Jürgen Branke,et al.  About Selecting the Personal Best in Multi-Objective Particle Swarm Optimization , 2006, PPSN.

[25]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[26]  Marco Laumanns,et al.  Convergence of stochastic search algorithms to gap-free pareto front approximations , 2007, GECCO '07.

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

[28]  David A. Van Veldhuizen,et al.  Evolutionary Computation and Convergence to a Pareto Front , 1998 .