Multi-objective differential evolution - algorithm, convergence analysis, and applications

The revival of multi-objective optimization (MOO) is mostly due to the recent development of evolutionary multi-objective optimization that allows the generation of the whole Pareto optimal front. Several evolutionary algorithms have been developed for this purpose. This paper focuses on the recent development of differential evolution (DE) algorithms for the multi-objective optimization purposes. Although there are a few other papers on the extension of DE concept to the MOO domain, this paper is intended to provide an overall picture of one specific multi-objective differential evolution (MODE) algorithm. In the MODE, the DE concept for the continuous single-objective optimization is extended to MOO for both continuous and discrete problems (C-MODE and D-MODE, respectively). The MODE is modeled in the context of Markov framework and global random search. Convergence properties are developed for both C-MODE and D-MODE. In particular, a set of parameter-setting guidelines for the C-MODE is derived based on the mathematical analysis. An application of the D-MODE to the planning of design, supply, and manufacturing resources in product development is also reported in this paper

[1]  H. Abbass,et al.  PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

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

[3]  K..  Multiobjective Optimization Using a Pareto Differential Evolution Approach , 2022 .

[4]  Arthur C. Sanderson,et al.  Modeling and convergence analysis of a continuous multi-objective differential evolution algorithm , 2005, 2005 IEEE Congress on Evolutionary Computation.

[5]  K..  Multiobjective Optimization Using a Pareto Differential Evolution Approach , 2022 .

[6]  Günter Rudolph,et al.  Convergence analysis of canonical genetic algorithms , 1994, IEEE Trans. Neural Networks.

[7]  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.

[8]  Arthur C. Sanderson,et al.  Network-Based Distributed Planning Using Coevolutionary Algorithms , 2004, Series in Intelligent Control and Intelligent Automation.

[9]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

[10]  Arthur C. Sanderson,et al.  Modeling and convergence analysis of distributed coevolutionary algorithms , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

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

[13]  Arthur C. Sanderson,et al.  Pareto-based multi-objective differential evolution , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[14]  Günter Rudolph,et al.  Convergence properties of some multi-objective evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[15]  Joe Suzuki,et al.  A Markov chain analysis on simple genetic algorithms , 1995, IEEE Trans. Syst. Man Cybern..

[16]  Günter Rudolph,et al.  Convergence of evolutionary algorithms in general search spaces , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[17]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

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

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

[20]  Arthur C. Sanderson,et al.  Multi-objective differential evolution and its application to enterprise planning , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

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

[22]  Thomas Hanne,et al.  On the convergence of multiobjective evolutionary algorithms , 1999, Eur. J. Oper. Res..

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

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

[25]  Arthur C. Sanderson,et al.  Minimal representation multisensor fusion using differential evolution , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[26]  D. Fogel.  ASYMPTOTIC CONVERGENCE PROPERTIES OF GENETIC ALGORITHMS AND EVOLUTIONARY PROGRAMMING: ANALYSIS AND EXPERIMENTS , 1994 .

[27]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

[28]  Arthur C. Sanderson,et al.  Multi-objective differential evolution: theory and applications , 2004 .

[29]  Arthur C. Sanderson,et al.  Multi-objective evolutionary decision support for design-supplier-manufacturing planning , 2005, IEEE International Conference on Automation Science and Engineering, 2005..

[30]  Gregory F. Lawler.  Introduction to Stochastic Processes , 1995 .