Modeling and convergence analysis of a continuous multi-objective differential evolution algorithm

This paper reports a mathematical modeling and convergence analysis of a continuous multi-objective differential evolution (C-MODE) algorithm that is proposed very recently. This C-MODE is studied in the context of global random search. The convergence of the population to the Pareto optimal solutions with probability one is developed. In order to facilitate the understanding of the C-MODE operators in a continuous space, a mathematical analysis of the operators is conducted based upon a Gaussian distributed initial population. A set of guidelines is derived for the parameter setting of the C-MODE based on the theoretical results from the mathematical analysis. A simulation analysis on a specific numerical example is conducted to validate the mathematical analytical results and parameter-setting guidelines. The performance comparison based on a suite of complex benchmark functions also demonstrates the merits of such parameter-setting guidelines

[1]  A. A. Zhigli︠a︡vskiĭ,et al.  Theory of Global Random Search , 1991 .

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

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

[4]  R. Subbu,et al.  Modeling and convergence analysis of distributed co-evolutionary algorithms , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[5]  Arthur C. Sanderson,et al.  Multi-objective differential evolution - algorithm, convergence analysis, and applications , 2005, 2005 IEEE Congress on Evolutionary Computation.

[6]  Marco Laumanns,et al.  Running time analysis of multiobjective evolutionary algorithms on pseudo-Boolean functions , 2004, IEEE Transactions on Evolutionary Computation.

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

[8]  Atam P. Dhawan,et al.  Genetic Algorithms as Global Random Search Methods: An Alternative Perspective , 1995, Evolutionary Computation.

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

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

[11]  G. Rudolph.  On a multi-objective evolutionary algorithm and its convergence to the Pareto set , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

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

[14]  Marc Roubens,et al.  Multiple criteria decision making , 1994 .

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

[16]  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).

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

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

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

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

[21]  Francesco Palmieri,et al.  Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. Part I: Basic properties of selection and mutation , 1994, IEEE Trans. Neural Networks.

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