Finding multiple solutions for multimodal optimization problems using a multi-objective evolutionary approach

In a multimodal optimization task, the main purpose is to find multiple optimal (global and local) solutions associated with a single objective function. Starting with the preselection method suggested in 1970, most of the existing evolutionary algorithms based methodologies employ variants of niching in an existing single-objective evolutionary algorithm framework so that similar solutions in a population are de-emphasized in order to focus and maintain multiple distant yet near-optimal solutions. In this paper, we use a completely different and generic strategy in which a single-objective multimodal optimization problem in converted into a suitable bi-objective optimization problem so that all local and global optimal solutions become members of the resulting weak Pareto-optimal set. We solve up to 16-variable test-problems having as many as 48 optima and also demonstrate successful results on constrained multimodal test-problems, suggested for the first time. The concept of using multi-objective optimization for solving single-objective multimodal problems seems novel and interesting, and importantly opens further avenues for research.

[1]  Andreas Zell,et al.  A Clustering Based Niching EA for Multimodal Search Spaces , 2003, Artificial Evolution.

[2]  Ofer M. Shir,et al.  Niche Radius Adaptation in the CMA-ES Niching Algorithm , 2006, PPSN.

[3]  Zbigniew Michalewicz,et al.  Evolutionary Computation 1 , 2018 .

[4]  Kalyanmoy Deb,et al.  Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems , 1995, Complex Syst..

[5]  Richard A. Watson,et al.  Reducing Local Optima in Single-Objective Problems by Multi-objectivization , 2001, EMO.

[6]  Kenneth Alan De Jong,et al.  An analysis of the behavior of a class of genetic adaptive systems. , 1975 .

[7]  Zachary V. Hendershot.  A Differential Evolution Algorithm for Automatically Discovering Multiple Global Optima in Multidimensional, Discontinuous Spaces , 2004, MAICS.

[8]  Ralph R. Martin,et al.  A Sequential Niche Technique for Multimodal Function Optimization , 1993, Evolutionary Computation.

[9]  Aravind Srinivasan,et al.  Innovization: innovating design principles through optimization , 2006, GECCO.

[10]  Günter Rudolph,et al.  Solving multimodal problems via multiobjective techniques with Application to phase equilibrium detection , 2007, 2007 IEEE Congress on Evolutionary Computation.

[11]  Carlos A. Coello Coello,et al.  A Review of Particle Swarm Optimization Methods Used for Multimodal Optimization , 2009, Innovations in Swarm Intelligence.

[12]  Kalyanmoy Deb,et al.  Comparison of multi-modal optimization algorithms based on evolutionary algorithms , 2006, GECCO.

[13]  P. John Clarkson,et al.  A Species Conserving Genetic Algorithm for Multimodal Function Optimization , 2002, Evolutionary Computation.

[14]  Alain Pétrowski,et al.  A clearing procedure as a niching method for genetic algorithms , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[15]  Xiaodong Li,et al.  A Generator for Multimodal Test Functions with Multiple Global Optima , 2008, SEAL.

[16]  David E. Goldberg,et al.  Probabilistic Crowding: Deterministic Crowding with Probabilistic Replacement , 1999 .

[17]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[18]  Kalyanmoy Deb,et al.  Multimodal Deceptive Functions , 1993, Complex Syst..

[19]  Ofer M. Shir,et al.  Niching in evolution strategies , 2005, GECCO '05.

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

[21]  David E. Goldberg,et al.  Genetic Algorithms with Sharing for Multimodalfunction Optimization , 1987, ICGA.

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

[23]  A. Ravindran,et al.  Engineering Optimization: Methods and Applications , 2006 .

[24]  Kalyanmoy Deb,et al.  An Investigation of Niche and Species Formation in Genetic Function Optimization , 1989, ICGA.