Nonlinear mappings in problem solving and their PSO-based development

Authors:
Adam Pedrycz;Fangyan Dong;Kaoru Hirota
Affiliations:
Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology G3-49, 4259 Nagatsuta, Midori-ku, Yokohama ...;Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology G3-49, 4259 Nagatsuta, Midori-ku, Yokohama ...;Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology G3-49, 4259 Nagatsuta, Midori-ku, Yokohama ...
Venue:
Information Sciences: an International Journal
Year:
2011

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Abstract

The study is devoted to a concept and algorithmic realization of nonlinear mappings aimed at increasing the effectiveness of the problem solving method. Given the original input space X and a certain problem solving method M, designed is a nonlinear mapping @f so that the method operating in the transformed space M(@f(X)) becomes more efficient. The nonlinear mappings realize a transformation of X through contractions and expansions of selected regions of the original space. In particular, we show how a piecewise linear mapping is optimized by using particle swarm optimization (PSO) and a suitable fitness function quantifying the objective of the problem. Several families of problems are investigated and illustrated through illustrative experimental results.