Nonlinear mappings in problem solving and their PSO-based development

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 ϕ so that the method operating in the transformed space M(ϕ(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.