PRECISION EVOLUTIONARY OPTIMIZATION PART II: IMPLEMENTATION AND APPLICATIONS

Abstract

Implementation and applications of a new approach to multiobjective optimization by evolutionary algorithms are presented. After non-dominated sorting for Pareto formation, a novel non-linear ranking is proposed during the fitness evaluation and tournament selection, as well as elitism. The non-linear ranking is based on a probabilistic model, which models the density of the genetic population throughout the generations by means of an exponential distribution. From this model, a robust probabilistic distance measure is established. The distance comprises a penalty parameter in an embedded form, which plays an important role for the convergence of the optimization process as it varies in an adaptive form during the generations in progress. Because of the embedded form, the penalty parameter is inherently tuned for every constraint, making the convergence, robust, fast, accurate, and stable. By the nonlinear ranking procedure, also the stiffness among the constraints is handled effectively. Convergence process is backed-up with an additional probabilistic threshold applied to the population, classifying them as productive and unproductive infeasible solutions. The details of the underlying theoretical work are presented in the first part of this sequel. The present work at hand describes the algorithmic implementation in detail, and the outstanding performance of the optimization process is exemplified by computer experiments. The problems used in the experiments are selected from the existing literature for the purpose of eventual benchmark comparisons.

Keywords

• Evolutionary algorithm
• multiobjective optimization
• constraint optimization
• probabilistic modeling

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