PRECISION EVOLUTIONARY OPTIMIZATION PART I: NONLINEAR RANKING APPROACH

Abstract

Theoretical foundations of a robust approach for multiobjective optimization by evolutionary algorithms are introduced. The optimization method used is the conventional penalty function approach, which is also known as bi-objective method. The novelty of the method stems from the dynamic variation of the commensurate penalty parameter for each objective treated as constraint. The parameters collectively define the right slope of the tangent as to the optimal front during the search. The slope conforms to the theoretical considerations so that the robust and fast convergence of the search is accomplished throughout the search up to micro level in the range of 10-10 or beyond with precision as well as with accuracy thanks to a robust probabilistic distance measure established in this work. The measure is used for nonlinear ranking among the population members of the evolutionary process, and the method is implemented by a computer program called NS-NR developed for this research. The effectiveness of the method is exemplified by a demonstrative computer experiment minimizing a highly non-linear, non-polynomial, non-quadratic etc. function. The algorithm description in detail and further several applications are presented in the second part of this research. The problems used in computer experiments are selected from the existing literature for comparison while the experiments carried out and reported here to demonstrate the simplicity vs effectiveness of the algorithm.

Keywords

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

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