PROBABILISTIC SORTING FOR EFFECTIVE ELITISM IN MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS

Abstract

respect a new approach is presented, which is a probabilistic sorting for effective elitism and ensuing improved and robust convergence. This is achieved by an adaptive probabilistic model representing the commensurate probability density of the random solutions throughout the generations that it yields a probabilistic distance measure which is nonlinear with respect to the range of solutions as to their location in the objectives space. The implementation of the theoretical results leads an effective evolutionary optimization algorithm accomplished in two stages. In the first stage linear non-dominated sorting, tournament selection and elitism is carried out in objective space. In the second stage, the same is executed in a transformed objective space, where probabilistic distance measure for ranking prevails. The effectiveness of the method is exemplified by a demonstrative computer experiment. The problem treated is selected from the existing literature for comparison, while the experiment carried out and reported here demonstrates the marked performance of the approach. The experiment complies with the theoretical foundations, so that the robust and fast convergence with precision as well as with accuracy is accomplished throughout the search up to 10-10 range or beyond, limited exclusively by machine precision.

Keywords

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

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