A New Solution Approach for Grouping Problems Based on Evolution Strategies

Abstract

Since its foundation in 1994, the grouping genetic algorithm (GGA) is the only evolutionary algorithm heavily modified to suit the structure of grouping problems. In this paper we design the grouping version of evolution strategies (ES). It is well-known that ES maintains a Gaussian mutation, recombination and a selection operator for optimizing non-linear continuous functions. Therefore, the development of grouping evolution strategies (GES) for solving grouping problems that are discrete in nature, calls for developing operators having the major characteristics of the original ones and being respondent to the structure of grouping problems. We propose a mutation operator analogous to the original one that works with groups instead of scalars and use it in a two phase procedure to generate the new solution. We implement (1+Lambda)-GES and evaluate its performance versus GGA on some of hard benchmarked instances of the bin packing problem. Computational results testify that our approach is efficient and can be regarded as a promising solver for the wide class of grouping problems.