Multiobjective genetic algorithms made easy: selection sharing and mating restriction

This paper aims to illustrate how an existing GA can be modified and set up to explore the relevant trade-offs between multiple objectives with a minimum of effort. While Pareto and Pareto-like ranking schemes can be easily implemented, current guidelines on the associated set-up of techniques such as sharing and mating restriction are intricate and/or based on more or less rough assumptions about the cost landscape, making them impractical. However, if fitness sharing is reinterpreted as a technique involving the estimation of the population density at the points defined by each individual by so-called kernel methods, the setting of the sharing parameter comes to depend only on the size and current distribution of the population, and not on the problem. Kernel density estimation, a technique from statistics and data analysis, is introduced and shown to find direct application in sharing and mating restriction, simplifying implementation and avoiding the introduction of any more tunable parameters in the GA formulation. After a brief introduction to multiobjective optimization and a discussion of preference articulation in GAs, the main differences between single-objective and multiobjective GAs are highlighted, and the conversion of an existing GA into a multiobjective GA described by means of an example. Simple experimental results are presented towards the end of the paper.