A new mechanism to maintain diversity in multi-objective metaheuristics

Abstract

In this article, a new mechanism to spread the solutions generated by a multi-objective evolutionary algorithm is proposed. This approach is based on the use of stripes that are applied in objective function space and is independent of the search engine adopted. Additionally, it overcomes some of the drawbacks of other previous proposals such as the ϵ-dominance method. In order to validate the proposed approach, it is coupled to a multi-objective particle swarm optimizer and its performance is assessed with respect to that of state-of-the-art algorithms, using standard test problems and performance measures taken from the specialized literature. The results indicate that the proposed approach is a viable diversity maintenance mechanism that can be incorporated to any multi-objective metaheuristic used for multi-objective optimization.

Keywords:

• multi-objective optimization
• metaheuristics
• evolutionary algorithms
• ϵ-dominance
• particle swarm optimization

AMS Subject Classifications:

• 90-08
• 65K99
• 68W20

Acknowledgements

Gregorio Toscano Pulido gratefully acknowledges support from CONACyT project No. 105060. Carlos A. Coello Coello gratefully acknowledges support from CONACyT project No. 103570. He is also affiliated to the UMI LAFMIA 3175 CNRS at CINVESTAV-IPN.

Notes

1. Most modern MOEAs use an elite set in which the solutions that are ‘globally’ nondominated (i.e., nondominated with respect to all the individuals that have been processed so far) are stored. This set is theoretically required in order to guarantee convergence 29.

2. The hypervolume is the area under the curve for the two-dimensional case or the volume under the surface for the three-dimensional case.