Assessing the convergence of rank-based multiobjective genetic algorithms

Many problems in engineering and related areas require the simultaneous optimisation of multiple objectives and to this end, rank-based genetic algorithms have proved very successful. The key issue of convergence of vector optimisations, however, has not hitherto been explicitly addressed. In this paper we introduce rank histograms both to assess convergence of a given single genetic optimisation and to combine results from multiple runs to test for the adequacy of the individual optimisations. Results are presented on two analytic benchmark multiobjective problems where the optimal solution set is known a priori, and on a problem in partitioning a pattern recognition task