Archiving Strategies for On-Line Decision Making in Evolutionary Multi-Objective Optimization

In this paper, we are studying a generalized version of the strength Pareto evolutionary algorithm 2 (SPEA2). By replacing the algorithmic-internal role of the Pareto-dominance relation with a different, not necessarily transitive relation, the algorithm can become capable to search for the maximum set of the replacing relation. Thus, the SPEA2 algorithm can also become capable of on-line decision making during the evolutionary search. The approach will be exemplified by using the maxmin-fair relation among objective vectors that avoids extremities of a subset of a few objectives only. But without the Pareto-dominance relation, also the way of filling the archive of the SPEA2 algorithm has to be revised. The matter becomes complicated by the fact that the replacing relations might be only transitive in some subpspaces - as it is the case for the maxmin-fair relation. Different methods for maintaining an archive are proposed and experimentally compared. The results of the study suggest, for the case of a larger number of objectives, to use an archiving strategy, which is based on transitive subspaces of the replacing relation.