Solving multi-scenario cardinality constrained optimization problems via multi-objective evolutionary algorithms

Abstract

Cardinality constrained optimization problems (CCOPs) are fixed-size subset selection problems with applications in several fields. CCOPs comprising multiple scenarios, such as cardinality values that form an interval, can be defined as multi-scenario CCOPs (MSCCOPs). An MSCCOP is expected to optimize the objective value of each cardinality to support decision-making processes. When the computation is conducted using traditional optimization algorithms, an MSCCOP often requires several passes (algorithmic runs) to obtain all the (near-)optima, where each pass handles a specific cardinality. Such separate passes abandon most of the knowledge (including the potential superior solution structures) learned in one pass that can also be used to improve the results of other passes. By considering this situation, we propose a generic transformation strategy that can be referred to as the Mucard strategy, which converts an MSCCOP into a low-dimensional multi-objective optimization problem (MOP) to simultaneously obtain all the (near-)optima of the MSCCOP in a single algorithmic run. In essence, the Mucard strategy combines separate passes that deal with distinct variable spaces into a single pass, enabling knowledge reuse and knowledge interchange of each cardinality among genetic individuals. The performance of the Mucard strategy was demonstrated using two typical MSCCOPs. For a given number of evolved individuals, the Mucard strategy improved the accuracy of the obtained solutions because of the in-process knowledge than that obtained by untransformed evolutionary algorithms, while reducing the average runtime. Furthermore, the equivalence between the optimal solutions of the transformed MOP and the untransformed MSCCOP can be theoretically proved.