On the approximation ability of evolutionary optimization with application to minimum set cover

Evolutionary algorithms (EAs) are a large family of heuristic optimization algorithms inspired by natural phenomena, and are often used in practice to obtain satisficing instead of optimal solutions. In this work, we investigate a largely underexplored issue: the approximation performance of EAs in terms of how close the obtained solution is to an optimal solution. We study an EA framework named simple EA with isolated population (SEIP) that can be implemented as a single- or multi-objective EA. We present general approximation results of SEIP, and specifically on the minimum set cover problem, we find that SEIP achieves the currently best-achievable approximation ratio. Moreover, on an instance class of the k-set cover problem, we disclose how SEIP can overcome the difficulty that limits the greedy algorithm.

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