Evolutionary Algorithms as Guaranteed Approximation Optimizers

Evolutionary algorithms (EAs) are heuristic algorithms inspired from natural evolution. They are often used to obtain good enough solutions in practice. In this paper, we investigate a largely underexplored issue: the approximation performance of EAs, i.e., how much the obtained solution is close to the optimal solution. We study an EA framework simple evolutionary algorithm with isolated population, abbreviated as SEIP, which is generalized from recent advances in multi-objective EAs. We analyze the approximation performance of SEIP through partial ratio, which characterizes the behaviors of SEIP that lead to solutions with guaranteed approximation ratios. Specifically, we analyze SEIP on the set cover problem which is NP-hard. We find that, for unbounded set cover problem, SEIP efficiently achievesHn-approximation ratio, the asymptotic lower bound; and for the k-set cover problem, it efficiently achieves (k k−1 8k9 )-approximation ratio, the currently best-achievable result, using bit-wise mutation. Moreover, on an instance class of k-set cover problem, we disclose how SEIP using either one-bit mutation or bit-wise mutation can overcome the difficulty that obstructs the greedy algorithm. These results suggest that EAs can serve as highly practical tools for obtaining approximate