Computer Science – Neural and Evolutionary Computing
Scientific paper
2010-11-17
Computer Science
Neural and Evolutionary Computing
Scientific paper
10.1016/j.artint.2012.01.001
Evolutionary algorithms (EAs) are heuristic algorithms inspired by natural evolution. They are often used to obtain satisficing solutions in practice. In this paper, we investigate a largely underexplored issue: the approximation performance of EAs in terms of how close the solution obtained 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 analyze the approximation performance of SEIP using the partial ratio, which characterizes the approximation ratio that can be guaranteed. Specifically, we analyze SEIP using a set cover problem that is NP-hard. We find that in a simple configuration, SEIP efficiently achieves an $H_n$-approximation ratio, the asymptotic lower bound, for the unbounded set cover problem. We also find that SEIP efficiently achieves an $(H_k-\frac{k-1}/{8k^9})$-approximation ratio, the currently best-achievable result, for the k-set cover problem. Moreover, for an instance class of the k-set cover problem, we disclose how SEIP, using either one-bit or bit-wise mutation, can overcome the difficulty that limits the greedy algorithm.
Yao Xin
Yu Yang
Zhou Zhi-Hua
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