多目标进化算法的参数化分析及加权顶点覆盖问题
Parameterized Analysis of Multi-objective Evolutionary Algorithms and the Weighted Vertex Cover Problem
摘要：
Kratsch和Neumann（2013）在参数化复杂性分析的背景下对经典顶点覆盖问题的进化多目标优化进行了严格的运行时分析。在本文中，我们将分析扩展到加权顶点覆盖问题，并提供了一个固定参数的进化算法关于OPT，成本的最优解的问题。此外，使用的多样性机制，我们提出了一个多目标进化算法，找到一个2-近似在期望的多项式时间，并引入一个基于种群的进化算法，找到一个$(1+\varepsilon)$ -近似在期望的时间$O(n\cdot 2^{\min \{n,2(1- \varepsilon)OPT \}} + n^3)$。
英文摘要：
A rigorous runtime analysis of evolutionary multi-objective optimization for the classical vertex cover problem in the context of parameterized complexity analysis has been presented by Kratsch and Neumann (2013). In this paper, we extend the analysis to the weighted vertex cover problem and provide a fixed parameter evolutionary algorithm with respect to OPT, the cost of the the optimal solution for the problem. Moreover, using a diversity mechanisms, we present a multi-objective evolutionary algorithm that finds a 2-approximation in expected polynomial time and introduce a population-based evolutionary algorithm which finds a $(1+\varepsilon)$-approximation in expected time $O(n\cdot 2^{\min \{n,2(1- \varepsilon)OPT \}} + n^3)$.
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