TSP(1,2)问题的进化优化分析

IF 1.4 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS International Journal of Computational Science and Engineering Pub Date : 2016-01-01 DOI:10.1504/IJCSE.2016.10007955

Xiaoyun Xia, Xinsheng Lai, Chen Yi

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引用次数: 1

摘要

TSP(1,2)问题是旅行推销员问题的一种np困难的特殊情况。提出了包括进化算法在内的许多启发式算法来解决TSP(1,2)问题。然而，对于TSP(1,2)问题，我们对ea的性能知之甚少。本文对这一问题给出了(1+1)EA的近似分析。结果表明，(1+1)EA和(µ+ λ) EA分别可以在期望多项式运行时间O(n3)和O((µ/λ)n3 + n)下获得该问题的3/2近似比。进一步证明了在TSP(1,2)问题上，(1+1)蚁群算法可以提供比简单蚁群算法更紧的上界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The analysis of evolutionary optimisation on the TSP(1,2) problem

TSP(1,2) problem is a special case of the travelling salesperson problem which is NP-hard. Many heuristics including evolutionary algorithms (EAs) are proposed to solve the TSP(1,2) problem. However, we know little about the performance of the EAs for the TSP(1,2) problem. This paper presents an approximation analysis of the (1+1) EA on this problem. It is shown that both the (1+1) EA and (µ + λ) EA can obtain 3/2 approximation ratio for this problem in expected polynomial runtime O(n3) and O ((µ/λ)n3 + n) , respectively. Furthermore, we prove that the (1+1) EA can provide a much tighter upper bound than a simple ACO on the TSP(1,2) problem.

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来源期刊

International Journal of Computational Science and Engineering COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.00

自引率

40.00%

发文量

期刊介绍： Computational science and engineering is an emerging and promising discipline in shaping future research and development activities in both academia and industry, in fields ranging from engineering, science, finance, and economics, to arts and humanities. New challenges arise in the modelling of complex systems, sophisticated algorithms, advanced scientific and engineering computing and associated (multidisciplinary) problem-solving environments. Because the solution of large and complex problems must cope with tight timing schedules, powerful algorithms and computational techniques, are inevitable. IJCSE addresses the state of the art of all aspects of computational science and engineering with emphasis on computational methods and techniques for science and engineering applications.