On algorithm-dependent boundary case identification for problem classes

Authors:
Chao Qian;Yang Yu;Zhi-Hua Zhou
Affiliations:
National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China;National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China;National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China
Venue:
PPSN'12 Proceedings of the 12th international conference on Parallel Problem Solving from Nature - Volume Part I
Year:
2012

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Abstract

Running time analysis of metaheuristic search algorithms has attracted a lot of attention. When studying a metaheuristic algorithm over a problem class, a natural question is what are the easiest and the hardest cases of the problem class. The answer can be helpful for simplifying the analysis of an algorithm over a problem class as well as understanding the strength and weakness of an algorithm. This algorithm-dependent boundary case identification problem is investigated in this paper. We derive a general theorem for the identification, and apply it to a case that the (1+1)-EA with mutation probability less than 0.5 is used over the problem class of pseudo-Boolean functions with a unique global optimum.