Fitness Landscapes Based on Sorting and Shortest Paths Problems
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In this paper, we present a new representation for individuals in the single-source shortest path problem. Contrary to previous approaches, it has the natural property that different vertex degrees do not induce unfairness in the mutation step. In particular, at any time each edge has roughly the same probability of being added to or removed from the current individual. This turns out to be a crucial property. Mainly based on this, we prove superior bounds for the optimization time two evolutionary algorithms for the single-source shortest path problem. For both the multi-criteria formulation of the problem (introduced by Scharnow, Tinnefeld and Wegener (2002, 2004)) and the single-criteria one (regarded in Baswana et al. (2009)), we improve the existing bounds by a factor of n2/m, where m denotes the number of edges and n the number of vertices of the underlying graph. Given that most graphs found in practical applications are sparse, this is a considerable gain.