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Evolutionary Computation

Winter 2017, Vol. 25, No. 4, Pages 673-705
(doi: 10.1162/evco_a_00199)
© 2017 Massachusetts Institute of Technology
Expected Fitness Gains of Randomized Search Heuristics for the Traveling Salesperson Problem
Article PDF (1.78 MB)

Randomized search heuristics are frequently applied to NP-hard combinatorial optimization problems. The runtime analysis of randomized search heuristics has contributed tremendously to our theoretical understanding. Recently, randomized search heuristics have been examined regarding their achievable progress within a fixed-time budget. We follow this approach and present a fixed-budget analysis for an NP-hard combinatorial optimization problem. We consider the well-known Traveling Salesperson Problem (TSP) and analyze the fitness increase that randomized search heuristics are able to achieve within a given fixed-time budget. In particular, we analyze Manhattan and Euclidean TSP instances and Randomized Local Search (RLS), (1+1) EA and (1+λ) EA algorithms for the TSP in a smoothed complexity setting, and derive the lower bounds of the expected fitness gain for a specified number of generations.