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Expected Fitness Gains of Randomized Search Heuristics for the Traveling Salesperson Problem
Samadhi Nallaperuma1, Frank Neumann2, Dirk Sudholt3
1Algorithms, Department of Computer Science, The University of Sheffield, Sheffield, S1 4DP, United Kingdom s.nallaperuma@sheffield.ac.uk.
Abstract:
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+[Formula: see text]) 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.
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