Discrete/Binary Approach

In a traveling salesman problem, if the set of nodes is divided into clusters so that a single node from each cluster can be visited, then the problem is known as the generalized traveling salesman problem where the objective is to find a tour with minimum cost passing through only a single node from each cluster. In this chapter, a discrete differential evolution algorithm is presented to solve the problem on a set of benchmark instances. The discrete differential evolution algorithm is hybridized with local search improvement heuristics to further improve the solution quality. Some speed-up methods presented by the authors previously are employed to accelerate the greedy node insertion into a tour. The performance of the hybrid discrete differential evolution algorithm is tested on a set of benchmark instances with symmetric distances ranging from 51 (11) to 1084 (217) nodes (clusters) from the literature. Computational results show its highly competitive performance in comparison to the best performing algorithms from the literature.

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