A Hybrid Genetic Algorithm for the Bottleneck Traveling Salesman Problem

Abstract

The bottleneck traveling salesman problem is to find a Hamiltonian circuit that minimizes the largest cost of any of its arcs in a graph. A simple genetic algorithm (GA) using sequential constructive crossover has been developed to obtain heuristic solution to the problem. The hybrid GA incorporates 2-opt search, another proposed local search and immigration to the simple GA for obtaining better solution. The efficiency of our hybrid GA to the problem against two existing heuristic algorithms has been examined for some symmetric TSPLIB instances. The comparative study shows the effectiveness of our hybrid algorithm. Finally, we present solutions to the problem for asymmetric TSPLIB instances.