International Journal of Computational Intelligence Research ISSN 0973-1873 Volume 6, Number 3 (2010), pp. 475–484 © Research India Publications http://www.ripublication.com/ijcir.htm A Hybrid Sequential Constructive Sampling Algorithm for the Bottleneck Traveling Salesman Problem Zakir H. Ahmed Department of Computer Science, Al-Imam Muhammad Ibn Saud Islamic University, PO. Box 5701, Riyadh 11432, Kingdom of Saudi Arabia E-mail: zhahmed@gmail.com Abstract The bottleneck traveling salesman problem (BTSP) is to find a Hamiltonian circuit that minimizes the largest cost of any of its arcs in a graph. A sequential constructive sampling algorithm has been developed to obtain heuristic solution to the problem. To improve the quality of the solution, we then apply a combined mutation operator that combines insertion, inversion and swap mutation operators. The hybrid algorithm incorporates the combined mutation operator to the sequential constructive sampling for the problem. The efficiency of the hybrid algorithm to the BTSP as against an existing heuristic algorithm has been examined for some TSPLIB instances. Keywords: Bottleneck Traveling Salesman Problem, Hybrid, Sequential Constructive Sampling, Combined Mutation Operator. Introduction The bottleneck traveling salesman problem (BTSP) is a variation of the usual traveling salesman problem (TSP). In BTSP, the objective is to find a Hamiltonian circuit that minimizes the largest cost of any of its arcs in a graph. It can be defined as follows: A network with n nodes (or cities), with 'node 1' (suppose) as ‘headquarters’ and a cost (or distance, or time etc.) matrix C=[c ij ] of order n associated with ordered node pairs (i,j) is given. Let {1=α 0 , α 1, α 2 ,....,α n-1 , α n =1} ≡ {1→α 1 →α 2 →..... →α n-1 →1} be a tour, representing irreducible permutations interpreted as simple cycles. The tour value is now defined as { } 1 ,...., 2 , 1 , 0 : max 1 , - = + n i c i i α α . The objective is to choose a tour which has minimum tour value.