EXPERIMENTAL ANALYSIS OF HEURISTICS FOR THE BOTTLENECK TRAVELING SALESMAN PROBLEM JOHN LARUSIC, ABRAHAM P. PUNNEN, AND ERIC AUBANEL Abstract. In this paper we develop efficient heuristic algorithms to solve the bottleneck traveling salesman problem (BTSP). Results of ex- tensive computational experiments are reported. Our heuristics pro- duced optimal solutions for all the test problems considered from TSPLIB, JM-instances, National TSP instances, and VLSI TSP instances in very reasonable running time. We also conducted experiments with specially constructed ‘hard’ instances of the BTSP that produced optimal solu- tions for all but seven problems. Some fast construction heuristics are also discussed. Our algorithms could easily be modified to solve related problems such as the maximum scatter TSP and testing hamiltonicity of a graph. Key Words: Traveling salesman problem, bottleneck TSP, experimental analysis, maximum scatter TSP. 1. Introduction Let G =(V,E) be a complete undirected graph on n nodes. For each edge (i, j ) ∈ E a non-negative cost c ij is prescribed. Then the bottleneck traveling salesman problem (BTSP) is to Minimize max{c ij :(i, j ) ∈ H } Subject to H ∈ Π, where Π is the collection of all Hamiltonian cycles (tours) in G. The matrix C =(c ij ) n×n is called the cost matrix associated with the BTSP. To the best of our knowledge, BTSP was introduced by Gilmore and Gomory [11] in 1964, where the edge costs were assumed to be specially structured. Related works on special cases of the BTSP include various ex- tensions of the Gilmore and Gomory class of problems [17, 18, 20, 23, 40, 41] and BTSP on a Halin graph [27]. Many of these special cases can be solved in polynomial time. For a state-of-the-art discussion on polynomially solv- able cases of the BTSP, we refer to book chapter by Kabadi and Punnen [18]. The BTSP with a general cost matrix was first studied by Gabovich et al. [9] in 1971. The BTSP is well known to be NP-hard. In fact, unless P = NP, This work was supported by NSERC discovery grants awarded to Abraham P. Punnen and Eric Aubanel. 1