An efficient heuristic algorithm for the bottleneck traveling salesman problem

Abstract

This paper describes a new heuristic algorithm for the bottleneck traveling salesman problem (BTSP), which exploits the formulation of BTSP as a traveling salesman problem (TSP). Computational tests show that our algorithm is quite effective. It found optimal solutions for many problems from the standard traveling salesman problem library (TSPLIB) problems. We also consider BTSP with an additional constraint and show that our BTSP heuristic can be modified to obtain a heuristic to solve this problem. Relationships between symmetric and asymmetric versions of BTSP are also discussed.

A Hybrid Genetic Algorithm for the Bottleneck Traveling Salesman Problem

“…We consider some of those instances to show the efficiency of our HGA against binary search threshold (BST) heuristic [Ramakrishnan et al 2009] and HSCS algorithm [Ahmed 2010b]. Table II shows the comparative study of different algorithms for those instances of sizes up to 318 only.…”

“…A sequential constructive sampling algorithm was developed by Ahmed [2000] to obtain heuristically optimal solution to the problem, and showed that the algorithm was better than the genetic algorithm of Ahmed et al [1999]. A binary search threshold heuristic has been developed to find heuristic solution for the general BTSP instances [Ramakrishnan et al 2009]. Recently, Ahmed [2010b] developed a hybrid sequential constructive sampling algorithm to find heuristic solution for the general BTSP instances and found better performance of the algorithm against algorithm of Ramakrishnan et al [2009] for some TSPLIB instances.…”

“…A binary search threshold heuristic has been developed to find heuristic solution for the general BTSP instances [Ramakrishnan et al 2009]. Recently, Ahmed [2010b] developed a hybrid sequential constructive sampling algorithm to find heuristic solution for the general BTSP instances and found better performance of the algorithm against algorithm of Ramakrishnan et al [2009] for some TSPLIB instances. Exact algorithms based on lexisearch have been developed to find exact optimal solution to the problem [Ahmed 2010c[Ahmed , 2011, but they fail to obtain exact solution for the asymmetric TSPLIB instances of size more than 71.…”

“…The hybrid GA incorporates 2-opt search and another proposed local search to the simple GA for obtaining better solutions. The efficiency of the hybrid GA to the problem against algorithms of Ramakrishnan et al [2009] and Ahmed [2010b] has been examined for some symmetric TSPLIB instances. Finally, we present solutions to the problem for asymmetric TSPLIB instances of sizes up to 323.…”

Unified encoding for hyper-heuristics with application to bioinformatics

“…This benchmark was used for the classic TSP and BTSP. It provides optimum values for the first problem, but for reference on the second problem the instances from (Ramakrishnan et al 2009;Larusic et al 2012;Ahmed 2010) were used. -UKP (inp, 2005)-this data set contains some knapsack instances with optimal values and the package also contains an instance generator.…”