A Time-Based Formulation and Upper Bounding Scheme for the Selective Travelling Salesperson Problem

• Published in: The Journal of the Operational Research Society Vol. 48; no. 5; pp. 511 - 518
• Main Authors: Millar, H. H., Kiragu, M.
• Format: Journal Article
• Language: English
• Published: Basingstoke Macmillan Press 01.05.1997; Palgrave; Taylor & Francis Ltd
• Subjects: Animal, plant and microbial ecology; Applied ecology; Applied sciences; Biological and medical sciences; Exact sciences and technology; Exploitation and management of natural biological resources (hunting, fishing and exploited populations survey, etc.); Fisheries; Fisheries management; Flows in networks. Combinatorial problems; Fundamental and applied biological sciences. Psychology; Heuristics; Integer programming; Integers; Mathematical models; Methods; Objective functions; Ocean fisheries; Operational research and scientific management; Operational research. Management science; Operations research; Optimal solutions; Studies; Theoretical Papers; Vehicle operation; Vehicles; Canada; Integer programming; Lower bound; Upper bound; Network; Travelling salesman problem; Combinatorial optimization; Fishing
• ISSN: 0160-5682; 1476-9360; 0160-5682
• DOI: 10.1038/sj.jors.2600398

The selective travelling salesperson problem (STSP) involves determining a tour of maximal value over a set of cities subject to a tour length constraint. The problem has the characteristic that not all cities have to be visited. An integer formulation which combines permutation variables with flow variables is presented. An upper bounding scheme for the number of nodes visited in the final solution is used to reduce the size of the integer programme. The problem is solved using an off-the-shelf mixed-integer solver called CPLEX. Results demonstrating the usefulness of the bound are presented. The methodology is also applied to solve a 15-zone fisheries surveillance problem.