224 European Journal of Operational Research 41 (1989) 224-231 North-Holland Theory and Methodology Algorithms to solve the orienteering A comparison * problem: C. Peter KELLER Department of Geography, University of Victoria, Victoria, B.C., Canada Abstract: The multiobjective vending problem (MVP) (Keller, 1985) is a generalization of the traveling salesman problem (TSP) where it is not necessary to visit all nodes in the problem definition. A special case of the MVP is the orienteering problem (OP) (Tsiligirides, 1984; Golden et al., 1985). The problems are NP-hard. A heuristic was designed to solve the general MVP (Keller, 1985). Three other heuristics were designed to solve the OP (Tsiligirides, 1984; Golden et al., 1985). The algorithms underlying these heuristics are outlined. Their performances are compared against three OP problems. ( Keywords: Traveling salesman problem, generalization, orienteering problem, heuristics, performance comparison 1. Introduction The multiobjective vending problem (MVP) (Keller, 1985) is a generalization of the traveling salesman problem (TSP) where it is not necessary to visit all nodes in the problem definition. The objective is to examine the trade-off relationship between maximizing reward potential by visiting as many nodes as possible, at the same time minimizing penalty for traveling the links by visit- ing as few nodes as possible. A conceptually simi- lar problem concerns the orienteering problem (OP) discussed by Tsiligirides (1984), and Golden et al. (1985). It has been demonstrated that both problems are NP-hard (Garey and Johnson, 1979; Keller, 1985; Golden et al., 1985). The objective of this paper is to evaluate and discuss the performance of four algorithms written to solve the above two problems for three sets of OP data. Tsiligirides (1984), Keller (1985) and Goldert et al. (1985) have suggested that the MVP and the OP have numerous applications. The rela- tive performance of algorithms to solve these problems are therefore of interest. The paper com- mences by outlining the two problem definitions. Next, the different solution approaches are sum- marized. The performances of the algorithms are compared using Tsiligirides (1984) three score orienteering problems. 2. Problem definition * This research has been supported by NSERC grant no. A 6533. Received November1987; revised May 1988 The TSP is conceptually defined as follows: Given a set of n nodes, determine the shortest complete circuit that connects all nodes so that 0377-2217/89/$3.50 © 1989, ElsevierSciencePublishers B.V. (North-Holland)