Models and Algorithms for the Constrained Orienteering Problem

The constrained orienteering problem (COP) can be expressed as: Given an undirected weighted graph G = (V,E) and a subset S subset of V. Each node has a score, each edge has a weight indicating distance or time between the two adjacent nodes. The starting node and ending node are specified. Given a fixed amount of weight denoting the total distance or total time, the goal is to determine a walk from the starting node to the ending node through a subset of nodes including all the nodes in S, in order to maximize the total score of the walk. This problem is a generalization of the orienteering problem or a special case of the Steiner Tree problem. In this paper, we first formulate the COP problem into an integer linear programming based on network flow theory and solve it to obtain the exact optimal solution for examples of small size. Then we give a heuristic algorithm for solving the large instances of the problem. Finally, we give computational results of both exact and heuristic algorithms which demonstrate the efficient of the algorithm.