Iterated local search algorithm for solving the orienteering problem with soft time windows
In orienteering problem (OP) a set of potential customers is given; the service for these customers is optional during the current planning time horizon since the travel cost of the route is limited. The travel cost is often expressed as the travel time or the travel distance. Thus, a positive value called profit is associated with every customer making its visit more or less attractive. The name of this routing problem originates from a game in which competitors have to visit a set of control
... oints in a given area. If the control point is visited, the competitor gets a profit. The winner of the game is the competitor who collects maximum profits and gets to the end point within a prescribed amount of time. As a routing problem, the OP consists in finding the route visiting a subset of customers that maximizes the total collected profit while satisfying the maximum duration constraint. The OP is also known in the literature as the Selective Traveling Salesman Problem (Thomadsen and Stidsen 2003), the Maximum Collection Problem (Butt and Cavalier 1994) and the Bank Robber Problem (Awerbuch et al. 1998) . Few vehicle routing problems have such applicability as OP. This problem arises in a variety of applications including design of tourist trips to maximize the value of the visited attractions (Vansteenwegen and Oudheusden 2007), recruiting of athletes from high schools for a college team (Butt and Cavalier 1994), delivery of home heating fuel where Abstract In this paper we study the orienteering problem with time windows (OPTW) and the impact of relaxing the time windows on the profit collected by the vehicle. The way of relaxing time windows adopted in the orienteering problem with soft time windows (OPSTW) that we study in this research is a late service relaxation that allows linearly penalized late services to customers. We solve this problem heuristically by considering a hybrid iterated local search. The results of the computational study show that the proposed approach is able to achieve promising solutions on the OPTW test instances available in the literature, one new best solution is found. On the newly generated test instances of the OPSTW, the results show that the profit collected by the OPSTW is better than the profit collected by the OPTW.