In this paper, heuristic solution techniques for the multi-objective orienteering problem are developed. The motivation stems from the problem of planning individual tourist routes in a city. Each point of interest in a city provides different benefits for different categories (e.g., culture, shopping). Each tourist has different preferences for the different categories when selecting and visiting the points of interests (e.g., museums, churches). Hence, a multi-objective decision situation arises. To determine all the Pareto optimal solutions, two metaheuristic search techniques are developed and applied. We use the Pareto ant colony optimization algorithm and extend the design of the variable neighborhood search method to the multi-objective case. Both methods are hybridized with path relinking procedures. The performances of the two algorithms are tested on several benchmark instances as well as on real world instances from different Austrian regions and the cities of Vienna and Padua. The computational results show that both implemented methods are well performing algorithms to solve the multi-objective orienteering problem.

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Abstract. In this paper we first provide a thorough performance comparison of the three main Ant Colony Optimization (ACO) paradigms for the Vehicle Routing Problem (VRP), namely the Rank based Ant System, the Max-Min Ant System and the Ant Colony System. Based on the results of this comparison we then implement a parallelization strategy to increase computational efficiency and study the effects of increasing the number of processors.