A multi-objective open set orienteering problem

Abstract

We have constructed a multi-objective set orienteering problem to model real-world problems more fittingly than the existing models. It attaches (i) a predefined profit associated with each cluster of customers, and (ii) a preset maximum service time associated with each customer of all the clusters. When a customer from cluster visits, it allows the earning of a profit score. Our purpose is primarily to search for a route that (i) on the one hand allows us to service each cluster for maximizing customer satisfaction and (ii) on the other hand allows us to maximize our profits, too. The model assumes that the more time we spend on servicing, the more customer satisfaction it yields. It tries to cover as many clusters as possible within a specified time budget. In this paper, we also consider third-party logistics to allow the flexibility of ending our journey at any cluster of our choice. The proposed model is solved using the nondominated sorting genetic algorithm and the strength Pareto evolutionary algorithm. Here, we also generate the dataset to test the proposed model by using instances from the literature of the generalized traveling salesman problem. Finally, we present a comparative result analysis with the help of some statistical tools and discuss the results.