The Categorized Orienteering Problem with Count-Dependent Profits

Abstract

This article addresses the Categorized Orienteering Problem with Count-Dependent Profits (COPCDP), in which nodes are clustered into different categories, and each category is assigned an interest rate. The goal is to find a tour among all nodes from various categories, which maximizes the total collected profit. However, different from the basic Orienteering Problem (OP), the profit of each node is not fixed, but decreases based on the number of nodes selected from the same category. This way, it is encouraged to visit fewer nodes from the same category. The COPCDP may have different exciting applications, but in this research, it is focused on its application in personal tourist trip planning. Two meta-heuristic algorithms based on the combination of a Genetic Algorithm with a Variable Neighborhood Descent structure (GA-VND), as well as a Simulated Annealing algorithm combined with a Variable Neighborhood Search (SA-VNS), are proposed. Computational experiments over a large set of instances show the efficiency of both algorithms. However, the GA-VND is proved to perform better in terms of solution quality. Additionally, a real-size problem instance based on the real data from the megacity of Tehran is generated and solved by using the proposed GA-VND to prove the usability of the method in practice.