Traveling salesman problems with profits and stochastic customers

Abstract

In this paper, we introduce a class of new selection and routing problems, and name it as the traveling salesman problem with profits and stochastic customers (TSPPSC), which is an extension of the traveling salesman problem with profits (TSPP). The class of new problems is put forward to address how to deal with stochastic customer presence under the environment in which an associated profit is obtained once a customer is visited. It is defined on a complete graph in which profits are associated with the vertices and travel costs are associated with the edges. Each vertex (customer) has a probability of requiring a visit. The objective is the simultaneous optimization of the expected collected profits and expected travel costs. According to the way the two objectives (profits and travel costs) are addressed, TSPPSC is categorized into three subproblems. Mathematical formulations are provided for these problems and a genetic algorithm is proposed to solve one of these subproblems. Computational experiments conducted on several sets of instances show a good performance of the proposed algorithm.

The Traveling Salesman Problem with Stochastic and Correlated Customers

“…Voccia, Campbell, and Thomas (2013) subsequently enhance this problem to also penalize early arrivals and name it the PTSP with time windows accordingly. Zhang et al (2018) propose a version of the PTSP where a profit is made from every customer visit, such that both profit Wissink: TSP with Stochastic and Correlated Customers Transportation Science, 2023, vol. 57, no.…”

A matheuristic algorithm for the pollution and energy minimization traveling salesman problems

“…Genetic Algorithms are effective metaheuristic algorithms that have been successfully applied to solve the ATSP and several of its variants (Potvin, 1996; Yuan et al., 2013; Morán‐Mirabal et al., 2014; Groba et al., 2015; Zhang et al., 2018). Often these algorithms use only single operators for crossover and mutation, disregarding the potential synergy of multioperators.…”

Maximizing Total Net Profit for Traveling Salesman Problem with Profits Using Metaheuristic Algorithms

“…The authors compared the system they developed in the study with different methods in the literature. Zhang et al [9] have defined a new version of TSPP considering stochastic customer presence. For the newly defined problem, the authors presented a nonlinear integer programming model and proposed a genetic algorithm for the solution.…”