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

Abstract

The pollution traveling salesman problem (PTSP) and the energy minimization traveling salesman problem (EMTSP) generalize the well‐known asymmetric traveling salesman problem by including environmental issues and the goal of reducing carbon emissions. Both problems call for determining a Hamiltonian tour that, in the PTSP, minimizes a function of fuel consumption and driver cost (where the fuel consumption depends on the distance traveled, the vehicle speed, and the vehicle load), while, in the EMTSP, minimizes a function depending on the vehicle load and the traveled distances. For both PTSP and EMTSP, we propose a matheuristic algorithm that uses the solution of the linear programming relaxation of a mixed integer linear programming model for the considered problem to determine good initial feasible solutions, applies a multioperator genetic algorithm to improve these solutions, and refines the best solution found through an iterated local search procedure. In order to evaluate the performance of the proposed matheuristics, we compare them with exact and heuristic algorithms from the literature on benchmark instances of both problems.

A metaheuristic for the double traveling salesman problem with partial last‐in‐first‐out loading constraints

“…Additionally, the exact algorithms could also benefit from a warm start obtained by applying our proposed approach. Finally, it could be interesting to extend the proposed algorithm to solve some of the variants of the TSP recently published (Bernardino and Paias, 2021; Cacchiani et al., 2023; Cuellar‐Usaquén et al., 2023).…”

Matheuristics: survey and synthesis

“…(1991). More recently, LP solutions have been used as seeds for standard metaheuristic search (Cacchiani et al., 2023).…”

“…Other notable examples include an 'iterative rounding' heuristic for shift scheduling, given in Thompson (1990), and a similar heuristic for lot-sizing with setups, in Maes et al (1991). More recently, LP solutions have been used as seeds for standard metaheuristic search (Cacchiani et al, 2023).…”

A three-phase algorithm for the pollution traveling Salesman problem

“…Recently, Cacchiani et al [ 26 ] introduced a matheuristic approach for addressing the PTSP. Their method leverages the relaxation solution derived from a Mixed Integer Linear Programming (MILP) model specific to the PTSP, thereby obtaining high-quality feasible initial solutions.…”