A bi-objective study of the minimum latency problem

Abstract

We study a bi-objective problem called the Minimum Latency-Distance Problem (mldp) that aims to minimise travel time and latency of a single-vehicle tour designed to serve a set of client requests. This tour is a Hamiltonian cycle for which we aim to simultaneously minimise the total travel time of the vehicle and the total waiting time (i.e., latency) of the clients along the tour. This problem is relevant in contexts where both client satisfaction and company profit are prioritise. We propose two heuristic methods for approximating Pareto fronts for mldp: SMSA that is based on a classic multi-objective algorithm and EiLS that is based on a novel evolutionary algorithm with intelligent local search. We report computational experiments on a set of artificially generated problem instances using an exact method and the two proposed heuristics, comparing the obtained fronts in terms of various quality metrics.

A Memetic Algorithm for the Cumulative Capacitated Vehicle Routing Problem Including Priority Indexes

“…These metrics have shown their successful implementation in biobjective VRPs [19,39]. The number of non-dominated points measures the ability of each method to find efficient fronts.…”

“…Regarding the study of biobjective vehicle routing problems considering the customer-centric approach, few contributions can be found in the literature: the traveling repairman problem with profits (TRPP) [17], the k-Traveling Repairmen Problem with Profits (k-TRPP) under uncertainty [18], and a biobjective study of the minimum latency problem [19]. In the first work [17], the authors considered the k-TRP with the objective function that monotonically decreases over time.…”

“…For this, the authors proposed a mean-risk formulation and a heuristic approach based on an adaptive neighborhood search for the k-TRPP under uncertainty, providing high-quality results for small and medium-size instances. Finally, the most recent work [19] studies the Minimum Latency-Distance Problem (MLDP), analyzing the conflict between the total distance traveled by the vehicles and the total waiting time of the customers. The authors proposed a mathematical formulation and two heuristic procedures inspired on evolutionary algorithms, obtaining optimal results for instances up to 40 customers and extending the computational experimentation over the metaheuristics for instances up to 256 customers.…”

The multiobjective traveling salesman–repairman problem with profits: design and implementation of a variable neighborhood descent algorithm for a real scenario

“…The only attempt to solve this problem from a biobjective point of view without aggregating the functions has been done by Bruni et al (2020) whose authors proposed an iterated local search to that end. A different biobjective variant was addressed by Arellano-Arriaga et al (2019) whose objectives are to minimize the total travel cost and the latency and the authors assume that the profit can be viewed as opposite to the total travel cost. They implement an evolutionary algorithm based on an intelligent local search based on the ideas followed by Molina et al (2018).…”