A hybrid particle swarm optimization algorithm for the capacitated location routing problem

Purpose–The purpose of this paper is to solve the capacitated location routing problem(CLRP),which is an NP-hard problem that involves making strategic decisions as well as tactical and operational decisions,using a hybrid particle swarm optimization(PSO)algorithm.Design/methodology/approach–PSO,which is a population-based metaheuristic,is combined with a variable neighborhood strategy variable neighborhood search to solve the CLRP.Findings–The algorithm is tested on a set of instances available in the literature and gave good quality solutions,results are compared to those obtained by other metaheuristic,evolutionary and PSO algorithms.Originality/value–Local search is a time consuming phase in hybrid PSO algorithms,a set of neighborhood structures suitable for the solution representation used in the PSO algorithm is proposed in the VNS phase,moves are applied directly to particles,a clear decoding method is adopted to evaluate a particle(solution)and there is no need to re-encode solutions in the form of particles after applying local search.

Free-floating bike-sharing green relocation problem considering greenhouse gas emissions

This paper introduces the problem of green bike relocation considering greenhouse gas emissions in free-floating bike-sharing systems(FFBSSs)and establishes a mathematical model of the problem.This model minimizes the total imbalance degree of bikes in the FFBSS and the greenhouse gas emissions generated by relocation in the FFBSS.Before the relocation phase,the FFBSS is divided into multiple relocation areas using a two-layer clustering method to reduce the scale of the relocation problem.In the relocation phase,the relocation route problem is converted into a pickup and delivery vehicle-routing problem.Then,an adaptive variable neighbourhood tabu search algorithm with a three-dimensional tabu list is proposed,which can simultaneously solve the relocation problem and the routing problem.A computational study based on the actual FFBSS used in Shanghai shows that this method can effectively solve the green relocation problem of FFBSSs.