Optimal multi-depot location decision using particle swarm optimization

Abstract

The depot locations have a significant effect on the transportation cost in the multi-depot vehicle routing problem. A two-tier particle swarm optimization framework is proposed, in which an external particle swarm optimization and an internal particle swarm optimization are used to determine the optimal depot locations and the optimal multi-depot vehicle routing problem solution, respectively. In the internal particle swarm optimization, a novel particle encoding scheme is used to minimize the computational cost by concurrently allocating the customers to depots, assigning the customers to vehicles, and determining the optimal routing path for each vehicle. The quality of the solutions is enhanced through a designed mutation local search with savings scheme. To verify the effectiveness of the proposed scheme, six standard multi-depot vehicle routing problem instances are tested and compared. It is shown that the use of the external particle swarm optimization scheme to optimize the multi-depot locations reduces the average routing distance obtained by the internal particle swarm optimization by around 13.16% on average. Furthermore, for a real-world case, the proposed two-tier particle swarm optimization scheme reduces the total routing cost by around 18%. Restated, the proposed particle swarm optimization algorithm provides an effective and efficient tool for solving practical multi-depot vehicle routing problems. Notably, the proposed scheme can be used as a reference model for obtaining the optimal locations in a variety of scheduling problems.

Imperialist Competitive Algorithm with Independence and Constrained Assimilation

“…A recent survey of metaheuristic algorithms [46] suggests that two of the most common algorithms used for solving MDVRP are Ant Colony Optimization (ACO) and Genetic Algorithm (GA). However, other algorithms like Particle Swarm Optimization (PSO) [58] and Ant Lion Optimization (ALO) [59] have also been successfully applied. GA is a nature-inspired algorithm that is based on the natural selection process.…”

Power system parameter matching and particle swarm optimization of battery underground loader

“…11 Shen and Chen used the PSO algorithm to optimize multi-depot location decisions and reduced their average routing distance by approximately 13.16%. 12 Chiou et al investigated a PSO-reinforced fuzzy PID controller for quadrotor attitude control and found that the new elite control parameter gains could be generated and updated rapidly. 13 Chen and Shen used the PSO algorithm to optimize dynamic search control for project scheduling problems and solved an activate operating priority problem and an activate operating mode sub-problem.…”

Improved Grasshopper Algorithm Based on Gravity Search Operator and Pigeon Colony Landmark Operator

“…These algorithms can use the useful information of the population to find the optimal solution [3]. These efficient and robust algorithms are used to solve a variety of problems, such as path planning [4], economic scheduling problem [5], inverter parameter identification [6], backpack problem [7] and location problem [8]. So far, various researchers have conducted in-depth research on these algorithms, and introduced many naturally-inspired meta-heuristic algorithms, such as particle swarm optimization (PSO) algorithm [9], bacterial foraging algorithm (BFA) [10], artificial fish swarm algorithm (AFSA) [11], artificial bee colony (ABC) algorithm [12], cuckoo search (CS) algorithm [13], bat algorithm (BA) [14], ant lion optimizer (ALO) [15], moth-flame optimization (MFO) algorithm [16], and salp swarm algorithm (SSA) [17], etc.…”

“…Operation flowchart of improved grasshopper algorithm.Initialize the swarmX i (i = 1, 2, • • • , n) Initialize c max , c min , R max , R min , G(0), αand maximum number of iterations TCalculate the fitness of each search agent Target = the best search agent while (l < T ) Update c using Eq (8). …”