Open AccessOpen Access


Parallel Equilibrium Optimizer Algorithm and Its Application in Capacitated Vehicle Routing Problem

Zonglin Fu1, Pei Hu1, Wei Li2, Jeng-Shyang Pan1,*, Shuchuan Chu1

1 College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao, 266590, China
2 Faculty of the Built Environment, University of New South Wales, NSW 2052, Australia

* Corresponding Author: Jeng-Shyang Pan. Email:

(This article belongs to this Special Issue: Machine Learning and Deep Learning for Transportation)

Intelligent Automation & Soft Computing 2021, 27(1), 233-247.


The Equilibrium Optimizer (EO) algorithm is a novel meta-heuristic algorithm based on the strength of physics. To achieve better global search capability, a Parallel Equilibrium Optimizer algorithm, named PEO, is proposed in this paper. PEO is inspired by the idea of parallelism and adopts two different communication strategies between groups to improve EO. The first strategy is used to speed up the convergence rate and the second strategy promotes the algorithm to search for a better solution. These two kinds of communication strategies are used in the early and later iterations of PEO respectively. To check the optimization effect of the proposed PEO algorithm, it is tested on 23 benchmark functions and compared with the Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Parallel Particle Swarm Optimization (PPSO), and EO as well. The empirical study demonstrates that the abilities of exploration and exploitation of PEO are superior to the above four algorithms in most benchmark functions. Finally, we apply PEO to solve the Capacitated Vehicle Routing Problem (CVRP) in the field of transportation. Experimental results show that PEO can achieve a better driving route.


Cite This Article

Z. Fu, P. Hu, W. Li, J. Pan and S. Chu, "Parallel equilibrium optimizer algorithm and its application in capacitated vehicle routing problem," Intelligent Automation & Soft Computing, vol. 27, no.1, pp. 233–247, 2021.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 2354


  • 1455


  • 1


Share Link