Parallel equilibrium optimizer algorithm and its application in capacitated vehicle routing problem

Zonglin Fu, Pei Hu, Wei Li, Jeng-Shyang Pan, Shuchuan Chu

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
47 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)233-247
Number of pages15
JournalIntelligent Automation and Soft Computing
Issue number1
Publication statusPublished - 7 Jan 2021
Externally publishedYes


  • Communication capacitated vehicle routing problem
  • Equilibrium optimizer
  • Parallelism


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