Applied Intelligence

, Volume 49, Issue 5, pp 1982–2000 | Cite as

A hybrid whale optimization algorithm based on modified differential evolution for global optimization problems

  • Jun LuoEmail author
  • Baoyu Shi


Whale optimization algorithm(WOA) is a biological-inspired optimization algorithm with the advantage of global optimization ability, less control parameters and easy implementation. It has been proven to be effective for solving global optimization problems. However, WOA can easily get stuck in the local optimum and may lose the population diversity, suffering from premature convergence. In this work, a hybrid whale optimization algorithm called MDE-WOA was proposed. Firstly, in order to enhance local optimum avoidance ability, a modified differential evolution operator with strong exploration capability is embedded in WOA with the aid of a lifespan mechanism. Additionally, an asynchronous model is employed to accelerate WOA’s convergence and improve its accuracy. The proposed MDE-WOA is tested with 13 numerical benchmark functions and 3 structural engineering optimization problems. The results show that MDE-WOA has better performance than others in terms of accuracy and robustness on a majority of cases.


Whale optimization algorithm Differential evolution Global optimization Benchmark functions 



The authors are grateful for the valuable comments and suggestions of editor and anonymous reviewers.

Compliance with Ethical Standards

Conflict of interests

The authors declared that they have no conflicts of interest to this work.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chongqing UniversityChongqingChina

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