Solving Constrained Non-linear Integer and Mixed-Integer Global Optimization Problems Using Enhanced Directed Differential Evolution Algorithm

  • Ali Khater Mohamed
  • Ali Wagdy MohamedEmail author
  • Ehab Zaki Elfeky
  • Mohamed Saleh
Part of the Studies in Computational Intelligence book series (SCI, volume 801)


This paper proposes an enhanced modified Differential Evolution algorithm (MI-EDDE) to solve global constrained optimization problems that consist of mixed/non-linear integer variables. The MI-EDDE algorithm, which is based on the constraints violation, introduces a new mutation rule that sort all individuals ascendingly due to their constraint violations (cv) value and then the population is divided into three clusters (best, better and worst) with sizes 100p%, (NP-2) * 100p% and 100p% respectively. Where p is the proportion of the partition with respect to the total number of individuals in the population (NP). MI-EDDE selects three random individuals, one of each partition to implement the mutation process. This new mutation scheme shown to enhance the global and local search capabilities and increases the convergence speed. Eighteen test problems with different features are tested to evaluate the performance of MI-EDDE, and a comparison is made with four state-of-the-art evolutionary algorithms. The results show superiority of MI-EDDE to the four algorithms in terms of the quality, efficiency and robustness of the final solutions. Moreover, MI-EDDE shows a superior performance in solving two high dimensional problems and finding better solutions than the known optimal solution.


Evolutionary computation Differential evolution Global optimization Novel mutation Handling constraints 


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Authors and Affiliations

  • Ali Khater Mohamed
    • 1
  • Ali Wagdy Mohamed
    • 2
    Email author
  • Ehab Zaki Elfeky
    • 3
  • Mohamed Saleh
    • 3
  1. 1.Department of Business AdministrationCollege of Sciences and Humanities, Majmaah UniversityMajmaahSaudi Arabia
  2. 2.Operations Research DepartmentInstitute of Statistical Studies and Research, Cairo UniversityGizaEgypt
  3. 3.Faculty of Computers and Information, Decision Support DepartmentCairo UniversityGizaEgypt

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