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

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Machine Learning Paradigms: Theory and Application

Part of the book series: Studies in Computational Intelligence ((SCI,volume 801))

Abstract

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.

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Authors and Affiliations

  1. Department of Business Administration, College of Sciences and Humanities, Majmaah University, Majmaah, 11952, Saudi Arabia

    Ali Khater Mohamed

  2. Operations Research Department, Institute of Statistical Studies and Research, Cairo University, Giza, 12613, Egypt

    Ali Wagdy Mohamed

  3. Faculty of Computers and Information, Decision Support Department, Cairo University, Giza, 12613, Egypt

    Ehab Zaki Elfeky & Mohamed Saleh

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  1. Ali Khater Mohamed
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  2. Ali Wagdy Mohamed
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  3. Ehab Zaki Elfeky
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  4. Mohamed Saleh
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Correspondence to Ali Wagdy Mohamed .

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  1. Faculty of Computers and Information, Cairo University, Giza, Egypt

    Aboul Ella Hassanien

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Mohamed, A.K., Mohamed, A.W., Elfeky, E.Z., Saleh, M. (2019). Solving Constrained Non-linear Integer and Mixed-Integer Global Optimization Problems Using Enhanced Directed Differential Evolution Algorithm. In: Hassanien, A. (eds) Machine Learning Paradigms: Theory and Application. Studies in Computational Intelligence, vol 801. Springer, Cham. https://doi.org/10.1007/978-3-030-02357-7_16

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