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An efficient modified differential evolution algorithm for solving constrained non-linear integer and mixed-integer global optimization problems

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Abstract

In this paper, an efficient modified Differential Evolution algorithm, named EMDE, is proposed for solving constrained non-linear integer and mixed-integer global optimization problems. In the proposed algorithm, new triangular mutation rule based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best,better and the worst individuals among the three randomly selected vectors is introduced. The proposed novel approach to mutation operator is shown to enhance the global and local search capabilities and to increase the convergence speed of the new algorithm compared with basic DE. EMDE uses Deb’s constraint handling technique based on feasibility and the sum of constraints violations without any additional parameters. In order to evaluate and analyze the performance of EMDE, Numerical experiments on a set of 18 test problems with different features, including a comparison with basic DE and four state-of-the-art evolutionary algorithms are executed. Experimental results indicate that in terms of robustness, stability and efficiency, EMDE is significantly better than other five algorithms in solving these test problems. Furthermore, EMDE exhibits good performance in solving two high-dimensional problems, and it finds better solutions than the known ones. Hence, EMDE is superior to the compared algorithms.

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Authors and Affiliations

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

    Ali Wagdy Mohamed

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  1. Ali Wagdy Mohamed
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Correspondence to Ali Wagdy Mohamed.

Appendix

Appendix

Corrections on problems 6, 16 and 17.

Based on self check, there are few differences in problems 6, 16 and 17 in Ref. [40] from the original documents. Thus, the corrections on these problems are as follows.

Problem

Objective function or constraints

Ref. [40]

Correction

Original references

6

Constraint

x 4

3x 4

[32]

16

Constraint 1

9x 1

8x 1

[75]

17

Objective function

\(15x_{35}^{35} ,3x_{94}^{2}\)

\(15x_{35}^{3} ,3x_{94}^{2}\)

[75]

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Mohamed, A.W. An efficient modified differential evolution algorithm for solving constrained non-linear integer and mixed-integer global optimization problems. Int. J. Mach. Learn. & Cyber. 8, 989–1007 (2017). https://doi.org/10.1007/s13042-015-0479-6

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