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An efficient evolutionary algorithm for engineering design problems

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Abstract

This study introduces a multi-objective version of the recently proposed colonial competitive algorithm (CCA) called multi-objective colonial competitive algorithm. In contrast to original CCA, which used the combination of the objective functions to solve multi-objective problems, the proposed algorithm incorporates the Pareto concept to store simultaneously optimal solutions of multiple conflicting functions. Another novelty of this paper is the integration of the variable neighborhood search as an assimilation strategy, in order to improve the performance of the obtained solutions. To prove the effectiveness of the proposed algorithm, a set of standard test functions with high dimensions and some multi-objective engineering design problems are investigated. The results obtained amply demonstrate that the proposed approach is efficient and is able to yield a wide spread of solutions with good convergence to true Pareto fronts, compared with other proposed methods in the literature.

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Abbreviations

\(N_{\mathrm{imp}}\) :

Number of imperialists

\(\hbox {Cost}_{\mathrm{imp}}\) :

Cost of an imperialist

\(\hbox {Cost }_{\mathrm{col}}\) :

Cost of a colony

\(C_{{i}}\) :

Normalized cost of imperialist i

\(\hbox {TC}_{{i}}\) :

Total cost of empire i

\(\hbox {NTC}_{{i}}\) :

Normalized total cost of empire i

\(P_{{n}}\) :

Normalized power of \(n{\mathrm{th}}\) imperialist

\(\hbox {NC}_{{i}}\) :

Initial number of colonies in empire i

N :

Number of empires

\(N_{\mathrm{col}}\) :

Number of colonies

\(\gamma \) :

Deviation from original direction of colony

\(\beta \) :

Assimilation coefficient

\(\xi \) :

Coefficient share colonies

\(P_{\mathrm{Pi}}\) :

Possession probability of empire i

\(\Upsilon \) :

Convergence metric

\(\Delta \) :

Diversity metric

CCA:

Colony competitive algorithm

\(\theta \) :

Deviation angle of colony

X :

Direction parameter of colonies motion

d :

Distance between a colony and an imperialist

VNS:

Variable neighborhood search

SD:

Standard deviation

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Authors and Affiliations

  1. Mechanical engineering laboratory, National school of engineers, University of Monastir, Monastir, Tunisia

    Najlawi Bilel, Nejlaoui Mohamed & Affi Zouhaier

  2. Department of Mechanical Engineering, American University of Sharjah, Sharjah, UAE

    Romdhane Lotfi

Authors
  1. Najlawi Bilel
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  2. Nejlaoui Mohamed
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  3. Affi Zouhaier
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  4. Romdhane Lotfi
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Correspondence to Najlawi Bilel.

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Communicated by V. Loia.

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Bilel, N., Mohamed, N., Zouhaier, A. et al. An efficient evolutionary algorithm for engineering design problems. Soft Comput 23, 6197–6213 (2019). https://doi.org/10.1007/s00500-018-3273-z

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