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A guided epsilon-dominance arithmetic optimization algorithm for effective multi-objective optimization in engineering design problems

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Abstract

The Arithmetic Optimization Algorithm (AOA) was recently proposed as a solution for single-objective real continuous problems and has demonstrated superior performance in various contexts. This paper presents a multi-objective version of the algorithm to solve multi-objective problems. The MOAOA employs an archive repository to keep and retrieve the non-dominated solutions produced during optimization. The leaders are then selected from the population archive to lead the solutions of the main population toward the potential search locations. The epsilon-dominance and crowding distance strategies balance the convergence and diversity of the obtained Pareto set. To assess the effectiveness and efficiency of the proposed algorithm, it was tested on various dimensions of multi-objective benchmarks, among them: five unconstrained test functions taken from ZDT-series and four multi-objective constrained tests functions (BNH, SRN, TNK, OSY). Also, it is evaluated on four multi-objective structural design problems, such as welded beam design, speed-reduced design, disk brake design, and four-bar truss design. The algorithm is compared with three algorithms widely used in multi-objectives optimization, such as MSSA, MOEA-D, and MOGWO. The comparison results demonstrate that MOAOA outperforms all other algorithms in terms of both convergence and diversity of solutions, achieving a score of (100%,100%) in the ZDT tests, (75%,50%) in the constrained test functions, and (75%,75%) for the structural design problems.

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Data is available from the authors upon reasonable request.

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Authors and Affiliations

  1. Department of Computer Science, University of Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj, Algeria

    Djaafar Zouache & Farid Boumaza

  2. LRIA Laboratory, University of Science and Technology Houari Boumediene, Algiers, Algeria

    Djaafar Zouache

  3. Computer Science Department, Prince Hussein Bin Abdullah Faculty for Information Technology, Al al-Bayt University, Mafraq, 25113, Jordan

    Laith Abualigah

  4. Department of Electrical and Computer Engineering, Lebanese American University, Byblos, 13-5053, Lebanon

    Laith Abualigah

  5. Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, 19328, Jordan

    Laith Abualigah

  6. MEU Research Unit, Middle East University, Amman, 11831, Jordan

    Laith Abualigah

  7. Applied Science Research Center, Applied Science Private University, Amman, 11931, Jordan

    Laith Abualigah

  8. School of Computer Sciences, Universiti Sains Malaysia, Pulau Pinang, 11800, Malaysia

    Laith Abualigah

  9. School of Engineering and Technology, Sunway University Malaysia, Petaling Jaya, 27500, Malaysia

    Laith Abualigah

  10. Department of Computer Science, University of Oran1, Oran, Algeria

    Farid Boumaza

Authors
  1. Djaafar Zouache
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  2. Laith Abualigah
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Correspondence to Djaafar Zouache.

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Zouache, D., Abualigah, L. & Boumaza, F. A guided epsilon-dominance arithmetic optimization algorithm for effective multi-objective optimization in engineering design problems. Multimed Tools Appl 83, 31673–31700 (2024). https://doi.org/10.1007/s11042-023-16633-x

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