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An arithmetic and geometric mean-based multi-objective moth-flame optimization algorithm

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Abstract

Expanding the capacity of optimization algorithms for simultaneous optimization of multiple competing objectives is a crucial aspect of research. This study presents MnMOMFO, a novel non-dominated sorting (NDS) and crowding distance (CD)-based multi-objective variant of the moth-flame optimization (MFO) algorithm for multi-objective optimization problems. The algorithm incorporates arithmetic and geometric mean concepts to address MFO’s limitations and to improve its performance. Subsequently, we extend this enhanced MFO into a multi-objective variant, leveraging NDS and CD strategies to achieve a well-distributed Pareto optimal front. The effectiveness of the proposed MnMOMFO algorithm is rigorously evaluated across three distinct phases. In the initial phase, we scrutinize its performance on four ZDT multi-objective optimization problems, employing four performance metrics—general distance, inverted general distance, spacing, and spread metric. Comparative analyses with select competitive multi-objective optimization algorithms comprehensively understand MnMOMFO’s efficacy. Secondly, 24 complex multi-objective IEEE CEC 2020 test suits are considered on two performance metrics. Namely, Pareto sets proximity and the inverted generational distance in decision space. In the third phase, five real-world engineering problems are considered to measure the problem-solving ability of the MnMOMFO algorithm. The results from the experiments indicated that the MnMOMFO was the best candidate algorithm, achieving more than 95% superior results for multi-objective ZDT benchmark problems, IEEE CEC 2020 test functions, and real-life issues in contrast to several other algorithms. The experimental outcomes substantiate MnMOMFO’s superiority, establishing it as a robust and efficient algorithm for multi-objective optimization challenges with broad applicability to real-world engineering problems.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Agartala, Agartala, Tripura, 799046, India

    Saroj Kumar Sahoo, Apu Kumar Saha & Salpa Reang

  2. Faculty of Computers and Information, Minia University, Minia, Egypt

    Essam H. Houssein & Marwa M. Emam

  3. Department of Electrical and Electronics Engineering, Dayananda Sagar College of Engineering, Bangalore, Karnataka, 560078, India

    M. Premkumar

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  1. Saroj Kumar Sahoo
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SKS: Software, Conceptualization, Formal analysis, Data curation, Writing—original draft. AKS: Conceptualization, Methodology, Visualization, Supervision, Writing—review and editing. EHH: Supervision, Methodology, Formal analysis, Visualization, Writing—review and editing. MP: Methodology, Formal analysis, Visualization, Writing—review and editing. SR: Methodology, Investigation, Data curation, Writing—original draft. MME: Software, Conceptualization, Formal analysis, Data curation, Writing—original draft, Writing—review and editing. All authors read and approved the final paper.

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Correspondence to Apu Kumar Saha or Marwa M. Emam.

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Appendix

Appendix

See Tables 22 and 23.

Table 22 Details of ZDT (ZDT1, ZDT2, ZDT3 and ZDT6) multi-objective benchmark functions
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Table 23 Details of DTLZ (DTLZ1 and DTLZ6) problem
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Sahoo, S.K., Saha, A.K., Houssein, E.H. et al. An arithmetic and geometric mean-based multi-objective moth-flame optimization algorithm. Cluster Comput (2024). https://doi.org/10.1007/s10586-024-04301-0

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