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An Archive-Guided Equilibrium Optimizer Based on Epsilon Dominance for Multi-Objective Optimization Problems

Author

Listed:
  • Nour Elhouda Chalabi

    (Computer Science Department, Mohamed Boudiaf University of Msila, Msila 28000, Algeria)

  • Abdelouahab Attia

    (Computer Science Department, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj, Bordj Bou Arreridj 34000, Algeria)

  • Abderraouf Bouziane

    (Computer Science Department, University Mohamed El Bachir El Ibrahimi of Bordj Bou Arreridj, Bordj Bou Arreridj 34000, Algeria)

  • Mahmoud Hassaballah

    (Department of Computer Science, College of Computer Engineering and Sciences, Prince Sattam Bin Abdulaziz University, AlKharj 16278, Saudi Arabia
    Department of Computer Science, Faculty of Computers and Information, South Valley University, Qena 83523, Egypt)

  • Abed Alanazi

    (Department of Computer Science, College of Computer Engineering and Sciences, Prince Sattam Bin Abdulaziz University, AlKharj 16278, Saudi Arabia)

  • Adel Binbusayyis

    (Department of Software Engineering, College of Computer Engineering and Sciences, Prince Sattam Bin Abdulaziz University, AlKharj 16278, Saudi Arabia)

Abstract

In real-world applications, many problems involve two or more conflicting objectives that need to be optimized at the same time. These are called multi-objective optimization problems (MOPs). To solve these problems, we introduced a guided multi-objective equilibrium optimizer (GMOEO) algorithm based on the equilibrium optimizer (EO), which was inspired by control–volume–mass balance models that use particles (solutions) and their respective concentrations (positions) as search agents in the search space. The GMOEO algorithm involves the integration of an external archive that acts as a guide and stores the optimal Pareto set during the exploration and exploitation of the search space. The key candidate population also acted as a guide, and Pareto dominance was employed to obtain the non-dominated solutions. The principal of ϵ -dominance was employed to update the archive solutions, such that they could then guide the particles to ensure better exploration and diversity during the optimization process. Furthermore, we utilized the fast non-dominated sort (FNS) and crowding distance methods for updating the position of the particles efficiently in order to guarantee fast convergence in the direction of the Pareto optimal set and to maintain diversity. The GMOEO algorithm obtained a set of solutions that achieved the best compromise among the competing objectives. GMOEO was tested and validated against various benchmarks, namely the ZDT and DTLZ test functions. Furthermore, a benchmarking study was conducted using cone- ϵ -dominance as an update strategy for the archive solutions. In addition, several well-known multi-objective algorithms, such as the multi-objective particle-swarm optimization (MOPSO) and the multi-objective grey-wolf optimization (MOGWO), were compared to the proposed algorithm. The experimental results proved definitively that the proposed GMOEO algorithm is a powerful tool for solving MOPs.

Suggested Citation

  • Nour Elhouda Chalabi & Abdelouahab Attia & Abderraouf Bouziane & Mahmoud Hassaballah & Abed Alanazi & Adel Binbusayyis, 2023. "An Archive-Guided Equilibrium Optimizer Based on Epsilon Dominance for Multi-Objective Optimization Problems," Mathematics, MDPI, vol. 11(12), pages 1-30, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2680-:d:1169975
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    References listed on IDEAS

    as
    1. Mahmoodabadi, M.J., 2023. "An optimal robust fuzzy adaptive integral sliding mode controller based upon a multi-objective grey wolf optimization algorithm for a nonlinear uncertain chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Abdelghani Dahou & Samia Allaoua Chelloug & Mai Alduailij & Mohamed Abd Elaziz, 2023. "Improved Feature Selection Based on Chaos Game Optimization for Social Internet of Things with a Novel Deep Learning Model," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    3. Jeewaka Perera & Shih-Hsi Liu & Marjan Mernik & Matej Črepinšek & Miha Ravber, 2023. "A Graph Pointer Network-Based Multi-Objective Deep Reinforcement Learning Algorithm for Solving the Traveling Salesman Problem," Mathematics, MDPI, vol. 11(2), pages 1-21, January.
    4. Djaafar Zouache & Fouad Ben Abdelaziz & Mira Lefkir & Nour El-Houda Chalabi, 2021. "Guided Moth–Flame optimiser for multi-objective optimization problems," Annals of Operations Research, Springer, vol. 296(1), pages 877-899, January.
    5. Kaveh, Mehrdad & Mesgari, Mohammad Saadi & Saeidian, Bahram, 2023. "Orchard Algorithm (OA): A new meta-heuristic algorithm for solving discrete and continuous optimization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 95-135.
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