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A New Hybrid Evolutionary Algorithm for the Treatment of Equality Constrained MOPs

Author

Listed:
  • Oliver Cuate

    (Department of Computer Science, Cinvestav-IPN, Mexico City 07360, Mexico)

  • Antonin Ponsich

    (Metropolitan Autonomous University, Azcapotzalco Unit, Av. San Pablo No. 180, Col. Reynosa Tamaulipas, Azcapotzalco 02200, Mexico)

  • Lourdes Uribe

    (Instituto Politécnico Nacional, Mexico City 07738, Mexico)

  • Saúl Zapotecas-Martínez

    (Department of Applied Mathematics and Systems, Metropolitan Autonomous University, Cuajimalpa Unit (UAM-C), Vasco de Quiroga 4871, Santa Fe Cuajimalpa 05370, Mexico)

  • Adriana Lara

    (Instituto Politécnico Nacional, Mexico City 07738, Mexico)

  • Oliver Schütze

    (Department of Computer Science, Cinvestav-IPN, Mexico City 07360, Mexico
    Dr. Rodolfo Quintero Ramirez Chair, Metropolitan Autonomous University, Cuajimalpa Unit (UAM-C), Vasco de Quiroga 4871, Santa Fe Cuajimalpa 05370, Mexico)

Abstract

Multi-objective evolutionary algorithms are widely used by researchers and practitioners to solve multi-objective optimization problems (MOPs), since they require minimal assumptions and are capable of computing a finite size approximation of the entire solution set in one run of the algorithm. So far, however, the adequate treatment of equality constraints has played a minor role. Equality constraints are particular since they typically reduce the dimension of the search space, which causes problems for stochastic search algorithms such as evolutionary strategies. In this paper, we show that multi-objective evolutionary algorithms hybridized with continuation-like techniques lead to fast and reliable numerical solvers. For this, we first propose three new problems with different characteristics that are indeed hard to solve by evolutionary algorithms. Next, we develop a variant of NSGA-II with a continuation method. We present numerical results on several equality-constrained MOPs to show that the resulting method is highly competitive to state-of-the-art evolutionary algorithms.

Suggested Citation

  • Oliver Cuate & Antonin Ponsich & Lourdes Uribe & Saúl Zapotecas-Martínez & Adriana Lara & Oliver Schütze, 2019. "A New Hybrid Evolutionary Algorithm for the Treatment of Equality Constrained MOPs," Mathematics, MDPI, vol. 8(1), pages 1-25, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:7-:d:299481
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    References listed on IDEAS

    as
    1. Liao, Zhiying & Rittscher, Jens, 2007. "A multi-objective supplier selection model under stochastic demand conditions," International Journal of Production Economics, Elsevier, vol. 105(1), pages 150-159, January.
    2. Barkat Ullah, Abu S.S.M. & Sarker, Ruhul & Lokan, Chris, 2012. "Handling equality constraints in evolutionary optimization," European Journal of Operational Research, Elsevier, vol. 221(3), pages 480-490.
    3. M. Dellnitz & O. Schütze & T. Hestermeyer, 2005. "Covering Pareto Sets by Multilevel Subdivision Techniques," Journal of Optimization Theory and Applications, Springer, vol. 124(1), pages 113-136, January.
    4. Thiemo Krink & Sandra Paterlini, 2011. "Multiobjective optimization using differential evolution for real-world portfolio optimization," Computational Management Science, Springer, vol. 8(1), pages 157-179, April.
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