Multi-objective optimization approach based on Minimum Population Search algorithm

  • Darian Reyes-Fernández-de-Bulnes Instituto Tecnológico de Tijuana
  • Antonio Bolufé-Röhler University of Prince Edward Island
  • Dania Tamayo-Vera Thinking Big Inc.


Minimum Population Search is a recently developed metaheuristic for optimization of mono-objective continuous problems, which has proven to be a very effective optimizing large scale and multi-modal problems. One of its key characteristic is the ability to perform an efficient exploration of large dimensional spaces. We assume that this feature may prove useful when optimizing multi-objective problems, thus this paper presents a study of how it can be adapted to a multi-objective approach. We performed experiments and comparisons with five multi-objective selection processes and we test the effectiveness of Thresheld Convergence on this class of problems. Following this analysis we suggest a Multi-objective variant of the algorithm. The proposed algorithm is compared with multi-objective evolutionary algorithms IBEA, NSGA2 and SPEA2 on several well-known test problems. Subsequently, we present two hybrid approaches with the IBEA and NSGA-II, these hybrids allow to further improve the achieved results.


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Biografía del autor/a

Antonio Bolufé-Röhler, University of Prince Edward Island

Dr. Bolufe-Rohler works on heuristic optimization and machine learning. Currently, his main research focuses on understanding and formalizing (meta)heuristic optimization. The short-term goal is to develop state of the art optimization algorithms and to apply them to diverse fields such as bioinformatics, economics or augmented reality. The long-term goal is to use insights from heuristic optimization to improve the core techniques of machine learning methods.


Bader, J., (2010). Hypervolume-Based Search for Multiobjective Optimization: Theory and Methods. Ph.D. dissertation, ETH Zurich, Switzerland.

Bleuler, S., M. Laumanns, L. Thiele and E. Zitzler (2003). PISA - A platform and programming language independent interface for search algorithms. LectureNotes in Computer Science, C. M. Fonseca, P. J. Fleming, E. Zitzler, K. Deb, and L. Thiele, Eds. Berlin: Springer, 494–508.

Bolufé-Röhler, A. and S. Chen (2013) Minimum Population Search - Lessons from building a heuristic technique with two population members. IEEE Congress on Evolutionary Computation: 2061–2068.

Bolufé-Röhler, A., S. Estévez-Velarde, A. Piad-Morffis, S. Chen and J. Montgomery (2013). Differential evolution with thresheld convergence. IEEE Congress on Evolutionary Computation: 40–47.

Bolufé-Röhler, A., A. Coto-Santiesteban, M. Rosa-Soto and S. Chen (2014). Minimum Population Search, an Application to Molecular Docking. Revista GECONTEC, 2 (3).

Bolufé-Röhler, A. and S. Chen (2014). Extending Minimum Population Search towards Large Scale Global Optimization. IEEE Congress on Evolutionary Computation: 845–852.

Bolufé-Röhler, A., S. Fiol-Gonzalez and S. Chen (2015). A Minimum Population Search Hybrid for Large Scale Global Optimization. IEEE Congress on Evolutionary Computation: 1958–1965.

Chen, S., Montgomery, J., Bolufé-Röhler, A. and Gonzalez-Fernandez, Y. (2015). A Review of Thresheld Convergence. Revista GECONTEC 3(1).

Conover, W. J. (1999). Practical Nonparametric Statistics, 3rd ed. John Wiley & Sons.

Deb, K. (2001) Multi-Objective Optimization using Evolutionary Algorithms. New York, EE.UU.: Wiley.

Deb, K., A. Pratap, S. Agarwal, and T. Meyarivan (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions Evolutionary Computation 6: 182–197.

Deb, K., L. Thiele, M. Laumanns, and Zitzler, E. (2005) Scalable test problems for evolutionary multi-objective optimization. Evolutionary Multi-objective Optimization. Springer, 105–145.

Deb, K. (2011). Multi-Objective Optimization Using Evolutionary Algorithms: An Introduction. Indian Institute of Technology Kanpur, India, Tech.Rep.

Deb, K., and H. Jain (2014). An Evolutionary Many-Objective OptimizationAlgorithm Using Reference-point Based Non-dominated Sorting Approach, Part I: Solving Problems with Box Constraints. IEEE Transactions on Evolutionary Computation, 18: 577–601.

Fonseca C. M. and P. J. Fleming (1993). Genetic algorithms for multi-objective optimization: Formulation, discussion and generalization. Proceedings of the 5th International Conference on Genetic Algorithms. California, USA: Morgan Kaufmann, 416–423.

Glorieux E., B. Svensson, F. Danielsson, and B. Lennartson (2017). Constructive cooperative coevolution for large-scale global optimisation. Journal of Heuristics, 23(6): 449–469.

Hansen M. P. and A. Jaszkiewicz (1999). Evaluating the Quality of Approximations to the Non-Dominated Set. Technical University of Denmark, Tech. Rep.

Knowles J. D., R. A. Watson, and D. W. Corne (2001). Reducing local optima in single objective problems by multi-objectivization. 1st International Conference on Evolutionary Multi-Criterion Optimization. Zurich, Switzerland: Springer, 269–283.

Piad-Morffis A., S. Estévez-Velarde, A. Bolufé-Röhler, J. Montgomery and S. Chen (2015). Evolution strategies with thresheld convergence. Evolutionary Computation (CEC), IEEE Congress: 2097–2104.

Talbi G. (2009). Metaheuristics: From design to implementation, 1st ed. John Wiley & Sons.

Tamayo-Vera, D., Bolufé-Röhler, A. and Chen, S. (2016). Estimation multi-variate normal algorithm with thresheld convergence. Evolutionary Computation (CEC), IEEE Congress: 3425–3432.

Zitzler, E. and L. Thiele (1999). Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 3: 257–271.

Zitzler, E., M. Laumanns, and L. Thiele (2001). SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Tech. Rep.

Zitzler, E., L. Thiele, M. Laumanns, C. M. Fonseca, and V. G. da Fonseca (2003). Performance assessment of multiobjective optimizers: an analysis and review. IEEE Transactions on Evolutionary Computation, 7: 117–132.

Zitzler, E. K. Deb and L. Thiele (2000). Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation, 8: 173–195.

Zitzler, E. and S. Kunzli (2004). Indicator-based selection in multi-objective search. Proceedings of the 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII), 832–842.
Cómo citar
Reyes-Fernández-de-Bulnes, D., Bolufé-Röhler, A., & Tamayo-Vera, D. (2019). Multi-objective optimization approach based on Minimum Population Search algorithm. GECONTEC: Revista Internacional De Gestión Del Conocimiento Y La Tecnología, 7(2), 1-19. Recuperado a partir de