Skip to main content
SpringerLink
Log in

Guided Moth–Flame optimiser for multi-objective optimization problems

  • S.I.: MOPGP 2017
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

This paper proposes a novel version of Moth–Flame optimiser for solving multi-objective problems (MOMFO). The main idea of this algorithm is that the Moth’s swarm explores the search space around the Flames set (leader solutions). To implement our approach, we integrate the unlimited external archive to guide the Moth’s swarm during the exploration search to find the Pareto solutions set. To ensure a good compromise between convergence and diversity when exploring the search space, we use the epsilon dominance principle to update the external archive. In addition, we use the non-dominated sort and crowding distance in updating the Flame solutions to ensure rapid convergence towards the Pareto solutions set. We validate the proposed algorithm on twelve test functions and compare our results with two well-known meta-heuristics. The results of the proposed algorithm show better convergence behavior with a better diversity of solutions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Abdelaziz, F. B., Krichen, S., & Chaouachi, J. (1999). A hybrid heuristic for multiobjective knapsack problems. In S. Voß, S. Martello, I. H. Osman, & C. Roucairol (Eds.), Meta-heuristics (pp. 205–212). Berlin: Springer.

  • Andersson, J. (2000). A survey of multiobjective optimization in engineering design. Department of Mechanical Engineering, Linktjping University Sweden.

  • Auger, A., Bader, J., Brockhoff, D., & Zitzler, E. (2012). Hypervolume-based multiobjective optimization: Theoretical foundations and practical implications. Theoretical Computer Science, 425, 75–103.

    Article  Google Scholar 

  • Bilgaiyan, S., Sagnika, S., & Das, M. (2015). A multi-objective cat swarm optimization algorithm for workflow scheduling in cloud computing environment. In M. Kamran (Ed.), Intelligent computing, communication and devices (pp. 73–84). Berlin: Springer.

  • Branke, J., Deb, K., Dierolf, H., Osswald, M., et al. (2004). Finding knees in multi-objective optimization. PPSN, 3242, 722–731.

    Google Scholar 

  • Cheng, R., Jin, Y., Olhofer, M., & Sendhoff, B. (2016). A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Transactions on Evolutionary Computation, 20(5), 773–791.

    Article  Google Scholar 

  • Coello, C. A. C., Pulido, G. T., & Lechuga, M. S. (2004). Handling multiple objectives with particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8(3), 256–279.

    Article  Google Scholar 

  • Coello, C. A. C., Van Veldhuizen, D. A., & Lamont, G. B. (2002). Evolutionary algorithms for solving multi-objective problems (Vol. 242). Berlin: Springer.

    Book  Google Scholar 

  • Das, I., & Dennis, J. E. (1998). Normal-boundary intersection: A new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization, 8(3), 631–657.

    Article  Google Scholar 

  • Deb, K., & Jain, H. (2014). An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Solving problems with box constraints. IEEE Transactions on Evolutionary Computation, 18(4), 577–601.

    Article  Google Scholar 

  • Deb, K., Mohan, M., & Mishra, S. (2005a). Evaluating the epsilon-domination based multi-objective evolutionary algorithm for a quick computation of pareto-optimal solutions. Evolutionary Computation, 13(4), 501–525.

    Article  Google Scholar 

  • Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197.

    Article  Google Scholar 

  • Deb, K., Thiele, L., Laumanns, M., & Zitzler, E. (2005b). Scalable test problems for evolutionary multiobjective optimization. Berlin: Springer.

    Book  Google Scholar 

  • Derrac, J., García, S., Molina, D., & Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, 1(1), 3–18.

    Article  Google Scholar 

  • El Aziz, M. A., Ewees, A. A., & Hassanien, A. E. (2017). Whale optimization algorithm and Moth–Flame optimization for multilevel thresholding image segmentation. Expert Systems with Applications, 83, 242–256.

    Article  Google Scholar 

  • Elarbi, M., Bechikh, S., Gupta, A., Said, L. B., & Ong, Y. S. (2018). A new decomposition-based NSGA-II for many-objective optimization. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48(7), 1191–1210.

    Article  Google Scholar 

  • Huband, S., Hingston, P., Barone, L., & While, L. (2006). A review of multiobjective test problems and a scalable test problem toolkit. IEEE Transactions on Evolutionary Computation, 10(5), 477–506.

    Article  Google Scholar 

  • Ibrahim, R. A., Elaziz, M. A., Ewees, A. A., Selim, I. M., & Lu, S. (2018). Galaxy images classification using hybrid brain storm optimization with Moth Flame optimization. Journal of Astronomical Telescopes, Instruments, and Systems, 4(3), 038001.

    Article  Google Scholar 

  • Jain, H., & Deb, K. (2014). An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: Handling constraints and extending to an adaptive approach. IEEE Transactions on Evolutionary Computation, 18(4), 602–622.

    Article  Google Scholar 

  • Jangir, N., Pandya, M. H., Trivedi, I. N., Bhesdadiya, R., Jangir, P., & Kumar, A . (2016) . Moth–Flame optimization algorithm for solving real challenging constrained engineering optimization problems. In 2016 IEEE Students’ conference on electrical, electronics and computer science (SCEECS) (pp. 1–5). IEEE.

  • Jangir, P., & Trivedi, I. N. (2018). Non-dominated sorting Moth Flame optimizer: A novel multi-objective optimization algorithm for solving engineering design problems. Engineering Technology Open Access Journal, 1–15.

  • Jariyatantiwait, C., & Yen, G. G. (2014). Multiobjective differential evolution based on fuzzy performance feedback. International Journal of Swarm Intelligence Research (IJSIR), 5(4), 45–64.

    Article  Google Scholar 

  • Jaszkiewicz, A. (2002). Genetic local search for multi-objective combinatorial optimization. European Journal of Operational Research, 137(1), 50–71.

    Article  Google Scholar 

  • Jiang, S., & Yang, S. (2017). A strength pareto evolutionary algorithm based on reference direction for multiobjective and many-objective optimization. IEEE Transactions on Evolutionary Computation, 21(3), 329–346.

    Article  Google Scholar 

  • Jiang, S., Zhang, J., Ong, Y. S., Zhang, A. N., & Tan, P. S. (2015). A simple and fast hypervolume indicator-based multiobjective evolutionary algorithm. IEEE Transactions on Cybernetics, 45(10), 2202–2213.

    Article  Google Scholar 

  • Kim, I. Y., & de Weck, O. L. (2005). Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Structural and Multidisciplinary Optimization, 29(2), 149–158.

    Article  Google Scholar 

  • Klamroth, K., & Wiecek, M. M. (2000). Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics, 47(1), 57–76.

    Article  Google Scholar 

  • Li, W. K., Wang, W. L., & Li, L. (2018). Optimization of water resources utilization by multi-objective Moth–Flame algorithm. Water Resources Management, 1–14

  • Ma, X., Qi, Y., Li, L., Liu, F., Jiao, L., & Wu, J. (2014). MOEA/D with uniform decomposition measurement for many-objective problems. Soft Computing, 18(12), 2541–2564.

    Article  Google Scholar 

  • Marler, R. T., & Arora, J. S. (2004). Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, 26(6), 369–395.

    Article  Google Scholar 

  • Messac, A., & Mattson, C. A. (2002). Generating well-distributed sets of pareto points for engineering design using physical programming. Optimization and Engineering, 3(4), 431–450.

    Article  Google Scholar 

  • Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowledge-Based Systems, 89, 228–249.

    Article  Google Scholar 

  • Mirjalili, S., Jangir, P., & Saremi, S. (2017a). Multi-objective ant lion optimizer: A multi-objective optimization algorithm for solving engineering problems. Applied Intelligence, 46(1), 79–95.

    Article  Google Scholar 

  • Mirjalili, S., Saremi, S., Mirjalili, S. M., & Coelho, L. D. S. (2016). Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization. Expert Systems with Applications, 47, 106–119.

    Article  Google Scholar 

  • Mirjalili, S. Z., Mirjalili, S., Saremi, S., Faris, H., & Aljarah, I. (2017b). Grasshopper optimization algorithm for multi-objective optimization problems. Applied Intelligence, 48(4), 1–16.

    Google Scholar 

  • Nanda, S. J., et al. (2016). Multi-objective moth flame optimization. In 2016 International conference on Advances in computing, communications and informatics (ICACCI) (pp. 2470–2476). IEEE.

  • Przybylski, A., Gandibleux, X., & Ehrgott, M. (2008). Two phase algorithms for the bi-objective assignment problem. European Journal of Operational Research, 185(2), 509–533.

    Article  Google Scholar 

  • Przybylski, A., Gandibleux, X., & Ehrgott, M. (2010). A two phase method for multi-objective integer programming and its application to the assignment problem with three objectives. Discrete Optimization, 7(3), 149–165.

    Article  Google Scholar 

  • Raith, A., & Ehrgott, M. (2009). A two-phase algorithm for the biobjective integer minimum cost flow problem. Computers & Operations Research, 36(6), 1945–1954.

    Article  Google Scholar 

  • Reyes-Sierra, M., Coello, C. C., et al. (2006). Multi-objective particle swarm optimizers: A survey of the state-of-the-art. International Journal of Computational Intelligence Research, 2(3), 287–308.

    Google Scholar 

  • Sadollah, A., Eskandar, H., & Kim, J. H. (2015). Water cycle algorithm for solving constrained multi-objective optimization problems. Applied Soft Computing, 27, 279–298.

    Article  Google Scholar 

  • Salcedo-Sanz, S., Manjarres, D., Pastor-Sánchez, Á., Del Ser, J., Portilla-Figueras, J. A., & Gil-Lopez, S. (2013). One-way urban traffic reconfiguration using a multi-objective harmony search approach. Expert Systems with Applications, 40(9), 3341–3350.

    Article  Google Scholar 

  • Savsani, V., & Tawhid, M. A. (2017). Non-dominated sorting Moth Flame optimization (NS-MFO) for multi-objective problems. Engineering Applications of Artificial Intelligence, 63, 20–32.

    Article  Google Scholar 

  • Schott, J. R. (1995). Fault tolerant design using single and multicriteria genetic algorithm optimization. DTIC Document: Tech. rep.

  • Soliman, G. M., Khorshid, M. M., & Abou-El-Enien, T. H. (2016). Modified Moth–Flame optimization algorithms for terrorism prediction. International Journal of Application or Innovation in Engineering and Management, 5, 47–58.

    Google Scholar 

  • Sun, J., Zhang, H., Zhou, A., Zhang, Q., & Zhang, K. (2018). A new learning-based adaptive multi-objective evolutionary algorithm. Swarm and Evolutionary Computation, 44, 304–319.

    Article  Google Scholar 

  • Tan, Y. Y., Jiao, Y. C., Li, H., & Wang, X. K. (2012). MOEA/D-SQA: A multi-objective memetic algorithm based on decomposition. Engineering Optimization, 44(9), 1095–1115.

    Article  Google Scholar 

  • Tian, Y., Cheng, R., Zhang, X., Su, Y., & Jin, Y. (2018). A strengthened dominance relation considering convergence and diversity for evolutionary many-objective optimization. IEEE Transactions on Evolutionary Computation, 23(2), 331–345.

    Article  Google Scholar 

  • Vincent, T., Seipp, F., Ruzika, S., Przybylski, A., & Gandibleux, X. (2013). Multiple objective branch and bound for mixed 0–1 linear programming: Corrections and improvements for the biobjective case. Computers & Operations Research, 40(1), 498–509.

    Article  Google Scholar 

  • Yang, X. S. (2013). Multiobjective firefly algorithm for continuous optimization. Engineering with Computers, 29(2), 175–184.

    Article  Google Scholar 

  • Zawbaa, H. M., Emary, E., Parv, B., & Sharawi, M. (2016). Feature selection approach based on Moth–Flame optimization algorithm. In IEEE Congress on evolutionary computation (CEC), 2016 (pp. 4612–4617). IEEE.

  • Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712–731.

    Article  Google Scholar 

  • Zhou, A., Qu, B. Y., Li, H., Zhao, S. Z., Suganthan, P. N., & Zhang, Q. (2011). Multiobjective evolutionary algorithms: A survey of the state of the art. Swarm and Evolutionary Computation, 1(1), 32–49.

    Article  Google Scholar 

  • Zitzler, E., Deb, K., & Thiele, L. (2000). Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation, 8(2), 173–195.

    Article  Google Scholar 

  • Zitzler, E., & Künzli, S. (2004). Indicator-based selection in multiobjective search. In International conference on parallel problem solving from nature (pp. 832–842). Springer.

  • Zitzler, E., Laumanns, M., Thiele, L., et al. (2001). SPEA2: Improving the strength pareto evolutionary algorithm. Eurogen, 3242, 95–100.

    Google Scholar 

  • Zitzler, E., & Thiele, L. (1998) . Multiobjective optimization using evolutionary algorithms—A comparative case study. In International conference on parallel problem solving from nature (pp. 292–301). Springer.

  • Zouache, D., Moussaoui, A., & Ben Abdelaziz, F. (2018). A cooperative swarm intelligence algorithm for multi-objective discrete optimization with application to the knapsack problem. European Journal of Operational Research, 264(1), 74–88.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Djaafar Zouache, Mira Lefkir & Nour El-Houda Chalabi

  2. NEOMA Business School, Rouen Campus, Mont-Saint-Aignan, France

    Fouad Ben Abdelaziz

Authors
  1. Djaafar Zouache
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fouad Ben Abdelaziz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mira Lefkir
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nour El-Houda Chalabi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fouad Ben Abdelaziz.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zouache, D., Abdelaziz, F.B., Lefkir, M. et al. Guided Moth–Flame optimiser for multi-objective optimization problems. Ann Oper Res 296, 877–899 (2021). https://doi.org/10.1007/s10479-019-03407-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-019-03407-8

Keywords

Search

Navigation