A polar-based guided multi-objective evolutionary algorithm to search for optimal solutions interested by decision-makers in a logistics network design problem
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In practical multi-objective optimization problems, respective decision-makers might be interested in some optimal solutions that have objective values closer to their specified values. Guided multi-objective evolutionary algorithms (guided MOEAs) have been significantly used to guide their evolutionary search direction toward these optimal solutions using by decision makers. However, most guided MOEAs need to be iteratively and interactively evaluated and then guided by decision-makers through re-formulating or re-weighting objectives, and it might negatively affect the algorithms performance. In this paper, a novel guided MOEA that uses a dynamic polar-based region around a particular point in objective space is proposed. Based on the region, new selection operations are designed such that the algorithm can guide the evolutionary search toward optimal solutions that are close to the particular point in objective space without the iterative and interactive efforts. The proposed guided MOEA is tested on the multi-criteria decision-making problem of flexible logistics network design with different desired points. Experimental results show that the proposed guided MOEA outperforms two most effective guided and non-guided MOEAs, R-NSGA-II and NSGA-II.
KeywordsMulti-objective optimization problems Guided multi-objective evolutionary algorithms Polar coordinate system Flexible logistics network design problem
The authors would like to thank the Universiti Teknologi Malaysia (UTM), for supporting this research.
- Branke, J., Kaubler, T., & Schmeck, H. (2000). Guiding multi-objective evolutionary algorithms toward interesting regions. Germany: Institute AIFB, University of Karlsruhe.Google Scholar
- Cvetkovic, D., & Parmee, I. (2002). Agent-based support within an interactive evolutionary design system. Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing, 16(5), 331–342.Google Scholar
- Cvetkovic, D., & Parmee, I. C. (2002). Preferences and their application in evolutionary multiobjective optimization. Ieee Transactions on Evolutionary Computation, 6(1), 42–57. doi: 10.1109/4235.985691.
- da Silva, E. K., Barbosa, H. J. C., & Lemonge, A. C. C. (2011). An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization. Optimization and Engineering, 12(1–2), 31–54.Google Scholar
- Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. West Sussex: Wiley.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. doi: 10.1109/4235.996017.
- Deb, K., Sundar, J., Udaya Bhaskara Rao, N., & Chaudhuri, S. (2006). Reference Point Based Multi-Objective Optimization Using Evolutionary Algorithms. International Journal of Computational Intelligence Research, 2(3), 273–286. http://repository.ias.ac.in/81053/.
- Fonseca, C., & Fleming, P. (1993). Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization. In S. Forrest (Ed.), the fifth international conference on genetic algorithms, San Mateo, California, (pp. 416–423). University of Illinois at Urbana Champaign, Morgan Kaufmann Publishers.Google Scholar
- Gen, M., Cheng, R., & Lin, L. (2008). Network models and optimization, multiobjective genetic algorithm approach. London: Springer.Google Scholar
- Gong, M., Liu, F., Zhang, W., Jiao, L., & Zhang, Q. Interactive MOEA/D for multi-objective decision making. In GECCO ’11 Proceedings of the 13th annual conference on Genetic and evolutionary computation, (pp. 721–728). New York, NY, USA: ACM. doi: 10.1145/2001576.2001675.
- Hitchcock, F. L. (1941). The distribution of a product from several sources to numerous localities. Journal of Mathematical Physics, 20, 220–230.Google Scholar
- Jin, Y. C., & Sendhoff, B. (2002). Incorporation of fuzzy preferences into evolutionay multiobjective optimization. In The 4th Asia-Pacific conference on simulated evolution and learning, Orchid Country Club, Singapore (vol. 1, pp. 26–30).Google Scholar
- Parmee, I. C., Cvetković, D. C., Watson, A. H., & Bonham, C. R. (2000). Multiobjective satisfaction within an interactive evolutionary design environment. Evolutionary Computatio, 8(2), doi: 10.1162/106365600568176.
- Rachmawati, L., & Srinivasan, D. (2010). Incorporation of Imprecise Goal Vectors into Evolutionary Multi-Objective Optimization. In Paper presented at the 2010 IEEE World Congress on Computational Intelligence. Spain: Barcelona.Google Scholar
- Rajabalipour Cheshmehgaz, H., Desa, M., & Wibowo, A. (2011). A flexible three-level logistic network design considering cost and time criteria with a multi-objective evolutionary algorithm. Journal of Intelligent Manufacturing (first online published), 1–17, doi: 10.1007/s10845-011-0584-7.
- Rajabalipour Cheshmehgaz, H., Desa, M. I., & Wibowo, A. (2012a). Effective local evolutionary searches distributed on an island model solving bi-objective optimization problems. Applied Intelligence (first online published). doi: 10.1007/s10489-012-0375-7.
- Rajabalipour Cheshmehgaz, H., Desa, M. I., & Wibowo, A. (2012b). An effective model of multiple multi-objective evolutionary algorithms with the assistance of regional multi-objective evolutionary algorithms: VIPMOEAs. Applied Soft Computing (first online published). doi: 10.1016/j.asoc.2012.04.027.
- Sato, H., Aguirre, H. E., & Tanaka, K. (2007). Local dominance including control of dominance area of solutions in MOEAs. In 2007 Ieee symposium on computational intelligence in multi-criteria decision making, 310–317, 402.Google Scholar
- Stalk, G., & Hout, T. M. (1990). Competing against Time. Research-Technology Management, 33(2), 19–24.Google Scholar
- Tan, K. C., Khor, E. F., Lee, T. H., & Sathikannan, R. (2003). An evolutionary algorithm with advanced goal and priority specification for multi-objective optimization. Journal of Artificial Intelligence Research, 18, 183–215.Google Scholar
- Timm, G., & Herbert, K. (2009). Comprehensive logistics. London: Springer.Google Scholar
- Vidal, C. J., & Goetschalckx, M. (1997). Strategic production-distribution models: A critical review with emphasis on global supply chain models. European Journal of Operational Research, 98(1), 1–18.Google Scholar
- Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: Improving the strength pareto evolutionary algorithm. Zurich, Switzerland: Swiss Federal Institute of Technology (ETH) Zurich.Google Scholar
- Zitzler, E., Thiele, L., & Bader, J. (2008). SPAM: Set preference algorithm for multiobjective optimization. Parallel Problem Solving from Nature—Ppsn X, Proceedings, 5199(847–858), 1164.Google Scholar