The application of multi-objective charged system search algorithm for optimization problems

Document Type : Research Note

Authors

1 Department of GIS Engineering, Faculty of Surveying Engineering, Tehran University, Tehran, Iran.

2 Department of Civil Engineering, University of Tabriz, Tabriz, Iran

Abstract

The charged system search algorithm is a relatively new optimization algorithm developed based on some principles from physics and mechanics. This paper presents an approach in which Pareto dominance is incorporated into the charged system search in order to allow this algorithm to handle problems with some multi-objective functions; the proposed algorithm will be called Multi-Objective Charged System Search (MOCSS). Well-known mathematical and engineering benchmarks are used to evaluate the proposed algorithm and the results have been compared with other new approaches. The results of implementing the new algorithm on some test problems show that the proposed algorithm outperforms the other algorithms in terms of Generational Distance, Maximum Spread, Spacing, Coverage of two Set and Hypervolume Indicator. Results of well-known mathematical examples indicate that the new approach is highly competitive and can be considered as a viable alternative to solve multi-objective optimization problems. These results encourage the application of the proposed method to more complex and real-world multi-objective optimization problems. The proposed method can deal with highly nonlinear problems with complex constraints and diverse Pareto optimal sets.

Keywords

Main Subjects


References:
1. Coello, C.C., Lamont, G.B., and Van Veldhuizen, D.A., Evolutionary Algorithms for Solving Multi- Objective Problems, Second Edition ed., Springer Science & Business Media, New York (2007).
2. Xiang, Y. and Zhou, Y. "A dynamic multi-colony artificial bee colony algorithm for multi-objective optimization", Applied Soft Computing, 35, pp. 766-785 (2015).
3. Yang, G.-Q., Liu, Y.-K., and Yang, K. "Multiobjective biogeography-based optimization for supply chain network design under uncertainty", Computers & Industrial Engineering, 85, pp. 145-156 (2015).
4. Lark, R.M. "Multi-objective optimization of spatial sampling", Spatial Statistics, 18, pp. 412-430 (2016).
5. Akay, B. and Karaboga, D. "A survey on the applications of artificial bee colony in signal, image, and video processing", Signal, Image and Video Processing, 9(4), pp. 967-990 (2015).
6. Nseef, S.K., Abdullah, S., Turky, A., and Kendall, G. "An adaptive multi-population artificial bee colony algorithm for dynamic optimisation problems", Knowledge-Based Systems, 104, pp. 14-23 (2016).
7. Kaveh, A., Laknejadi, K., and Alinejad, B. "Performance-based multi-objective optimization of large steel structures", Acta Mechanica, 223(2), pp. 355-369 (2012).
8. Osyczka, A. "Multicriteria optimization for engineering design", Design Optimization, 1, pp. 193-227 (1985).
9. Kaveh, A. and Laknejadi, K. "A hybrid evolutionary graph based multi-objective algorithm for layout optimization of truss structures", Acta Mechanica, 224(2), pp. 343-364 (2013).
10. Coello, C.A.C. "An updated survey of evolutionary multiobjective optimization techniques: State of the art and future trends", in: Proceedings of the Congress on Evolutionary Computation, pp. 3-13 (1999).
11. Gong, W., Cai, Z., and Zhu, L. "An effective multiobjective differential evolution algorithm for engineering design", Structural and Multidisciplinary Optimization, 38(2), pp. 137-157 (2009).
12. Pareto, V., Cours d'economie Politique, Librairie Droz (1964).
13. Kishor, A., Singh, P.K., and Prakash, J. "NSABC: Non-dominated sorting based multi-objective artificial bee colony algorithm and its application in data clustering", Neurocomputing, 216, pp. 514-533 (2016).
14. Li, T., Sun, X., Lu, Z., and Wu, Y. "A novel multiobjective optimization method based on sensitivity analysis", Mathematical Problems in Engineering, 2016 (2016).
15. Chiong, R., Nature-Inspired Algorithms for Optimisation, Springer-Verlag, Berlin Heidelberg (2009).
16. Miettinen, K., Nonlinear Multiobjective Optimization, MA: Kluwer Academic Publishers, Boston (1999).
17. Yang, X.-S., Karamanoglu, M., and He, X. "Multiobjective flower algorithm for optimization", Procedia Computer Science, 18, pp. 861-868 (2013).
18. Schaffer, J.D. "Multiple objective optimization with vector evaluated genetic algorithms", in: Proceedings of the 1st international Conference on Genetic Algorithms and their Applications, L. Erlbaum Associates Inc., USA, pp. 93-100 (1985).
19. Coello, C.A.C.C. and Pulido, G.T. "A micro-genetic algorithm for multiobjective optimization", in: E. Zitzler, K. Deb, L. Thiele, C.A.C. Coello, and D. Corne, Eds., First International Conference on Evolutionary Multi-Criterion Optimization, Springer-Verlag, pp. 126-140 (2001).
20. Srinvas, N. and Deb, K. "Multi-objective function optimization using non-dominated sorting genetic algorithms", Evolutionary Computation, 2(3), pp. 221- 248 (1994).
21. Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. "A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE Transactions on Evolutionary Computation, 6(2), pp. 182-197 (2002).
22. Zitzler, E. and Thiele, L. "Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach", IEEE Transactions on Evolutionary Computation, 3(4), pp. 257-271 (1999).
23. Zitzler, E., Laumanns, M., and Thiele, L., SPEA2: Improving the Strength Pareto Evolutionary Algorithm, in Swiss Federal Institute Technology, Zurich, Switzerland, pp. 95-100 (2001).
24. Knowles, J.D. and Corne, D.W. "Approximating the nondominated front using the Pareto archived evolution strategy", Evolutionary Computation, 8(2), pp. 149-172 (2000).
25. Madavan, N.K. "Multiobjective optimization using a Pareto differential evolution approach", in: Congress on Evolutionary Computation (CEC'2002), New Jersey, pp. 1145-1150 (2002).
26. Zhang, Q. and Li, H. "MOEA/D: A multiobjective evolutionary algorithm based on decomposition", IEEE Transactions on Evolutionary Computation, 11(6), pp. 712-731 (2007).
27. Li, H. and Zhang, Q. "Multiobjective optimization problems with complicated Pareto sets, MOEA/D and NSGA-II", IEEE Transactions on Evolutionary Computation, 13(2), pp. 284-302 (2009).
28. Kaveh, A. and Laknejadi, K. "A hybrid multi-objective particle swarm optimization and decision making procedure for optimal design of truss structures", Iranian Journal of Science and Technology, 35(C2), pp. 137- 154 (2011).
29. Kukkonen, S. and Lampinen, J. "GDE3: The third evolution step of generalized differential evolution", in: 2005 IEEE Congress on Evolutionary Computation, IEEE, pp. 443-450 (2005).
30. Chen, X., Du, W., and Qian, F. "Multi-objective differential evolution with ranking-based mutation operator and its application in chemical process optimization", Chemometrics and Intelligent Laboratory Systems, 136, pp. 85-96 (2014).
31. Coello, C.A.C. and Lechuga, M.S. "A proposal for multiple objective particle swarm optimization", in: Proceedings of the Congress on Evolutionary Computation (CEC'2002), pp. 1051-1056 (2002).
32. Robic, T. and Filipic, B. "DEMO: Differential evolution for multiobjective optimization", in: International Conference on Evolutionary Multi-Criterion Optimization, Springer, pp. 520-533 (2005).
33. Kaveh, A. and Laknejadi, K. "A novel hybrid charge system search and particle swarm optimization method for multi-objective optimization", Expert Systems with Applications, 38(12), pp. 15475-15488 (2011).
34. Babu, B. and Gujarathil, A.M. "Multi-objective differential evolution (MODE) for optimization of supply chain planning and management", in: 2007 IEEE Congress on Evolutionary Computation, IEEE, pp. 2732-2739 (2007).
35. Pham, D. and Ghanbarzadeh, A. "Multi-objective optimisation using the bees algorithm", in: 3rd International Virtual Conference on Intelligent Production Machines and Systems (IPROMS 2007), Whittles, Dunbeath, Scotland, pp. 111-116 (2007).
36. Jadaan, O.A., Rajamani, L., and Rao, C. "Nondominated ranked genetic algorithm for solving constrained multi-objective optimization problems", Journal of Theoretical & Applied Information Technology, 5(5), pp. 640-651 (2009).
37. Yang, X.-S. and Deb, S. "Multiobjective cuckoo search for design optimization", Computers & Operations Research, 40(6), pp. 1616-1624 (2013).
38. Yang, X.-S. "Multiobjective fire y algorithm for continuous optimization", Engineering with Computers, 29(2), pp. 175-184 (2013).
39. Kaveh, A. and Laknejadi, K. "A new multi-swarm multi-objective optimization method for structural design", Advances in Engineering Software, 58, pp. 54- 69 (2013).
40. Kaveh, A. and Laknejadi, K. "A swarm based memetic evolutionary algorithm for multi-objective optimization of large structures", Asian Journal of Civil Engineering, 16(5), pp. 621-649 (2015).
41. Erfani, T. and Sergei, V.U. "Directed search domain: a method for even generation of the Pareto frontier in multiobjective optimization", Engineering Optimization, 43(5), pp. 467-484 (2011).
42. Kaveh, A. and Massoudi, M.S. "Multi objective Optimization of structures using charged system search", Scientia Iranica, 21(6), pp. 1845-1860 (2014).
43. Kaveh, A. and Talatahari, S. "A novel heuristic optimization method: charged system search", Acta Mechanica, 213(3-4), pp. 267-289 (2010).
44. Kaveh, A. and Talatahari, S. "Charged system search for optimal design of frame structures", Applied Soft Computing, 12(1), pp. 382-393 (2012).
45. El-Sawy, A.A., Hussein, M.A., Zaki, E.-S.M., and Mousa, A.A.A. "Local search-inspired rough sets for improving multiobjective evolutionary algorithm", Applied Mathematics, 5(13), pp. 1993-2007 (2014).
46. Wagner, T., Beume, N., and Naujoks, B. "Pareto-, aggregation-, and indicator-based methods in manyobjective optimization", in: 4th International Conference on Evolutionary Multi-Criterion Optimization, Springer, Japan, pp. 742-756 (2007).
47. Luo, J., Liu, Q., Yang, Y., Li, X., Chen, M.-R., and Cao, W. "An artificial bee colony algorithm for multiobjective optimisation", Applied Soft Computing, 50, pp. 235-251 (2017).
48. Oyama, A., Shimoyama, K., and Fujii, K. "New constraint-handling method for multi-objective and multi-constraint evolutionary optimization", Transactions of the Japan Society for Aeronautical and Space Sciences, 50(167), pp. 56-62 (2007).
49. Van Veldhuizen, D.A., Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations, in: Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, DTIC Document, Ohio (1999).
50. Neema, M.N. and Ohgai, A. "Multi-objective location modeling of urban parks and open spaces: Continuous optimization", Computers, Environment and Urban Systems, 34(5), pp. 359-376 (2010).
51. Deb, K., Multi-Objective Optimization Using Evolutionary Algorithms, John Wiley & Sons, New York (2001).
52. Goldberg, D.E. and Richardson, J. "Genetic algorithms with sharing for multimodal function optimization", in: Genetic Algorithms and Their Applications: Proceedings of the Second International Conference on Genetic Algorithms, Hillsdale, NJ: Lawrence Erlbaum, Mahwah, pp. 41-49 (1987).
53. Zhang, Q., Zhou, A., Zhao, S., Suganthan, P.N., Liu, W., and Tiwari, S. "Multiobjective optimization test instances for the CEC 2009 special session and competition", in: University of Essex, Colchester, UK and Nanyang Technological University, Singapore, Special Session on Performance Assessment of Multi- Objective Optimization Algorithms, Technical Report (2008).
54. Huo, J. and Liu, L. "An improved multi-objective artificial bee colony optimization algorithm with regulation operators", Information, 8(1), p. 18 (2017).
55. Deb, K., Thiele, L., Laumanns, M., and Zitzler, E. "Scalable test problems for evolutionary multiobjective optimization", in: A. Ajith and G. Robert, Eds., Evolutionary Multiobjective Optimization, Theoretical Advances and Applications, Springer, USA, pp. 105- 145 (2005).
56. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., and Da Fonseca, V.G. "Performance assessment of multiobjective optimizers: an analysis and review", IEEE Transactions on Evolutionary Computation, 7(2), pp. 117-132 (2003).
57. Zitzler, E., Deb, K., and Thiele, L. "Comparison of multiobjective evolutionary algorithms: Empirical results", Evolutionary Computation, 8(2), pp. 173-195 (2000).
58. Van Veldhuizen, D.A. and Lamont, G.B., Multiobjective Evolutionary Algorithm Research: A History and Analysis, in: Citeseer, Department of Electrical and Computer Engineering. Graduate School of Engineering. Air Force Institute of Technology (1998).
59. Schott, J.R., Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization, in: Department of Aeronautics and Astronautics, DTIC Document, Cambridge (1995).
60. Li, K., Kwong, S., Cao, J., Li, M., Zheng, J., and Shen, R. "Achieving balance between proximity and diversity in multi-objective evolutionary algorithm", Information Sciences, 182(1), pp. 220-242 (2012).
61. Wilcoxon, F. "Individual comparisons by ranking methods", Biometrics Bulletin, 1(6), pp. 80-83 (1945).
62. Ray, T. and Liew, K.M. "A swarm metaphor for multiobjective design optimization", Engineering Optimization, 34(2), pp. 141-153 (2002).
63. Deb, K. "Evolutionary Multi-Criterion Optimization", in: K. Miettinen, P. Neittaanmaki, M.M. Makela and J. Periaux, Eds., Evolutionary Algorithms in Engineering and Computer Science, pp. 135-161 (2004).
64. Osyczka, A. and Kundu, S. "A genetic algorithm-based multicriteria optimization method", in: Proceedings 1st World Congress Structural Multidisciplinary Optimization, pp. 909-914 (1995).