Multiobjective particle swarm optimization with nondominated local and global sets. (English) Zbl 1208.90192
Summary: In multiobjective particle swarm optimization methods, selecting the local best and the global best for each particle of the population has a great impact on the convergence and diversity of solutions, especially when optimizing problems with high number of objectives. This paper presents an approach using two sets of nondominated solutions. The ability of the proposed approach to detect the true Pareto optimal solutions and capture the shape of the Pareto front is evaluated through experiments on well-known non-trivial multiobjective test problems as well as the real-life electric power dispatch problem. The diversity of the nondominated solutions obtained is demonstrated through different measures. The proposed approach is assessed through a comparative study with the reported results in the literature.
MSC:
| 90C59 | Approximation methods and heuristics in mathematical programming |
| 90C29 | Multi-objective and goal programming |
Keywords:
Pareto-optimal setReferences:
| [1] | Abido MA (2002a) Optimal design of power system stabilizers using particle swarm optimization. IEEE Trans Energy Convers 17(3):406–413 · doi:10.1109/TEC.2002.801992 |
| [2] | Abido MA (2002b) Optimal power flow using particle swarm optimization. Int J Electrical Power Energy Syst 24(7):563–571 · doi:10.1016/S0142-0615(01)00067-9 |
| [3] | Abido MA (2003) Environmental/economic power dispatch using multiobjective evolutionary algorithms. IEEE Trans Power Syst 18(4):1529–1537 · doi:10.1109/TPWRS.2003.818693 |
| [4] | Abido MA (2006) Multiobjective evolutionary algorithms for electric power dispatch problem. IEEE Trans Evol Comput 10(3):315–329 · doi:10.1109/TEVC.2005.857073 |
| [5] | Abido MA (2007) Two-level of nondominated solutions approach to multiobjective particle swarm optimization. In: Proceedings of the 2007 genetic and evolutionary computation conference, GECCO’2007, 7–11 July 2007, London, UK, pp 726–733 |
| [6] | Angeline P (1998) Evolutionary optimization versus particle swarm optimization: philosophy and performance differences. In: Proceedings of the 7th annual conference on evolutionary programming, March 1998, pp 601–610 |
| [7] | Branke J, Mostaghim S (2006) About selecting the personal best in multi-objective particle swarm optimization. In: Proceedings of the 9th international conference on parallel problem solving from nature–PPSN IX, Reykjavik, Iceland, 9–13 September 2006, pp 523–532 |
| [8] | Coello CAC (1999) A comprehensive survey of evolutionary-based multiobjective optimization techniques. Knowl Inf Syst 1(3):269–308 |
| [9] | Coello CAC, Lechuga MS (2002) MOPSO: a proposal for multiple objective particle swarm optimization. In: Congress on evolutionary computation (CEC’2002), vol 2. IEEE Service Center, Piscataway, New Jersey, May 2002, pp 1051–1056 |
| [10] | Coello CAC, Pulido GT, Lechuga MS (2004) Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 8(3):256–279 · doi:10.1109/TEVC.2004.826067 |
| [11] | Das DB, Patvardhan C (1998) New multi-objective stochastic search technique for economic load dispatch. IEE Proc Gener Transm Distrib 145(6):747–752 · doi:10.1049/ip-gtd:19982367 |
| [12] | Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley-interscience series in systems and optimization. Wiley, Chichester · Zbl 0970.90091 |
| [13] | Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithms: NSGA-II. IEEE Trans Evol Comput 6(2):182–197 · doi:10.1109/4235.996017 |
| [14] | Farag A, Al-Baiyat S, Cheng TC (1995) Economic load dispatch multiobjective optimization procedures using linear programming techniques. IEEE Trans Power Syst 10(2):731–738 · doi:10.1109/59.387910 |
| [15] | Fieldsend JE, Singh S (2002) A multi-objective algorithm based upon particle swarm optimization, an efficient data structure and turbulence. In: Proceedings of the 2002 U.K. workshop on computational intelligence, Birmingham, UK, 2–4 September 2002, pp 37–44 |
| [16] | Hu X, Eberhart R (2002) Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Congress on evolutionary computation (CEC’2002), vol 2, IEEE Service Center, Piscataway, New Jersey, May 2002, pp 1677–1681 |
| [17] | Hu X, Eberhart R, Shi Y (2003) Particle swarm with extended memory for multiobjective optimization. In: Proceedings of 2003 IEEE swarm intelligence symposium, Indianapolis, IN, USA, April 2003, pp 193–197 |
| [18] | Huang VL, Suganthan PN, Liang JJ (2006) Comprehensive learning particle swarm optimizer for solving multiobjective optimization problems. Int J Intell Syst 21(2):209–226 · Zbl 1155.90484 · doi:10.1002/int.20128 |
| [19] | Kennedy J (1997) The particle swarm: social adaptation of knowledge. In: Proceedings of the 1997 IEEE international conference on evolutionary computation ICEC’97, Indianapolis, Indiana, USA, pp 303–308 |
| [20] | Kennedy J, Eberhart R (2001) Swarm intelligence. Morgan Kaufmann Publishers, San Francisco, CA |
| [21] | Li X (2003) A nondominated sorting particle swarm optimizer for multiobjective optimization. In: Lecture Notes in Computer Science, Proceedings of genetic and evolutionary computation GECCO 2003, vol 2723, Part I, Berlin, Germany, July 2003, pp 37–48 · Zbl 1028.68827 |
| [22] | Lu H (2003) Dynamic population strategy assisted particle swarm optimization in multiobjective evolutionary algorithm design. IEEE Neural Network Society, IEEE NNS Student Research Grants 2002, Final reports 2003 |
| [23] | Mishra S (2005) A hybrid least square-fuzzy bacterial foraging strategy for harmonic estimation. IEEE Trans Evol Comput 9(1):61–73 · doi:10.1109/TEVC.2004.840144 |
| [24] | Morse JN (1980) Reducing the size of nondominated set: pruning by clustering. Comput Oper Res 7(1–2):55–66 · doi:10.1016/0305-0548(80)90014-3 |
| [25] | Mostaghim S, Teich J (2003a) Strategies for finding good local guides in multiobjective particle swarm optimization (MOPSO). In: Proceedings of 2003 IEEE swarm intelligence symposium, Indianapolis, IN, USA, April 2003, pp 26–33 |
| [26] | Mostaghim S, Teich J (2003b) The role of {\(\epsilon\)}-dominance in multiobjective particle swarm optimization methods. In: Proceedings of IEEE congress on evolutionary computation CEC’2003, Canberra, Australia, pp 1764–1771 |
| [27] | Mostaghim S, Teich J (2004) Covering pareto-optimal fronts by subswarms in multiobjective particle swarm optimization. In: Proceedings of IEEE congress on evolutionary computation CEC’2004, Portland, Oregon, USA, 19–23 June 2004, pp 1404–1411 |
| [28] | Ozcan E, Mohan C (1998) Analysis of a simple particle swarm optimization system. Intell Eng Syst Artif Neural Netw 8:253–258 |
| [29] | Parsopoulos KE, Vrahatis MN (2002) Particle swarm optimization method in multiobjective problems. In: Proceedings of the ACM 2002 symposium on applied computing (SAC’2002), pp 603–607 |
| [30] | Parsopoulos KE, Tasoulis DK, Vrahatis MN (2004) Multiobjective optimization using parallel vector evaluated particle swarm optimization. In: Proceedings of IASTED international conference on artificial intelligence and applications, as part of the 22nd IASTED international multi-conference on applied informatics, Innsbruck, Austria |
| [31] | Pulido GT, Coello Coello CA (2004) Using clustering techniques to improve the performance of a multi-objective particle swarm optimizer. In: Proceedings of the genetic and evolutionary computation conference, Seattle, Washington, USA, Springer-Verlag, Lecture Notes in Computer Science, vol 3102, June 2004, pp 225–237 |
| [32] | Reyes-Sierra M, Coello CAC (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res 2(3):287–308 |
| [33] | Schaffer JD (1984) Multiobjective optimization with vector evaluated genetic algorithms, PhD Thesis, Vanderbilt University, Nashville, USA |
| [34] | Shi Y, Eberhart R (1998) Parameter selection in particle swarm optimization. In: Proceedings of the 7th annual conference on evolutionary programming, March 1998, pp 591–600 |
| [35] | Song MP, Gu GC (2004) Research on particle swarm optimization: a review. In: Proceedings of the 3rd international conference on machine learning and cybernetics, Shanghai, Chaina, 26–29 August 2004, pp 2236–2241 |
| [36] | Tasgetiren MF, Sevkli M, Liang YC, Gencyilmaz G (2004) Particle swarm optimization algorithm for permutation flowshop sequencing problem. In: Proceedings of the 4th international workshop on ant colony optimization and swarm intelligence, ANTS2004, LNCS 3172. Springer-Verlag, Brussels, Belgium, 5–8 September 2004, pp 382–390 · Zbl 1110.90044 |
| [37] | Wachowiak MP, Smolíková R, Zheng Y, Zurada JM, Elmaghraby AS (2004) An approach to multimodal biomedical image registration utilizing particle swarm optimization. IEEE Trans Evol Comput 8(3):289–301 · doi:10.1109/TEVC.2004.826068 |
| [38] | Zhang Y, Huang S (2004) A novel multiobjective particle swarm optimization for Buoys-arrangement design. In: Proceedings of IEEE/WIC/ACM international conference on intelligent agent technology (IAT 2004), Beijing, China, 20–24 Sept 2004, pp 24–30 |
| [39] | Zitzler E, http://www.tik.ee.ethz.ch/\(\sim\)zitzler/testdata.html . Accessed 19 July 2009 |
| [40] | Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications, Ph.D. Thesis, Swiss Federal Institute of Technology, Zurich |
| [41] | Zitzler E, Thiele L (1998a) An evolutionary algorithm for multiobjective optimization: the strength pareto approach. TIK-Report, No. 43 |
| [42] | Zitzler E, Thiele L (1998b) Multiobjective optimization using evolutionary algorithms–a comparative case study. In: Parallel Problem Solving from Nature V, pp 292–301, Amsterdam, September 1998, Springer-Verlag |
| [43] | Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans Evol Comput 3(4):257–271 · doi:10.1109/4235.797969 |
| [44] | Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195 · doi:10.1162/106365600568202 |
| [45] | Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength pareto evolutionary algorithm. In: Proceedings of EUROGEN 2001, Athens, Greece, September 2001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
