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A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables

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Abstract

This paper presents a new multi-objective optimization algorithm called FC-MOPSO for optimal design of engineering problems with a small number of function evaluations. The proposed algorithm expands the main idea of the single-objective particle swarm optimization (PSO) algorithm to deal with constrained and unconstrained multi-objective problems (MOPs). FC-MOPSO employs an effective procedure in selection of the leader for each particle to ensure both diversity and fast convergence. Fifteen benchmark problems with continuous design variables are used to validate the performance of the proposed algorithm. Finally, a modified version of FC-MOPSO is introduced for handling discrete optimization problems. Its performance is demonstrated by optimizing five space truss structures. It is shown that the FC-MOPSO can effectively find acceptable approximations of Pareto fronts for structural MOPs within very limited number of function evaluations.

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References

  • Adeli H, Kamal O (1986) Efficient optimization of space trusses. Comput Struct 24:501–511. doi:10.1016/0045-7949(86)90327-5

    Article  MATH  Google Scholar 

  • AISC A (1989) Manual of steel construction-allowable stress design. American Institute of Steel Construction (AISC), Chicago

    Google Scholar 

  • Chafekar D, Shi L, Rasheed K, Xuan J (2005) Multiobjective GA optimization using reduced models. IEEE Trans Syst Man Cybern Part C Appl Rev 35:261–265. doi:10.1109/TSMCC.2004.841905

    Article  Google Scholar 

  • Chen J, Chen G, Guo W (2009) A discrete PSO for multi-objective optimization in VLSI floorplanning. In: Cai Z, Li Z, Kang Z, Liu Y (eds) Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics). Springer, Berlin Heidelberg, pp 400–410

    Google Scholar 

  • Chowdhury S, Tong W, Messac A, Zhang J (2013) A mixed-discrete particle swarm optimization algorithm with explicit diversity-preservation. Struct Multidiscip Optim 47:367–388. doi:10.1007/s00158-012-0851-z

    Article  MathSciNet  MATH  Google Scholar 

  • Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6:58–73. doi:10.1109/4235.985692

    Article  Google Scholar 

  • Coello Coello CA, Lechuga MS (2002) MOPSO: A proposal for multiple objective particle swarm optimization. In: Proceedings of the 2002 Congress on Evolutionary Computation, CEC 2002. IEEE, pp 1051–1056

  • Coello Coello C, Lamont GB, van Veldhuizen DA (2007) Evolutionary algorithms for solving multi-objective problems. Springer US, Boston

    MATH  Google Scholar 

  • Davarynejad M, Rezaei J, Vrancken J, et al (2011) Accelerating convergence towards the optimal pareto front. In: 2011 I.E. Congress of Evolutionary Computation, CEC 2011. IEEE, pp 2107–2114

  • Deb K, Deb D (2014) Analysing mutation schemes for real-parameter genetic algorithms. Int J Artif Intell Soft Comput 4:1. doi:10.1504/IJAISC.2014.059280

    Article  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197. doi:10.1109/4235.996017

    Article  Google Scholar 

  • Deb K, Pratap A, Meyarivan T (2001) Constrained test problems for multi-objective evolutionary optimization. In: Zitzler E, Thiele L, Deb K et al (eds) Evolutionary multi-criterion optimization. Springer, Berlin Heidelberg, pp 284–298

    Chapter  Google Scholar 

  • Durillo JJ, Nebro AJ (2011) jMetal: A Java framework for multi-objective optimization. Adv Eng Softw 42:760–771. doi:10.1016/j.advengsoft.2011.05.014

    Article  Google Scholar 

  • Erbatur F, Hasançebi O, Tütüncü İ, Kılıç H (2000) Optimal design of planar and space structures with genetic algorithms. Comput Struct 75:209–224. doi:10.1016/S0045-7949(99)00084-X

    Article  Google Scholar 

  • Eskandari H, Geiger CD (2008) A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems. J Heuristics 14:203–241. doi:10.1007/s10732-007-9037-z

    Article  MATH  Google Scholar 

  • Fonseca CM, Knowles JD, Thiele L, Zitzler E (2005) A tutorial on the performance assessment of stochastic multiobjective optimizers. In: Third International Conference on Evolutionary Multi-Criterion Optimization (EMO 2005). p 240

  • Gholizadeh S (2013) Layout optimization of truss structures by hybridizing cellular automata and particle swarm optimization. Comput Struct 125:86–99. doi:10.1016/j.compstruc.2013.04.024

    Article  Google Scholar 

  • Goldberg DE, Richardson J (1987) Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the Second International Conference on Genetic Algorithms on Genetic Algorithms and Their Application. L. Erlbaum Associates Inc., Hillsdale, NJ, USA, pp 41–49

  • Golinski J (1970) Optimal synthesis problems solved by means of nonlinear programming and random methods. J Mech 5:287–309. doi:10.1016/0022-2569(70)90064-9

    Article  Google Scholar 

  • Gong Y, Xue Y, Xu L (2013) Optimal capacity design of eccentrically braced steel frameworks using nonlinear response history analysis. Eng Struct 48:28–36. doi:10.1016/j.engstruct.2012.10.001

    Article  Google Scholar 

  • Jansen PW, Perez RE (2011) Constrained structural design optimization via a parallel augmented Lagrangian particle swarm optimization approach. Comput Struct 89:1352–1366. doi:10.1016/j.compstruc.2011.03.011

    Article  Google Scholar 

  • Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks. IEEE, pp 1942–1948

  • Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. In: 1997 I.E. International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation. IEEE, pp 4104–4108

  • Kurpati A, Azarm S, Wu J (2002) Constraint handling improvements for multiobjective genetic algorithms. Struct Multidiscip Optim 23:204–213. doi:10.1007/s00158-002-0178-2

    Article  Google Scholar 

  • Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798. doi:10.1016/j.compstruc.2004.01.002

    Article  Google Scholar 

  • Luh GC, Chueh CH (2004) Multi-objective optimal design of truss structure with immune algorithm. Comput Struct 82:829–844. doi:10.1016/j.compstruc.2004.03.003

    Article  MathSciNet  Google Scholar 

  • Mortazavi A, Toğan V (2016) Simultaneous size, shape, and topology optimization of truss structures using integrated particle swarm optimizer. Struct Multidiscip Optim 54:715–736. doi:10.1007/s00158-016-1449-7

    Article  MathSciNet  Google Scholar 

  • Nebro AJ, Durillo JJ, Nieto G, et al (2009) SMPSO: A new pso-based metaheuristic for multi-objective optimization. In: 2009 I.E. Symposium on Computational Intelligence in Multi-Criteria Decision-Making, MCDM 2009 - Proceedings. IEEE, pp 66–73

  • Paya I, Yepes V, González-Vidosa F, Hospitaler A (2008) Multiobjective optimization of concrete frames by simulated annealing. Comput Civ Infrastruct Eng 23:596–610. doi:10.1111/j.1467-8667.2008.00561.x

    Article  MATH  Google Scholar 

  • Ray T, Kang T, Kian Chye S (2001) Multiobjective design optimization by an evolutionary algorithm. Eng Optim 33:399–424. doi:10.1080/03052150108940926

    Article  Google Scholar 

  • Reyes-Sierra M, Coello Coello CA (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intell Res 2:287–308

    MathSciNet  Google Scholar 

  • Santana-Quintero LV, Montaño AA, Coello Coello CA (2010) A review of techniques for handling expensive functions in evolutionary multi-objective optimization. In: Tenne Y, Goh C-K (eds) Computational intelligence in expensive optimization problems. Springer, Berlin Heidelberg, pp 29–59

    Chapter  Google Scholar 

  • Sierra MR, Coello Coello CA (2005) Improving PSO-based multi-objective optimization using crowding, mutation and ∈−dominance. In: Coello Coello CA, Hernández Aguirre A, Zitzler E (eds) Evolutionary multi-criterion optimization: Third International Conference, EMO 2005, Guanajuato, Mexico, March 9–11, 2005, Proceedings. Springer, Berlin Heidelberg, pp 505–519

    Chapter  Google Scholar 

  • Simon D (2013) Evolutionary optimization algorithms. John Wiley & Sons, Hoboken

    Google Scholar 

  • Soh CK, Yang J (1996) Fuzzy controlled genetic algorithm search for shape optimization. J Comput Civ Eng 10:143–150. doi:10.1061/(ASCE)0887-3801(1996)10:2(143)

    Article  Google Scholar 

  • Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2:221–248. doi:10.1162/evco.1994.2.3.221

    Article  Google Scholar 

  • Talatahari S, Kaveh A, Sheikholeslami R (2012) Chaotic imperialist competitive algorithm for optimum design of truss structures. Struct Multidiscip Optim 46:355–367. doi:10.1007/s00158-011-0754-4

    Article  Google Scholar 

  • Tanaka M, Watanabe H, Furukawa Y, Tanino T (1995) GA-based decision support system for multicriteria optimization. In: IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century. IEEE, pp 1556–1561 vol. 2

  • Tong W, Chowdhury S, Messac A (2016) A multi-objective mixed-discrete particle swarm optimization with multi-domain diversity preservation. Struct Multidiscip Optim 53:471–488. doi:10.1007/s00158-015-1319-8

    Article  MathSciNet  Google Scholar 

  • Yan J, Li C, Wang Z, et al (2007) Diversity metrics in multi-objective optimization: Review and perspective. In: IEEE ICIT 2007–2007 I.E. International Conference on Integration Technology. IEEE, pp 553–557

  • Yen GG (2009) An adaptive penalty function for handling constraint in multi-objective evolutionary optimization. In: Mezura-Montes E (ed) Constraint-handling in evolutionary optimization. Springer, Berlin, Heidelberg, pp 121–143

    Chapter  Google Scholar 

  • Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8:173–195. doi:10.1162/106365600568202

    Article  Google Scholar 

  • Zitzler E, Laumanns M, Thiele L (2002) SPEA2: Improving the strength pareto evolutionary algorithm. In: Giannakoglou K, Tsahalis D, Periaux P, et al (eds) Evolutionary methods for design, optimization and control with applications to industrial problems. CIMNE, Barcelona, pp 95–100

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, School of Engineering, Shiraz University, Shiraz, Fars, Iran

    Vahid Mokarram & Mohammad Reza Banan

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  1. Vahid Mokarram
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  2. Mohammad Reza Banan
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Correspondence to Mohammad Reza Banan.

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Mokarram, V., Banan, M.R. A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables. Struct Multidisc Optim 57, 509–533 (2018). https://doi.org/10.1007/s00158-017-1764-7

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  • DOI: https://doi.org/10.1007/s00158-017-1764-7

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