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Proposal of a nonlinear multi-objective genetic algorithm using conic scalarization to the design of cellular manufacturing systems

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Abstract

This paper presents a nonlinear multi-objective mathematical model to obtain quality solutions for design problems of cellular manufacturing systems. The objectives of the multi-objective model are, simultaneously, (1) to minimize the number of exceptional elements among manufacturing cells, (2) to minimize the number of voids in a cell, and (3) to minimize cell load variation. In this paper, a new multi-objective genetic algorithm (GA) approach has been proposed to solve the multi-objective problem. In contrast to existing GA approaches, this GA approach contains some revised genetic operators and uses a conic scalarization method to convert the mathematical model’s objectives in a single objective function. This approach has been tested and compared with two test problems and some source models collected from the literature. The results have shown that the problem-solving performance of the proposed multi-objective approach is at least as good as the existing approaches in designing the cellular system, and in many cases better than them.

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References

  • Abido MA (2007) Two-level of nondominated solutions approach to multiobjective particle swarm optimization. In Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, pp 726–733

  • Arkat J, Hosseini L, Farahani MH (2011) Minimization of exceptional elements and voids in the cell formation problem using a multi-objective genetic algorithm. Expert Syst Appl 38:9597–9602

    Article  Google Scholar 

  • Askin RG, Subramanian SP (1987) A cost based heuristic for GT configuration. Int J Prod Res 25:101–113

  • Ballakur A, Steudel HJ (1987) A within-cell based heuristic for designing cellular manufacturing systems. Int J Prod Res 25:639–665

    Article  Google Scholar 

  • Bazaraa MS, Sherali HD, Shetty CM (1993) Nonlinear Programming: Theory and Algorithms. John Wiley & Sons Inc, New York

    MATH  Google Scholar 

  • Carrie AS (1973) Numerical taxonomy applied to group technology and plant layout. Int J Prod Res 11(4):399–416

  • Chan FTS, Lau KW, Chan LY, Lo VHY (2008) Cell formation problem with consideration of both intracellular and intercellular movements. Int J Prod Res 46(10):2589–2620

    Article  MATH  Google Scholar 

  • Chen M (1998) A mathematical programming model for system reconfiguration in a dynamic cellular manufacturing environment. Ann Oper Res 77:109–128

    Article  MATH  Google Scholar 

  • Ehrgott M (2005) Multicriteria optimization. Springer, Berlin

    MATH  Google Scholar 

  • Ehrgott M, Waters C, Kasimbeyli R, Ustun O (2009) Multiobjective programming and multiattribute utility functions in portfolio optimization. INFOR 47:31–42

    MathSciNet  Google Scholar 

  • El-Baz AM (2004) A genetic algorithm for facility layout problems of different manufacturing environments. Comput Ind Eng 47:233–246

    Article  Google Scholar 

  • Gasimov RN (2001) Characterization of the Benson proper efficiency and scalarization in nonconvex vector optimization. In: Koksalan M, Zionts S (eds) Multiple Criteria Decision Making in the New Millennium Lecture Notes in Economics and Mathematical Systems. Springer, Berlin, pp 189–198

    Chapter  Google Scholar 

  • Gasimov RN, Sipahioglu A, Sarac T (2007) A multi-objective programming approach to 1.5-dimensional assortment problem. Eur J Oper Res 179:64–79

    Article  MATH  Google Scholar 

  • Goldberg DE (1989) Genetic algorithms: Search, optimization & machine learning. Addison-Wesley, MA

    MATH  Google Scholar 

  • Goncalves J, Resende M (2004) An evolutionary algorithm for manufacturing cell formation. Comput Ind Eng 47:247–273

  • Holland JH (1975) Adaptation in Natural and Artificial System. Univ. of Michigan Press, Ann Arbor

    Google Scholar 

  • Hsu CM, Su CT (1998) Multi-objective machine-component grouping in cellular manufacturing: a genetic algorithm. Prod Plan Control 9(2):155–166

    Article  MathSciNet  Google Scholar 

  • Javadian N, Rezaeian J, Mali Y (2007) Multi-objective cellular manufacturing system under machines with different life-cycle using genetic algorithm. Eng Technol 30:247–251

    Google Scholar 

  • Jeon G, Leep HR, Parsaei HR, Wong JP (1998) Part family formation based on alternative routes during machine failure. J Comput Ind Eng 35(1–2):73–76

    Article  Google Scholar 

  • Kasimbeyli RA (2010) Nonlinear cone separation theorem and scalarization in nonconvex vector optimization. SIAM J Optim 20:1591–1619

    Article  MathSciNet  Google Scholar 

  • Kasimbeyli R (2011) Computing efficient solutions of nonconvex multi-objective problems via scalarization. Proceedings of the 11th WSEAS International Conference on Signal Processing, Computational Geometry and Artificial Vision, pp 193–198

  • Kasimbeyli R (2013) A conic scalarization method in multi-objective optimization. J Global Optim 56:279–297

    Article  MATH  MathSciNet  Google Scholar 

  • Kaya Y, Uyar M, Tekin R (2011) A novel crossover operator for genetic algorithms: ring crossover. CoRR abs/1105.0355

  • Kharbat F, Bull L, Odeh M (2005) Revisiting genetic selection in the XCS learning classifier system. Evol Comput 3:2061–2068

    Google Scholar 

  • Kor H, Iranmanesh H, Haleh H, Hatefi SM (2009) A multi-objective genetic algorithm for optimization of cellular manufacturing system. Int Conf Comput Eng Technol 2009:252–256

    Google Scholar 

  • Kusiak A (1987) The generalized group technology concept. Int J Prod Res 25:561–569

  • Mahdavi I, Paydar MM, Solimanpur M, Heidarzade A (2009) Genetic algorithm approach for solving a cell formation problem in cellular manufacturing. Expert Syst Appl 36:6598–6604

    Article  Google Scholar 

  • Malakooti B, Yang Z (2002) Multiple criteria approach and generation of efficient alternatives for machine-part family formation in group technology. IIE Trans 34:837–846

    Google Scholar 

  • Moghaddam RT, Ranjbar-Bourani M, Amin GR, Siadat A (2012) A cell formation problem considering machine utilization and alternative process routes by scatter search. J Intell Manuf 23:1127–1139

    Article  Google Scholar 

  • Nagi R, Harhalakis G, Proth JM (1990) Multiple routing and capacity considerations in group technology applications. Int J Prod Res 28(12):2243–2257

  • Onwubolu GC, Mutingi M (2001) A genetic algorithm approach to cellular manufacturing systems. Comput Ind Eng 39:125–144

    Article  Google Scholar 

  • Sankaran S, Kasilingam RG (1990) An integrated approach to cell formation and part routing in group technology manufacturing systems. Eng Optimiz 16:235–245

  • Sayers W (2009) Genetic algorithms and neural networks. Faculty of Advanced Technology 3:24–25

  • Sofianopoulou S (1999) Manufacturing cells design with alternative process plans and/or replicate machines. Int J Prod Res 37(3):707–720

  • Solimanpur M, Karman MA (2010) Solving facilities location problem in the presence of alternative processing routes using a genetic algorithm. Comput Ind Eng 59:830–839

    Article  Google Scholar 

  • Solimanpur M, Vrat P, Shankar R (2004) A multi-objective genetic algorithm approach to the design of cellular manufacturing systems. Int J Prod Res 42(7):1419–1441

    Article  MATH  Google Scholar 

  • Spiliopoulos K, Sofianopoulou S (2007) Manufacturing cells design with alternative routings in generalized group technology: reducing the complexity of the solution space. Int J Prod Res 45(6):1355–1367

  • Ustun O, Kasimbeyli R (2012) Combined forecasts in portfolio optimization: ageneralized approach. Comput Oper Res 39:805–819

    Article  MATH  MathSciNet  Google Scholar 

  • Venugopal V, Narendran TT (1992) A genetic algorithm approach to the machining grouping problem with multiple objectives. Comput Ind Eng 22(4):469–480

  • Wang X, Tang J, Gong J, Chen M (2008) A nonlinear multi-objective mathematical model of dynamic cell formation. Chin Control Decis Conf IEEE 2008:991–998

    Google Scholar 

  • Wierzbicki AP (1980) The use of reference objectives in multiobjective optimization. In: Fandel G, Gal T (eds) Multiple criteria decision making: theory and applications. Lecture notes in economics and mathematical systems, vol. 177. Springer, Berlin, pp. 468–486

  • Won Y, Kim S (1997) Multiple criteria clustering algorithm for solving the group technology problem with multiple process routings. Comput Ind Eng 32(1):207–220

  • Wu TH, Chen JF, Yeh JY (2004) A decomposition approach to the cell formation problem with alternative process plans. Int J Adv Manuf Technol 24:834–840

    Article  Google Scholar 

  • Wu X, Chu CH, Wang Y, Yan W (2007) A genetic algorithm for cellular manufacturing design and layout. Eur J Oper Res 181:156–167

    Article  MATH  Google Scholar 

  • Yalcin GD, Erginel N (2011) Determining weights in multi-objective linear programming under fuzziness. Proceedings of the World Congress on Engineering Vol. II WCE 2011, July 6–8, London, UK

  • Yasuda K, Hu L, Yin Y (2005) A grouping genetic algorithm for the multi-objective cell formation problem. Int J Prod Res 43(4):829–853

    Article  Google Scholar 

  • Zhao C, Wu Z (2000) A genetic algorithm for manufacturing cell formation with multiple routes and multiple objectives. Int J Prod Res 38(2):385–395

    Article  MATH  Google Scholar 

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Correspondence to İhsan Erozan.

Appendices

Appendix 1

See Fig. 6.

Fig. 6
figure 6

An example for an unfeasible solution of a system with three cells

Appendix 2

See Table 6.

Table 6 Test problem-A

Appendix 3

See Table 7.

Table 7 Test problem-B

Appendix 4

See Table 8.

Table 8 The interaction with decision maker(s) for Sankaran’s problem. Population Size: 30, Crossover Rate: 0.9, Mutation Rate: 0.004, Number of Generations: 30

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Erozan, İ., Torkul, O. & Ustun, O. Proposal of a nonlinear multi-objective genetic algorithm using conic scalarization to the design of cellular manufacturing systems. Flex Serv Manuf J 27, 30–57 (2015). https://doi.org/10.1007/s10696-014-9194-y

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