A Lagrangian-ACO matheuristic for car sequencing
Tóm tắt
In this study, we investigate a hybrid Lagrangian relaxation ant colony optimisation for optimisation version of the car sequencing problem. Several cars are required to be scheduled on an assembly line and each car requires a number of options such as sunroof and/or air conditioning. These cars are required to be sequenced such that sub-sequences of specific sizes may only include a limited number of any option. While this is usually a hard constraint, in this study we treat it as a soft constraint and further require the utilisation of options be modulated across the sequence leading to the optimisation problem. We investigate various Lagrangian heuristics, ant colony optimisation (ACO) and hybrids of these methods. The results show that the Lagrangian-ACO hybrid is the best performing method for up to 300 cars.
Tài liệu tham khảo
Abramson D, Giddy J, Kotler L (2000) High performance parametric modeling with Nimrod/G: killer application for the global grid? In: International Parallel and Distributed Processing Symposium (IPDPS). IEEE Computer Society, Washington, DC, USA, pp 520–528
Anghinolfi D, Paolucci M, Sacone S, Siri S (2011) Integer programming and ant colony optimization for planning intermodal freight transportation operations. In: 2011 IEEE Conference on Automation Science and Engineering (CASE), pages 214–219
Anstreicher KM, Wolsey LA (2009) Two “well-known” properties of subgradient optimization. Math Progr 120(1):213–220
Bautista J, Pereira J, Adenso-Díaz B (2008) A beam search approach for the optimization version of the car sequencing problem. Ann Oper Res 159:233–244
Bertsekas DP, Nedić A, Ozdaglar AE (2003) Convex analysis and optimization. Athena Scientific, Cambridge
Blum C (2005) Beam-ACO: hybridizing ant colony optimization with beam search: an application to open shop scheduling. Comput Oper Res 32:1565–1591
Blum C, Blesa M, Roli A, Sampels M (eds) (2008) Hybrid metaheuristics: an emerging approach to optimization. Studies in Computational Intelligence, vol 114. Springer, Berlin
Boschetti M, Maniezzo V (2009) Benders decomposition, Lagrangian relaxation and metaheuristic design. J Heuristics 15(3):283–312
Camazine S, Deneubourg J-L, Franks NR, Sneyd J, Theraulaz G, Bonabeau E (2001) Self-organization in biological systems. Princeton University Press, Princeton
Coello C (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods in Appl Mech Eng 191:1245–1287
Dincbus M, Simonis H, Hentenryck P (1988) Solving the car-sequencing problem in constraint logic programming. In: 8th European Conference on Artificial Intelligence-ECAI 88. Pitmann Publishing, London, pp 290–295
Dorigo M (1992) Optimization, learning and natural algorithms. PhD thesis, Dip. Elettronica
Dorigo M, Stűtzle T (2004) Ant colony optimization. MIT Press, Cambridge
Ernst AT (2010) A hybrid Lagrangian particle swarm optimization algorithm for the degree-constrained minimum spanning tree problem. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC 2010, Barcelona. IEEE, pp 1–8
Fisher M (2004) The Lagrangian relaxation method for solving integer programming problems. Manag Sci 50(12):1861–1871
Gent I (1998) Two results on car sequencing problems. Technical Report APES02. University of St. Andrews, St. Andrews, UK
Gent I, Walsh T (1999) CSPLIB: a benchmark library for constraints. Technical Report APES-09-1999. University of St. Andrews, St. Andrews, UK
Glover FW, Kochenberger GA (eds) Handbook of metaheuristics, International series in operations research and management science, vol 57. Springer, Berlin
Gottlieb J, Puchta M, Solnon C (2003) A study of greedy, local search and ACO for car sequencing problems. Lect Notes Comput Sci 2611:245–282
Gravel M, Gagné C, Price W (2004) Review and comparison of three methods for the solution of the car-sequencing problem. J Oper Res Soc 56:1287–1295
Hentenryck P, Simonis H, Dincbus M (1992) Constraint satisfaction using constraint logic programming. Artif Intell 58:113–159
Khichane M, Albert P, Solnon C (2008) CP with ACO. Lect Notes Comput Sci 5015:328–332
Kis T (2004) On the complexity of the car sequencing problem. Oper Res Lett 32:331–335
López-Ibáñez M, Blum C, Thiruvady D, Ernst AT, Meyer B (2009) Beam-ACO based on stochastic sampling for makespan optimization concerning the TSP with time windows. Lect Notes Comput Sci 5482:97–108
Maniezzo V, Boschetti M, Jelasity M (2004) An ant approach to membership overlay design. In: Dorigo M, Birattari M, Blum C, Gambardella LM, Mondada F, Stntzle T (eds) Ant colony optimization and swarm intelligence, vol 3172., Lecture Notes in Computer ScienceSpringer, Berlin, pp 37–48
Maniezzo V, Stützle T, Voß S (eds) Matheuristics—hybridizing metaheuristics and mathematical programming, Annals of information systems, vol 10. Springer, Berlin
Marriott K, Stuckey P (1998) Programming with constraints. MIT Press, Cambridge
Meyer B, Ernst A (2004) Integrating ACO and constraint propagation. Lecture notes in computer science: ant colony, optimization and swarm intelligence, vol 3172, pp 166–177
Gurobi Optimization (2010) Gurobi optimizer version 5.0. Available from: http://www.gurobi.com/
Parrello B, Kebat W, Wos L (1986) Job-shop scheduling using automated reasoning: a case study of the car sequencing problem. J Autom Reason 2:1–42
Perron L, Shaw P (2004) Combining forces to solve the car sequencing problem. In: CPAIOR-04, vol 3011. Springer, Berlin, pp 225–239
Puchinger J, Raidl GR (2004) An evolutionary algorithm for column generation in integer programming: an effective approach for 2D bin packing. Lect Notes Comput Sci 3242:642–651
Puchinger J, Raidl GR (2005) Combining metaheuristics and exact algorithms in combinatorial optimization: a survey and classification. Lect Notes Comput Sci 3562:41–53
Ren Z-G, Feng Z-R, Zhang A-M (2012) Fusing ant colony optimization with Lagrangian relaxation for the multiple-choice multidimensional knapsack problem. Inf. Sci. 182(1):15–29
Solnon C, Dat V, Cung A, Nguyen, Artigues C (2008) The car sequencing problem: overview of state-of-the-art methods and industrial case-study of the ROADEF’2005 challenge problem. Eur J Oper Res 191:912–927
Thiruvady D (2012) Hybrids of stochastic metaheuristics and constraint programming for combinatorial optimization. PhD thesis, Calyton School of Information Technology
Thiruvady D, Blum C, Meyer B, Ernst AT (2009) Hybridizing beam-ACO with constraint programming for single machine job scheduling. Lect Notes Comput Sci 5818:30–44
Thiruvady D, Singh G, Ernst AT, Meyer B (2012) Constraint-based ACO for a shared resource constrained scheduling problem. Int J Prod Econ 141(1):230–242
Thiruvady DR, Meyer B, Ernst AT (2011) Car sequencing with constraint-based ACO. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, GECCO ’11. ACM, New York, pp 163–170
Valente JMS, Alves RAFS (2008) Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups. Comput Oper Res 35(7):2388–2405