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Multi-directional local search. (English) Zbl 1349.90751
Summary: This paper introduces multi-directional local search, a metaheuristic for multi-objective optimization. We first motivate the method and present an algorithmic framework for it. We then apply it to several known multi-objective problems such as the multi-objective multi-dimensional knapsack problem, the bi-objective set packing problem and the bi-objective orienteering problem. Experimental results show that our method systematically provides solution sets of comparable quality with state-of-the-art methods applied to benchmark instances of these problems, within reasonable CPU effort. We conclude that the proposed algorithmic framework is a viable option when solving multi-objective optimization problems.

90C29 Multi-objective and goal programming
90C27 Combinatorial optimization
Full Text: DOI
[1] João Alves, M.; Almeida, M., MOTGA: a multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem, Computers & operations research, 34, 3458-3470, (2007) · Zbl 1127.90059
[2] Alves, M.J.; Climaco, J., An interactive method for 0-1 multiobjective problems using simulated annealing and tabu search, Journal of heuristics, 6, 385-403, (2000) · Zbl 1071.90561
[3] Bazgan, C.; Hugot, H.; Vanderpooten, D., Solving efficiently the 0-1 multi-objective knapsack problem, Computers & operations research, 36, 260-279, (2009) · Zbl 1175.90323
[4] Bérubé, J.F.; Gendreau, M.; Potvin, J.Y., An exact epsilon-constraint method for bi-objective combinatorial optimization problems: application to the traveling salesman problem with profits, European journal of operational research, 194, 39-50, (2009) · Zbl 1179.90274
[5] Branke, J.; Greco, S.; Slowínski, R.; Zielniewicz, P., Interactive evolutionary multiobjective optimization using robust ordinal regression, (), 554-568 · Zbl 1428.90148
[6] Chao IM. Algorithms and solutions to multi-level vehicle routing problems. PhD thesis. College Park, MD, USA. Chairman-Bruce L. Golden; 1993.
[7] Chao, I.M.; Golden, B.L.; Wasil, E.A., A fast and effective heuristic for the orienteering problem, European journal of operational research, 88, 475-489, (1996) · Zbl 0911.90146
[8] Coello, C.A.C.; Christiansen, A.D., Two new GA-based methods for multiobjective optimization, Civil engineering and environmental systems, 15, 207-243, (1998)
[9] Coello Coello, A.; Van Veldhuizen, D.; Lamont, G., Evolutionary algorithms for solving multi-objective problems, (2002), Kluwer Academic Publishers · Zbl 1130.90002
[10] Czyzak, P.; Jaszkiewicz, A., Pareto simulated annealing—a metaheuristic technique for multiple-objective combinatorial optimization, Journal of multi-criteria decision analysis, 7, 34-47, (1998) · Zbl 0904.90146
[11] Da Fonseca VG, Fonseca CM, Hall AO. Inferential performance assessment of stochastic optimisers and the attainment function. In: First international conference on evolutionary multi-criterion optimization. Springer-Verlag; 2001. p. 213-25.
[12] Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T., A fast and elitist multi-objective genetic algorithm: NSGA II, IEEE transactions on evolutionary computation, 6, 182-197, (2002)
[13] Delorme X. Modélisation et résolution de problèmes liés à l’exploitation d’infrastructures ferroviaires. PhD thesis. Université de Valenciennes et du Hainaut Cambrésis [in French]; 2003.
[14] Delorme, X.; Gandibleux, X.; Degoutin, F., Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem, European journal of operational research, 204, 206-217, (2010) · Zbl 1178.90303
[15] Doerner, K.F.; Gutjahr, W.J.; Hartl, R.F.; Strauss, C.; Stummer, C., Pareto ant colony optimization: a metaheuristic approach to multiobjective portfolio selection, Annals of operations research, 131, 79-99, (2004) · Zbl 1067.91028
[16] Escudero, L.; Landete, M.; Marín, A., A branch-and-cut algorithm for the winner determination problem, Decision support systems, 46, 649-659, (2009)
[17] Festa, P.; Resende, M., GRASP: an annotated bibliography, (), 325-367 · Zbl 1017.90001
[18] Figueira, J.R.; Greco, S.; Slowínski, R., Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method, European journal of operational research, 195, 460-486, (2009) · Zbl 1159.91341
[19] Florios, K.; Mavrotas, G.; Diakoulaki, D., Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms, European journal of operational research, 203, 14-21, (2010) · Zbl 1177.90341
[20] Fonseca C, Paquete L, López-Ibáñez M. An improved dimension-sweep algorithm for the hypervolume indicator. In: IEEE congress on evolutionary computation; 2006. p. 1157-63.
[21] Fonseca CM, Fleming PJ. Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Genetic algorithms: proceedings of the fifth international conference; 1993. p. 416-23.
[22] Framinan, J.; Leisten, R., A multi-objective iterated greedy search for flowshop scheduling with makespan and flowtime criteria, OR spectrum, 30, 787-804, (2008) · Zbl 1193.90099
[23] Gandibleux, X.; Fréville, A., Tabu search based procedure for solving the 0-1 multiobjective knapsack problem: the two objectives case, Journal of heuristics, 6, 361-383, (2000) · Zbl 0969.90079
[24] Gandibleux, X.; Mezdaoui, N.; Fréville, A., A tabu search procedure to solve multiobjective combinatorial optimization problems, (), 103-108
[25] Glover, F.; Laguna, M., Tabu search, (1997), Kluwer Norwell · Zbl 0930.90083
[26] Hapke, M.; Jaszkiewicz, A.; Slowinski, R., Pareto simulated annealing for fuzzy multi-objective combinatorial optimization, Journal of heuristics, 6, 329-345, (2000) · Zbl 1071.90588
[27] Hoos, H.; Stützle, T., Stochastic local search: foundations & applications, (2004), Elsevier/Morgan Kaufmann San Francisco, CA, USA · Zbl 1126.68032
[28] Jaszkiewicz, A., On the performance of multiple-objective genetic local search on the 0/1 knapsack problem—a comparative experiment, IEEE transactions on evolutionary computation, 6, 402-412, (2002)
[29] Jaszkiewicz, A.; Branke, J., Interactive multiobjective evolutionary algorithms, (), 179-193
[30] Jaszkiewicz, A.; Ferhat, A.B., Solving multiple criteria problems by interactive trichotomy segmentation, European journal of operational research, 113, 271-280, (1999) · Zbl 0938.90037
[31] Khare, V.; Yao, X.; Deb, K., Performance scaling of multi-objective evolutionary algorithms, (), 376-390 · Zbl 1036.90541
[32] Knowles, J.; Corne, D., Approximating the nondominated front using the Pareto archived evolution strategy, Evolutionary computation, 8, 149-172, (2000)
[33] Knowles J, Thiele L, Zitzler E. A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical report TIK-report no. 214. Computer engineering and Networks Laboratory, ETH Zurich; 2006.
[34] Laumanns, M.; Thiele, L.; Zitzler, E., An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method, European journal of operational research, 169, 932-942, (2006) · Zbl 1079.90122
[35] Lusby R, Larsen J, Ryan D, Ehrgott M. Routing trains through railway junctions: a new set packing approach. Technical report. Informatics and Mathematical Modelling, Technical University of Denmark, DTU; 2006.
[36] Mavrotas, G.; Diakoulaki, D., A branch and bound algorithm for mixed zero-one multiple objective linear programming, European journal of operational research, 107, 530-541, (1998) · Zbl 0943.90063
[37] Minella, G.; Ruiz, R.; Ciavotta, M., Restarted iterated Pareto greedy algorithm for multi-objective flowshop scheduling problems, Computers & operations research, 38, 1521-1533, (2011)
[38] Mostaghim, S.; Teich, J., Quad-trees: a data structure for storing Pareto sets in multiobjective evolutionary algorithms with elitism, (), 81-104, [Advanced information and knowledge processing] · Zbl 1079.90124
[39] Paquete, L.; Chiarandini, M.; Stützle, T., Pareto local optimum sets in the biobjective traveling salesman problem: an experimental study, Lecture notes in economics and mathematical systems: metaheuristics for multiobjective optimization, vol. 535, 177-200, (2004) · Zbl 1070.90102
[40] Paquete, L.; Schiavinotto, T.; Stützle, T., On local optima in multiobjective combinatorial optimization problems, Annals of operations research, 156, 83-97, (2007) · Zbl 1145.90067
[41] Parragh, S.N.; Doerner, K.F.; Gandibleux, X.; Hartl, R.F., A heuristic two-phase solution method for the multi-objective dial-a-ride problem, Networks, 54, 227-242, (2009) · Zbl 1204.90096
[42] Pisinger, D.; Ropke, S., A general heuristic for vehicle routing problems, Computers & operations research, 34, 2403-2435, (2007) · Zbl 1144.90318
[43] Pisinger, D.; Ropke, S., Large neighborhood search, (), 399-419
[44] Ropke, S.; Pisinger, D., An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows, Transportation science, 40, 455-472, (2006)
[45] Schaffer, J., Multiple objective optimization with vector evaluated genetic algorithms, (), 93-100 · Zbl 0676.68047
[46] Schilde, M.; Doerner, K.F.; Hartl, R.F.; Kiechle, G., Metaheuristics for the bi-objective orienteering problem, Swarm intelligence, 3, 179-201, (2009)
[47] Schrimpf, G.; Schneider, J.; Stamm-Wilbrandt, H.; Dueck, G., Record breaking optimization results using the ruin and recreate principle, Journal of computational physics, 159, 139-171, (2000) · Zbl 0997.90105
[48] Shaw P. Using constraint programming and local search methods to solve vehicle routing problems. In: Principles and practice of constraint programming CP98. Springer-Verlag; 1998. p. 417-31.
[49] Srinivas, K., Multiobjective optimization using non-dominated sorting in genetic algorithms, Evolutionary computation, 2, 221-248, (1994)
[50] Tricoire, F.; Romauch, M.; Doerner, K.F.; Hartl, R.F., Heuristics for the multi-period orienteering problem with multiple time windows, Computers & operations research, 37, 351-367, (2010) · Zbl 1175.90212
[51] Tsiligirides, T., Heuristic methods applied to orienteering, The journal of the operational research society, 35, 797-809, (1984)
[52] Ulungu, E.; Teghem, J.; Fortemps, P.; Tuyttens, D., MOSA method: a tool for solving multiobjective combinatorial optimization problems, Journal of multi-criteria decision analysis, 8, 221-236, (1999) · Zbl 0935.90034
[53] Ulungu, E.L.; Teghem, J.; Fortemps, P., Heuristics for multiobjective combinatorial optimization by simulated annealing, (), 228-238
[54] Van Veldhuizen, D.; Lamont, G., Multiobjective evolutionary algorithms: analyzing the state-of-the-art, Evolutionary computation, 8, 125-147, (2000)
[55] Varadharajan, T.; Rajendran, C., A multi-objective simulated-annealing algorithm for scheduling in flowshops to minimize the makespan and total flowtime of jobs, European journal of operational research, 167, 772-795, (2005) · Zbl 1154.90499
[56] Zhang, Q.; Li, H., MOEA/D: a multiobjective evolutionary algorithm based on decomposition, IEEE transactions on evolutionary computation, 11, 712-731, (2007)
[57] Zitzler E, Laumanns M, Thiele L. Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Evolutionary methods for design, optimisation, and control, CIMNE, Barcelona, Spain; 2002. p. 95-100.
[58] Zitzler, E.; Thiele, L., Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach, IEEE transactions on evolutionary computation, 3, 257-271, (1999)
[59] Zitzler, E.; Thiele, L.; Laumanns, M., Performance assessment of multiobjective optimizers: an analysis and review, IEEE transactions on evolutionary computation, 7, 117-132, (2002)
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