Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms

European Journal of Operational Research

Volumn 203, Issue 1, 2010, Pages 14-21

  Florios, Kostas ^a   Mavrotas, George ^a   Diakoulaki, Danae ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Branch and bound; Evolutionary algorithms; Knapsack problem; Multiobjective

Indexed keywords

ADAPTIVE PARAMETERS; APPROXIMATE ALGORITHMS; BRANCH AND BOUND; BRANCH AND BOUNDS; BRANCHING HEURISTICS; CONSTRAINT METHODS; DATA SETS; DEGREE OF APPROXIMATION; EPSILON-CONSTRAINT METHOD; EXACT ALGORITHMS; GENERAL PURPOSE; KNAPSACK PROBLEM; KNAPSACK PROBLEMS; META HEURISTICS; MULTI OBJECTIVE EVOLUTIONARY ALGORITHMS; MULTI-CONSTRAINTS; MULTI-CRITERIA; MULTIOBJECTIVE; NSGA-II; OBJECTIVE FUNCTIONS; OPERATIONAL RESEARCH; PARETO FRONT; SPECIFIC PROBLEMS;

ADAPTIVE ALGORITHMS; APPROXIMATION ALGORITHMS; HEURISTIC METHODS; INTEGER PROGRAMMING; LINEAR PROGRAMMING; MULTIOBJECTIVE OPTIMIZATION;

EVOLUTIONARY ALGORITHMS;

EID: 70350574016     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2009.06.024     Document Type: Article

References (40)

1. Alves M.J., and Almeida M. MOTGA: A multiobjective Tchebycheff based genetic algorithm for the multidimensional knapsack problem. Computers and Operations Research 34 (2007) 3458-3470
2. Alves M.J., and Clímaco J. A review of interactive methods for multiobjective integer and mixed-integer programming. European Journal of Operational Research 180 (2007) 99-115
3. Bazgan C., Hugot H., and Vanderpooten D. Solving efficiently the 0-1 multi-objective knapsack problem. Computers and Operations Research 36 (2009) 260-279
4. Bazgan C., Hugot H., and Vanderpooten D. Implementing an efficient fptas for the 0-1 multi-objective knapsack problem. European Journal of Operational Research 198 (2009) 47-56
5. Bleuler S., Laumanns M., Thiele L., and Zitzler E. PISA - A platform and programming language independent interface for search algorithms. In: Fonseca C., Fleming P., Zitzler E., Deb K., and Thiele L. (Eds). Evolutionary Multi-Criterion Optimization (2003), Springer-Verlag, Heidelberg 494-508
6. Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E., 2003b. The PISA Homepage. .
7. Captivo M.E., Clímaco J., Figueira J., Martins E., and Santos J.L. Solving bicriteria 0-1 knapsack problems using a labeling algorithm. Computers and Operations Research 30 (2003) 1865-1886
8. Coello Coello C.A., Van Veldhuizen D.A., and Lamont G.A. Evolutionary Algorithms for Solving Multi-Objective Problems (2002), Kluwer Academic Publishers, Boston, MA
9. Deb K. Multi-Objective Optimization Using Evolutionary Algorithms (2001), John Wiley and Sons, Chichester
10. Deb K., Pratap A., Agarwal S., and Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6 (2002) 182-197
11. Dongarra, J.J., 2008. Performance of various computers using standard linear equations software. Linpack Benchmark Report, University of Tennessee Computer Science Technical Report, CS-89-85.
12. Ehrgott M. A discussion of scalarization techniques for multiple objective integer programming. Annals of Operational Research 147 (2006) 343-360
13. Erlebach T., Kellerer H., and Pferschy U. Approximating multiobjective knapsack problems. Management Science 48 12 (2002) 1603-1612
14. Gandibleux X., and Freville A. Tabu search based procedure for solving the 0-1 multiobjective knapsack problem: The two objectives case. Journal of Heuristics 6 (2000) 361-383
15. Gomes da Silva C., Clímaco J., and Figueira J. A scatter search method for the bi-criteria multi-dimensional {0,1}-knapsack problem using surrogate relaxation. Journal of Mathematical Modelling and Algorithms 3 (2004) 183-208
16. Gomes da Silva C., Clímaco J., and Figueira J. A scatter search method for bi-criteria {0,1} knapsack problems. European Journal of Operational Research 169 (2006) 373-391
17. Gomes da Silva C., Figueira J., and Clímaco J. Integrating partial optimization with scatter search for solving bi-criteria {0,1} knapsack problems. European Journal of Operational Research 177 (2007) 1656-1677
18. Gomes da Silva C., Clímaco J., and Figueira J. Core problems in bi-criteria {0,1}-knapsack problems. Computers and Operations Research 35 (2007) 2292-2306
19. 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 4 (2002) 402-412
20. Jaszkiewicz A. On the computational efficiency of multiple objective metaheuristics. The knapsack problem case study. European Journal of Operational Research 158 (2004) 418-433
21. Khare V., Yao X., and Deb K. Performance scaling of multi-objective evolutionary algorithms. In: Fonseca C.M., et al. (Ed). EMO 2003. LNCS vol. 2632 (2003), Springer-Verlag, Berlin, Heidelberg 376-390
22. Klamroth K., and Wiecek M.M. Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics 47 (2000) 57-76
23. Kumar R., and Banerjee N. Analysis of a multiobjective evolutionary algorithm on the 0-1 knapsack problem. Theoretical Computer Science 358 (2006) 104-120
24. Land A.H., and Doig A.G. An automatic method of solving discrete programming problems. Econometrica 28 3 (1960) 497-520
25. Laumanns, M., Thiele, L., Zitzler, E., 2005. An adaptive scheme to generate the Pareto front based on the epsilon-constraint method. In: Branke, J., Deb, K., Miettinen, K., Steuer, R. (Eds.), Practical Approaches to Multi-Objective Optimization, Dagstuhl Seminar Proceedings, vol. 04461. URN: urn:nbn:de:0030-drops-2465, URL: http://drops.dagstuhl.de/opus/volltexte/2005/246.
26. Laumanns M., Thiele L., and Zitzler E. An efficient, adaptive parameter variation scheme for Metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169 (2006) 932-942
27. Li H., Zhang Q., Tsang E., and Ford J.A. Hybrid estimation of distribution algorithm for multiobjective knapsack problem. In: Gottlieb J., and Raidl G.R. (Eds). EvoCOP 2004. LNCS vol. 3004 (2004), Springer-Verlag, Berlin, Heidelberg 145-154
28. López-Ibáñez M., Paquete L., and Stützle T. Hybrid population-based algorithms for the bi-objective quadratic assignment problem. Journal of Mathematical Modelling and Algorithms 5 (2006) 111-137
29. Martello S., and Toth P. Knapsack Problems (1990), Wiley, New York
30. Mavrotas G., and Diakoulaki D. A branch and bound algorithm for mixed zero-one multiple objective linear programming. European Journal of Operational Research 107 (1998) 530-541
31. Mavrotas G., and Diakoulaki D. Multi-criteria branch and bound: A vector maximization algorithm for mixed 0-1 multiple objective linear programming. Applied Mathematics and Computation 171 (2005) 53-71
32. Nemhauser G.L., and Wolsey L.A. Integer and Combinatorial Optimization (1999), Wiley
33. Shukla P.K., and Deb K. On finding multiple pareto-optimal solutions using classical and evolutionary generating methods. European Journal of Operational Research 181 (2007) 1630-1652
34. Teghem J., Tuyttens D., and Ulungu E.L. An interactive heuristic method for multi-objective combinatorial optimization. Computers and Operations Research 27 (2000) 621-634
35. Visée M., Teghem J., Pirlot M., and Ulungu E.L. Two-phases method and branch and bound procedures to solve the bi-objective knapsack problem. Journal of Global Optimization 12 (1998) 139-155
36. Zhang C.W., and Ong H.L. Solving the biobjective zero-one knapsack problem by an efficient LP-based heuristic. European Journal of Operational Research 159 (2004) 545-557
37. Zitzler, E., 1999. Evolutionary algorithms for multiobjective optimization: methods and applications. PhD Thesis, Swiss Federal Institute of Technology (ETH) Zurich, Switzerland.
38. Zitzler E., and Thiele L. Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation 3 4 (1999) 257-271
39. Zitzler E., Laumanns M., and Thiele L. SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou K., Tsahalis D., Periaux J., Papailiou K., and Fogarty T. (Eds). Evolutionary Methods for Design Optimization and Control (2002), CIMNE, Barcelona, Spain 19-26
40. Zitzler E., Laumanns M., and Bleuler S. A tutorial on evolutionary multiobjective optimization. In: Gandibleux X., Sevaux M., Sörensen K., and T'kindt V. (Eds). EU/ME & PM2O 2002. LNEMS vol. 535 (2004), Springer-Verlag, Berlin, Heidelberg 3-37