A Binary differential search algorithm for the 0–1 multidimensional knapsack problem

Applied Mathematical Modelling

Volumn 40, Issue 23-24, 2016, Pages 9788-9805

  Liu, Jianjun ^a   Wu, Changzhi ^b   Cao, Jiang ^a   Wang, Xiangyu ^b,c   Teo, Kok Lay ^b  

^a CHINA UNIVERSITY OF PETROLEUM   (China)

^b CURTIN UNIVERSITY   (Australia)

^c Kyung Hee University   (South Korea)

Author keywords

Binary optimization; Differential search; MKP

Indexed keywords

ALGORITHMS; BINS; BROWNIAN MOVEMENT; COMBINATORIAL OPTIMIZATION; HEURISTIC ALGORITHMS; NUMERICAL METHODS; OPERATIONS RESEARCH; OPTIMIZATION; STOCHASTIC SYSTEMS;

0-1 MULTIDIMENSIONAL KNAPSACK PROBLEMS; BINARY OPTIMIZATION; DIFFERENTIAL SEARCH; DISCRETE VARIABLES; META-HEURISTIC METHODS; MULTIDIMENSIONAL KNAPSACK PROBLEMS; PRODUCTION STRATEGY; ROUNDING OPERATION;

HEURISTIC METHODS;

EID: 84978800276     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2016.06.002     Document Type: Article

References (44)

1. [1] Frieze, A., Clarke, M., Approximation algorithms for the m-dimensional 0–1 knapsack problem: worst-case and probabilistic analyses. Eur. J. Oper. Res. 15:1 (1984), 100–109.
2. [2] Wilbaut, C., Hanafi, S., Salhi, S., A survey of effective heuristics and their application to a variety of knapsack problems. IMA J. Manag. Math. 19:3 (2008), 227–244.
3. [3] Nawrocki, J., Complak, W., Błażewicz, J., Kopczyńska, S., Maćkowiaki, M., The knapsack-lightening problem and its application to scheduling HRT tasks. Bull. Polish Acad. Sci.: Tech. Sci. 57:1 (2009), 71–77.
4. [4] Wu, C., Wang, X., Lin, J., Optimizations in project scheduling: a state-of-art survey. Optimization and Control Methods in Industrial Engineering and Construction, 2014, Springer, 161–177.
5. [5] Puchinger, J., Raidl, G.R., Pferschy, U., The multidimensional knapsack problem: structure and algorithms. INFORMS J. Comput. 22:2 (2010), 250–265.
6. [6] Zhang, Y., Zhang, F., Cai, M., Some new results on multi-dimension knapsack problem. J. Ind. Manag. Opt., 1(3), 2005, 315.
7. [7] Boussier, S., Vasquez, M., Vimont, Y., Hanafi, S., Michelon, P., A multi-level search strategy for the 0–1 multidimensional knapsack problem. Discr. Appl. Math. 158:2 (2010), 97–109.
8. [8] Varnamkhasti, M., Overview of the algorithms for solving the multidimensional knapsack problems. Adv. Stud. Biol. 4:1 (2012), 37–47.
9. [9] Wu, C., Li, C., Long, Q., A DC programming approach for sensor network localization with uncertainties in anchor positions. J. Ind. Manag. Opt. 10:3 (2014), 817–826.
10. [10] Long, Q., Wu, C., A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization. J. Ind. Manag. Opt. 10:4 (2014), 1279–1296.
11. [11] Liu, J., Zhu, H., Ma, Q., Zhang, L., Xu, H., An artificial bee colony algorithm with guide of global & local optima and asynchronous scaling factors for numerical optimization. Appl. Soft Comput. 37 (2015), 608–618.
12. [12] Sun, X., Sheng, H., Li, D., An exact algorithm for 0-1 polynomial knapsack problems. J. Ind. Manag. Opt., 3(2), 2007, 223.
13. [13] Zhou, J., Chen, D., Wang, Z., Xing, W., A conic approximation method for the 0-1 quadratic knapsack problem. Management 9:3 (2013), 531–547.
14. [14] Vasquez, M., Vimont, Y., Improved results on the 0–1 multidimensional knapsack problem. Eur. J. Oper. Res. 165:1 (2005), 70–81.
15. [15] Chih, M., Lin, C.-J., Chern, M.-S., Ou, T.-Y., Particle swarm optimization with time-varying acceleration coefficients for the multidimensional knapsack problem. Appl. Math. Model. 38:4 (2014), 1338–1350.
16. [16] Balev, S., Yanev, N., Fréville, A., Andonov, R., A dynamic programming based reduction procedure for the multidimensional 0–1 knapsack problem. Eur. J. Oper. Res. 186:1 (2008), 63–76.
17. [17] Boyer, V., El Baz, D., Elkihel, M., A dynamic programming method with lists for the knapsack sharing problem. Comput. Ind. Eng. 61:2 (2011), 274–278.
18. [18] Long, Q., Wu, C., Huang, T., Wang, X., A genetic algorithm for unconstrained multi-objective optimization. Swarm Evolut. Comput. 22 (2015), 1–14.
19. [19] Azad, M.A.K., Rocha, A.M.A., Fernandes, E.M., A simplified binary artificial fish swarm algorithm for 0–1 quadratic knapsack problems. J. Comput. Appl. Math. 259 (2014), 897–904.
20. [20] Bansal, J.C., Deep, K., A modified binary particle swarm optimization for knapsack problems. Appl. Math. Comput. 218:22 (2012), 11042–11061.
21. [21] Chih, M., Self-adaptive check and repair operator-based particle swarm optimization for the multidimensional knapsack problem. Appl. Soft Comput. 26 (2015), 378–389.
22. [22] Baykasoğlu, A., Ozsoydan, F.B., An improved firefly algorithm for solving dynamic multidimensional knapsack problems. Exp. Syst. Appl. 41:8 (2014), 3712–3725.
23. [23] Kong, M., Tian, P., Kao, Y., A new ant colony optimization algorithm for the multidimensional knapsack problem. Comput. Oper. Res. 35:8 (2008), 2672–2683.
24. [24] Sundar, S., Singh, A., Rossi, A., An artificial bee colony algorithm for the 0–1 multidimensional knapsack problem. Contemporary Computing, 2010, Springer, 141–151.
25. [25] Changdar, C., Mahapatra, G., Pal, R.K., An ant colony optimization approach for binary knapsack problem under fuzziness. Appl. Math. Comput. 223 (2013), 243–253.
26. [26] Wang, L., Zheng, X.-l., Wang, S.-y., A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem. Knowl. Based Syst. 48 (2013), 17–23.
27. [27] Gong, Q., Zhou, Y., Luo, Q., Hybrid artificial glowworm swarm optimization algorithm for solving multi-dimensional knapsack problem. Proc. Eng. 15 (2011), 2880–2884.
28. [28] Zhang, X., Huang, S., Hu, Y., Zhang, Y., Mahadevan, S., Deng, Y., Solving 0-1 knapsack problems based on amoeboid organism algorithm. Appl. Math. Comput. 219:19 (2013), 9959–9970.
29. [29] Bhattacharjee, K.K., Sarmah, S.P., Shuffled frog leaping algorithm and its application to 0/1 knapsack problem. Appl. Soft Comput. 19 (2014), 252–263.
30. [30] Gao, J., He, G., Liang, R., Feng, Z., A quantum-inspired artificial immune system for the multiobjective 0–1 knapsack problem. Appl. Math. Comput. 230 (2014), 120–137.
31. [31] Civicioglu, P., Transforming geocentric cartesian coordinates to geodetic coordinates by using differential search algorithm. Comput. Geosci. 46 (2012), 229–247.
32. [32] Liu, J., Teo, K., Wang, X., Wu, C., An exact penalty function-based differential search algorithm for constrained global optimization. Soft Comput., 2015, 1–9, 10.1007/s00500-015-1588-6.
33. [33] Liu, J., Wu, C., Wu, G., Wang, X., A novel differential search algorithm and applications for structure design. Appl. Math. Comput. 268:268 (2015), 246–269.
34. [34] Trianni, V., Tuci, E., Passino, K., Marshall, J.R., Swarm cognition: an interdisciplinary approach to the study of self-organising biological collectives. Swarm Intell. 5:1 (2011), 3–18.
35. [35] Wolpert, D.H., Macready, W.G., No free lunch theorems for optimization. Evolut. Comput., IEEE Trans. 1:1 (1997), 67–82.
36. [36] Yang, X.-S., He, X., Firefly algorithm: recent advances and applications. Int. J. Swarm Intell. 1:1 (2013), 36–50.
37. [37] Botev, Z.I., Kroese, D.P., An efficient algorithm for rare-event probability estimation, combinatorial optimization, and counting. Methodol. Comput. Appl. Probab. 10:4 (2008), 471–505.
38. [38] Wang, L., Singh, C., Unit commitment considering generator outages through a mixed-integer particle swarm optimization algorithm. Appl. Soft Comput. 9:3 (2009), 947–953.
39. [39] Chandrasekaran, K., Simon, S.P., Padhy, N.P., Binary real coded firefly algorithm for solving unit commitment problem. Inf. Sci. 249 (2013), 67–84.
40. [40] Azad, M.A.K., Rocha, A.M.A., Fernandes, E.M., Improved binary artificial fish swarm algorithm for the 0–1 multidimensional knapsack problems. Swarm Evolut. Comput. 14 (2014), 66–75.
41. [41] Sakawa, M., Kato, K., Genetic algorithms with double strings for 0–1 programming problems. Eur. J. Oper. Res. 144:3 (2003), 581–597.
42. [42] Montgomery, D.C., Design and Analysis of Experiments, 2008, John Wiley & Sons.
43. [43] Chu, P.C., Beasley, J.E., A genetic algorithm for the multidimensional knapsack problem. J. Heurist. 4:1 (1998), 63–86.
44. [44] Beasley, J.E., Or-library: distributing test problems by electronic mail. J. Oper. Res. Soc., 1990, 1069–1072 http://people.brunel.ac.uk/ mastjjb/jeb/info.html.