How to cite this paper
Rezazadeh, H. (2015). A Rough Sets based modified Scatter Search algorithm for solving 0-1 Knapsack problem.Decision Science Letters , 4(3), 425-440.
Refrences
Albano, A., & Orsini, R. (1980). A tree search approach to the M-partition and knapsack problems. The Computer Journal, 23(3), 256-261.
Archetti, C., Guastaroba, G., & Speranza, M. G. (2013). Reoptimizing the rural postman problem. Computers & Operations Research, 40(5), 1306-1313.
Bansal, J. C., & Deep, K. (2012). A modified binary particle swarm optimization for knapsack problems. Applied Mathematics and Computation, 218(22), 11042-11061.
Beausoleil, R. P., Baldoquin, G., & Montejo, R. A. (2008). Multi-start and path relinking methods to deal with multiobjective knapsack problems. Annals of Operations Research, 157(1), 105-133.
Belgacem, T., & Hifi, M. (2008). Sensitivity analysis of the optimum to perturbation of the profit of a subset of items in the binary knapsack problem. Discrete Optimization, 5(4), 755-761.
Bhattacharjee, K. K., & Sarmah, S. P. (2014). Shuffled frog leaping algorithm and its application to 0/1 knapsack problem. Applied Soft Computing, 19, 252-263.
Dantzig, G. B. (1957). Discrete-variable extremum problems. Operations research, 5(2), 266-288.
Gary, M. R., & Johnson, D. S. (1979). Computers and Intractability a Guide to the Theory of NP-Completeness. 1979. WH Freman and Co.
Glover, F. (1977). Heuristics for integer programming using surrogate constraints. Decision Sciences, 8(1), 156-166.
Glover, F., Laguna, M., & Marti, R. (2003). Scatter search and path relinking: Advances and applications. In Handbook of metaheuristics (pp. 1-35). Springer US.
Gorman, M. F., & Ahire, S. (2006). A major appliance manufacturer rethinks its inventory policies for service vehicles. Interfaces, 36(5), 407-419.
Gort?zar, F., Duarte, A., Laguna, M., & Mart?, R. (2010). Black box scatter search for general classes of binary optimization problems. Computers & Operations Research, 37(11), 1977-1986.
Granmo, O. C., Oommen, B. J., Myrer, S. A., & Olsen, M. G. (2007). Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 37(1), 166-175.
Guler, A., Nuriyev, U. G., Berberler, M. E., & Nuriyeva, F. (2012). Algorithms with guarantee value for knapsack problems. Optimization, 61(4), 477-488.
Kellerer, H., Pferschy, U., & Pisinger, D. (2004). Knapsack problems. Springer Science & Business Media.
Kumar, R., & Singh, P. K. (2010). Assessing solution quality of biobjective 0-1 knapsack problem using evolutionary and heuristic algorithms. Applied Soft Computing, 10(3), 711-718.
Kulkarni, A. J., & Shabir, H. (2014). Solving 0–1 knapsack problem using cohort intelligence algorithm. International Journal of Machine Learning and Cybernetics, 1-15.
Layeb, A. (2011). A novel quantum inspired cuckoo search for knapsack problems. International Journal of Bio-Inspired Computation, 3(5), 297-305.
Layeb, A. (2013). A hybrid quantum inspired harmony search algorithm for 0–1 optimization problems. Journal of Computational and Applied Mathematics,253, 14-25.
Lasserre, J. B., & Thanh, T. P. (2012). A “joint+ marginal” heuristic for 0/1 programs. Journal of Global Optimization, 54(4), 729-744.
Lin, C. J., & Chen, S. J. (1994). A systolic algorithm for solving knapsack problems. International Journal of Computer Mathematics, 54(1-2), 23-32.
Lin, F. T. (2008). Solving the knapsack problem with imprecise weight coefficients using genetic algorithms. European Journal of Operational Research, 185(1), 133-145.
Lin, G., Zhu, W., & Ali, M. M. (2011). An exact algorithm for the 0–1 linear knapsack problem with a single continuous variable. Journal of Global Optimization, 50(4), 657-673.
Lu, T. C., & Yu, G. R. (2013). An adaptive population multi-objective quantum-inspired evolutionary algorithm for multi-objective 0/1 knapsack problems. Information Sciences, 243, 39-56.
Marchand, H., & Wolsey, L. A. (1999). The 0-1 knapsack problem with a single continuous variable. Mathematical Programming, 85(1), 15-33.
Martello, S., Pisinger, D., & Toth, P. (1999). Dynamic programming and strong bounds for the 0-1 knapsack problem. Management Science, 45(3), 414-424.
Mrozek, A. (1992). Rough sets in computer implementation of rule-based control of industrial processes. In Intelligent Decision Support (pp. 19-31). Springer Netherlands.
Martello, S., Pisinger, D., & Toth, P. (2000). New trends in exact algorithms for the 0–1 knapsack problem. European Journal of Operational Research, 123(2), 325-332.
Nawrocki, J., Complak, W., B?a?ewicz, J., Kopczy?ska, S., & Ma?kowiaki, M. (2009). The Knapsack-Lightening problem and its application to scheduling HRT tasks. Bulletin of the Polish Academy of Sciences: Technical Sciences, 57(1), 71-77.
Pisinger, D. (1995). An expanding-core algorithm for the exact 0–1 knapsack problem. European Journal of Operational Research, 87(1), 175-187.
da Cunha, A. S., Bahiense, L., Lucena, A., & de Souza, C. C. (2010). A New Lagrangian Based Branch and Bound Algorithm for the 0-1 Knapsack Problem.Electronic Notes in Discrete Mathematics, 36, 623-630.
Kaparis, K., & Letchford, A. N. (2010). Separation algorithms for 0-1 knapsack polytopes. Mathematical programming, 124(1-2), 69-91.
Pawlak, Z., (1992).Rough set: A new approach to vagueness. In Zadeh, L. A., Kacprzyk, J., (Eds.), Fuzzy logic for the management of uncertainty. NY New York: Wiley, 105–108.
Pawlak, Z. (2002). Rough sets, decision algorithms and Bayes & apos; theorem.European Journal of Operational Research, 136(1), 181-189.
Rezazadeh, H., Mahini, R., & Zarei, M. (2011). Solving a dynamic virtual cell formation problem by linear programming embedded particle swarm optimization algorithm. Applied Soft Computing, 11(3), 3160-3169.
Sato, H., Aguirre, H., & Tanaka, K. (2013). Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems. Annals of Mathematics and Artificial Intelligence, 68(4), 197-224.
da Silva, C. G., Climaco, J., & Figueira, J. (2006). A scatter search method for bi-criteria {0, 1}-knapsack problems. European Journal of Operational Research,169(2), 373-391.
da Silva, C. G., Cl?maco, J., & Figueira, J. R. (2008). Core problems in bi-criteria {0, 1}-knapsack problems. Computers & Operations Research, 35(7), 2292-2306.
S?owi?ski, R. (Ed.). (1992). Intelligent decision support: handbook of applications and advances of the rough sets theory (Vol. 11). Springer Science & Business Media.
Taniguchi, F., Yamada, T., & Kataoka, S. (2009). A virtual pegging approach to the max–min optimization of the bi-criteria knapsack problem. International Journal of Computer Mathematics, 86(5), 779-793.
Truong, T. K., Li, K., & Xu, Y. (2013). Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem. Applied Soft Computing, 13(4), 1774-1780.
Vanderster, D. C., Dimopoulos, N. J., Parra-Hernandez, R., & Sobie, R. J. (2009). Resource allocation on computational grids using a utility model and the knapsack problem. Future Generation Computer Systems, 25(1), 35-50.
Wang, B., Dong, H., & He, Z. (1999). A chaotic annealing neural network with gain sharpening and its application to the 0/1 knapsack problem. Neural processing letters, 9(3), 243-247.
W?scher, G., HauBner, H., & Schumann, H. (2007). An improved typology of cutting and packing problems. European Journal of Operational Research,183(3), 1109-1130.
Wilbaut, C., Hanafi, S., & Salhi, S. (2008). A survey of effective heuristics and their application to a variety of knapsack problems. IMA Journal of Management Mathematics, 19(3), 227-244.
Yamada, T., Watanabe, K., & Kataoka, S. (2005). Algorithms to solve the knapsack constrained maximum spanning tree problem. International Journal of Computer Mathematics, 82(1), 23-34.
Yang, H. H., & Wang, S. W. (2011). Solving the 0/1 knapsack problem using rough sets and genetic algorithms. Journal of the Chinese Institute of Industrial Engineers, 28(5), 360-369.
Zhang, X., Huang, S., Hu, Y., Zhang, Y., Mahadevan, S., & Deng, Y. (2013). Solving 0-1 knapsack problems based on amoeboid organism algorithm. Applied Mathematics and Computation, 219(19), 9959-9970.
Zou, D., Gao, L., Li, S., & Wu, J. (2011). Solving 0–1 knapsack problem by a novel global harmony search algorithm. Applied Soft Computing, 11(2), 1556-1564.
Archetti, C., Guastaroba, G., & Speranza, M. G. (2013). Reoptimizing the rural postman problem. Computers & Operations Research, 40(5), 1306-1313.
Bansal, J. C., & Deep, K. (2012). A modified binary particle swarm optimization for knapsack problems. Applied Mathematics and Computation, 218(22), 11042-11061.
Beausoleil, R. P., Baldoquin, G., & Montejo, R. A. (2008). Multi-start and path relinking methods to deal with multiobjective knapsack problems. Annals of Operations Research, 157(1), 105-133.
Belgacem, T., & Hifi, M. (2008). Sensitivity analysis of the optimum to perturbation of the profit of a subset of items in the binary knapsack problem. Discrete Optimization, 5(4), 755-761.
Bhattacharjee, K. K., & Sarmah, S. P. (2014). Shuffled frog leaping algorithm and its application to 0/1 knapsack problem. Applied Soft Computing, 19, 252-263.
Dantzig, G. B. (1957). Discrete-variable extremum problems. Operations research, 5(2), 266-288.
Gary, M. R., & Johnson, D. S. (1979). Computers and Intractability a Guide to the Theory of NP-Completeness. 1979. WH Freman and Co.
Glover, F. (1977). Heuristics for integer programming using surrogate constraints. Decision Sciences, 8(1), 156-166.
Glover, F., Laguna, M., & Marti, R. (2003). Scatter search and path relinking: Advances and applications. In Handbook of metaheuristics (pp. 1-35). Springer US.
Gorman, M. F., & Ahire, S. (2006). A major appliance manufacturer rethinks its inventory policies for service vehicles. Interfaces, 36(5), 407-419.
Gort?zar, F., Duarte, A., Laguna, M., & Mart?, R. (2010). Black box scatter search for general classes of binary optimization problems. Computers & Operations Research, 37(11), 1977-1986.
Granmo, O. C., Oommen, B. J., Myrer, S. A., & Olsen, M. G. (2007). Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on, 37(1), 166-175.
Guler, A., Nuriyev, U. G., Berberler, M. E., & Nuriyeva, F. (2012). Algorithms with guarantee value for knapsack problems. Optimization, 61(4), 477-488.
Kellerer, H., Pferschy, U., & Pisinger, D. (2004). Knapsack problems. Springer Science & Business Media.
Kumar, R., & Singh, P. K. (2010). Assessing solution quality of biobjective 0-1 knapsack problem using evolutionary and heuristic algorithms. Applied Soft Computing, 10(3), 711-718.
Kulkarni, A. J., & Shabir, H. (2014). Solving 0–1 knapsack problem using cohort intelligence algorithm. International Journal of Machine Learning and Cybernetics, 1-15.
Layeb, A. (2011). A novel quantum inspired cuckoo search for knapsack problems. International Journal of Bio-Inspired Computation, 3(5), 297-305.
Layeb, A. (2013). A hybrid quantum inspired harmony search algorithm for 0–1 optimization problems. Journal of Computational and Applied Mathematics,253, 14-25.
Lasserre, J. B., & Thanh, T. P. (2012). A “joint+ marginal” heuristic for 0/1 programs. Journal of Global Optimization, 54(4), 729-744.
Lin, C. J., & Chen, S. J. (1994). A systolic algorithm for solving knapsack problems. International Journal of Computer Mathematics, 54(1-2), 23-32.
Lin, F. T. (2008). Solving the knapsack problem with imprecise weight coefficients using genetic algorithms. European Journal of Operational Research, 185(1), 133-145.
Lin, G., Zhu, W., & Ali, M. M. (2011). An exact algorithm for the 0–1 linear knapsack problem with a single continuous variable. Journal of Global Optimization, 50(4), 657-673.
Lu, T. C., & Yu, G. R. (2013). An adaptive population multi-objective quantum-inspired evolutionary algorithm for multi-objective 0/1 knapsack problems. Information Sciences, 243, 39-56.
Marchand, H., & Wolsey, L. A. (1999). The 0-1 knapsack problem with a single continuous variable. Mathematical Programming, 85(1), 15-33.
Martello, S., Pisinger, D., & Toth, P. (1999). Dynamic programming and strong bounds for the 0-1 knapsack problem. Management Science, 45(3), 414-424.
Mrozek, A. (1992). Rough sets in computer implementation of rule-based control of industrial processes. In Intelligent Decision Support (pp. 19-31). Springer Netherlands.
Martello, S., Pisinger, D., & Toth, P. (2000). New trends in exact algorithms for the 0–1 knapsack problem. European Journal of Operational Research, 123(2), 325-332.
Nawrocki, J., Complak, W., B?a?ewicz, J., Kopczy?ska, S., & Ma?kowiaki, M. (2009). The Knapsack-Lightening problem and its application to scheduling HRT tasks. Bulletin of the Polish Academy of Sciences: Technical Sciences, 57(1), 71-77.
Pisinger, D. (1995). An expanding-core algorithm for the exact 0–1 knapsack problem. European Journal of Operational Research, 87(1), 175-187.
da Cunha, A. S., Bahiense, L., Lucena, A., & de Souza, C. C. (2010). A New Lagrangian Based Branch and Bound Algorithm for the 0-1 Knapsack Problem.Electronic Notes in Discrete Mathematics, 36, 623-630.
Kaparis, K., & Letchford, A. N. (2010). Separation algorithms for 0-1 knapsack polytopes. Mathematical programming, 124(1-2), 69-91.
Pawlak, Z., (1992).Rough set: A new approach to vagueness. In Zadeh, L. A., Kacprzyk, J., (Eds.), Fuzzy logic for the management of uncertainty. NY New York: Wiley, 105–108.
Pawlak, Z. (2002). Rough sets, decision algorithms and Bayes & apos; theorem.European Journal of Operational Research, 136(1), 181-189.
Rezazadeh, H., Mahini, R., & Zarei, M. (2011). Solving a dynamic virtual cell formation problem by linear programming embedded particle swarm optimization algorithm. Applied Soft Computing, 11(3), 3160-3169.
Sato, H., Aguirre, H., & Tanaka, K. (2013). Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems. Annals of Mathematics and Artificial Intelligence, 68(4), 197-224.
da Silva, C. G., Climaco, J., & Figueira, J. (2006). A scatter search method for bi-criteria {0, 1}-knapsack problems. European Journal of Operational Research,169(2), 373-391.
da Silva, C. G., Cl?maco, J., & Figueira, J. R. (2008). Core problems in bi-criteria {0, 1}-knapsack problems. Computers & Operations Research, 35(7), 2292-2306.
S?owi?ski, R. (Ed.). (1992). Intelligent decision support: handbook of applications and advances of the rough sets theory (Vol. 11). Springer Science & Business Media.
Taniguchi, F., Yamada, T., & Kataoka, S. (2009). A virtual pegging approach to the max–min optimization of the bi-criteria knapsack problem. International Journal of Computer Mathematics, 86(5), 779-793.
Truong, T. K., Li, K., & Xu, Y. (2013). Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem. Applied Soft Computing, 13(4), 1774-1780.
Vanderster, D. C., Dimopoulos, N. J., Parra-Hernandez, R., & Sobie, R. J. (2009). Resource allocation on computational grids using a utility model and the knapsack problem. Future Generation Computer Systems, 25(1), 35-50.
Wang, B., Dong, H., & He, Z. (1999). A chaotic annealing neural network with gain sharpening and its application to the 0/1 knapsack problem. Neural processing letters, 9(3), 243-247.
W?scher, G., HauBner, H., & Schumann, H. (2007). An improved typology of cutting and packing problems. European Journal of Operational Research,183(3), 1109-1130.
Wilbaut, C., Hanafi, S., & Salhi, S. (2008). A survey of effective heuristics and their application to a variety of knapsack problems. IMA Journal of Management Mathematics, 19(3), 227-244.
Yamada, T., Watanabe, K., & Kataoka, S. (2005). Algorithms to solve the knapsack constrained maximum spanning tree problem. International Journal of Computer Mathematics, 82(1), 23-34.
Yang, H. H., & Wang, S. W. (2011). Solving the 0/1 knapsack problem using rough sets and genetic algorithms. Journal of the Chinese Institute of Industrial Engineers, 28(5), 360-369.
Zhang, X., Huang, S., Hu, Y., Zhang, Y., Mahadevan, S., & Deng, Y. (2013). Solving 0-1 knapsack problems based on amoeboid organism algorithm. Applied Mathematics and Computation, 219(19), 9959-9970.
Zou, D., Gao, L., Li, S., & Wu, J. (2011). Solving 0–1 knapsack problem by a novel global harmony search algorithm. Applied Soft Computing, 11(2), 1556-1564.