Abstract
The 0-1 knapsack problem (KP01) is one of the classical NP-hard problems in operation research and has a number of engineering applications. In this paper, the BABC-DE (binary artificial bee colony algorithm with differential evolution), a modified artificial bee colony algorithm, is proposed to solve KP01. In BABC-DE, a new binary searching operator which comprehensively considers the memory and neighbour information is designed in the employed bee phase, and the mutation and crossover operations of differential evolution are adopted in the onlooker bee phase. In order to make the searching solution feasible, a repair operator based on greedy strategy is employed. Experimental results on different dimensional KP01s verify the efficiency of the proposed method, and it gets superior performance compared with other five metaheuristic algorithms.
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References
Bansal JC, Deep K (2012) A modified binary particle swarm optimization for knapsack problems. Appl Math Comput 218(22):11:042–11:061
Bas E (2011) A capital budgeting problem for preventing workplace mobbing by using analytic hierarchy process and fuzzy 0–1 bidimensional knapsack model. Expert Systems with Applications 38(10):12:415–12:422
Billionnet A, Soutif É (2004) An exact method based on lagrangian decomposition for the 0–1 quadratic knapsack problem. Eur J Oper Res 157(3):565–575
Chaharsooghi SK, Kermani AHM (2008) An intelligent multi-colony multi-objective ant colony optimization (aco) for the 0–1 knapsack problem. In: IEEE congress on evolutionary computation, 2008. CEC 2008. (IEEE world congress on computational intelligence). IEEE, pp 1195–1202
Chen S, Gao C, Li X, Lu Y, Zhang Z (2015) A rank-based ant system algorithm for solving 0/1 knapsack problem. J Comput Inf Syst 11(20):7423–7430
Feng Y, Wang GG, Gao XZ (2016) A novel hybrid cuckoo search algorithm with global harmony search for 0-1 knapsack problems. Intern J Comput Intell Syst 9(6):1174–1190
Feng Y, Yang J, Wu C, Lu M, Zhao XJ (2016) Solving 0–1 knapsack problems by chaotic monarch butterfly optimization algorithm with gaussian mutation. Memetic Computing, pp 1–16
García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms behaviour: a case study on the cec2005 special session on real parameter optimization. J Heuristics 15(6):617
Gheisari S, Meybodi M (2016) Bnc-pso: structure learning of bayesian networks by particle swarm optimization. Inf Sci 348:272–289
Gilmore P, Gomory R (1966) The theory and computation of knapsack functions. Oper Res 14(6):1045–1074
Haddar B, Khemakhem M, Hanafi S, Wilbaut C (2015) A hybrid heuristic for the 0–1 knapsack sharing problem. Expert Syst Appl 42(10):4653–4666
Ji J, Wei H, Liu C, Yin B (2013) Artificial bee colony algorithm merged with pheromone communication mechanism for the 0-1 multidimensional knapsack problem. Math Probl Eng, 2013
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Tech. rep., Technical report-tr06, Erciyes university, engineering faculty, computer engineering department
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (abc) algorithm. J Glob Optim 39(3):459–471
Kolesar PJ (1967) A branch and bound algorithm for the knapsack problem. Manag Sci 13(9):723–735
Kong X, Gao L, Ouyang H, Li S (2015) A simplified binary harmony search algorithm for large scale 0–1 knapsack problems. Expert Syst Appl 42(12):5337–5355
Lv J, Wang X, Huang M, Cheng H, Li F (2016) Solving 0-1 knapsack problem by greedy degree and expectation efficiency. Appl Soft Comput 41:94–103
Marinakis Y, Marinaki M, Matsatsinis N (2009) A hybrid discrete artificial bee colony-grasp algorithm for clustering. In: International conference on computers & industrial engineering, 2009. CIE 2009. IEEE, pp 548–553
Martello S, Toth P (1977) An upper bound for the zero-one knapsack problem and a branch and bound algorithm. Eur J Oper Res 1(3):169–175
Martello S, Toth P (1990) Knapsack problems: algorithms and computer implementations. Wiley
Martello S, Pisinger D, Toth P (1999) Dynamic programming and strong bounds for the 0-1 knapsack problem. Manag Sci 45(3):414–424
Merkle R, Hellman M (1978) Hiding information and signatures in trapdoor knapsacks. IEEE Trans Inf Theory 24(5):525– 530
Mirjalili S, Lewis A (2013) S-shaped versus v-shaped transfer functions for binary particle swarm optimization. Swarm Evol Comput 9:1–14
Nauss RM (1976) An efficient algorithm for the 0-1 knapsack problem. Manag Sci 23(1):27–31
Nguyen BH, Xue B, Andreae P (2017) A novel binary particle swarm optimization algorithm and its applications on knapsack and feature selection problems. In: Proceedings of the intelligent and evolutionary systems: the 20th Asia Pacific symposium, IES 2016, Canberra, Australia, November 2016. Springer, pp 319– 332
Ozturk C, Hancer E, Karaboga D (2015) A novel binary artificial bee colony algorithm based on genetic operators. Inf Sci 297:154–170
Pavithr R et al (2016) Quantum inspired social evolution (qse) algorithm for 0-1 knapsack problem. Swarm Evol Comput 29:33–46
Peeta S, Salman FS, Gunnec D, Viswanath K (2010) Pre-disaster investment decisions for strengthening a highway network. Comput Oper Res 37(10):1708–1719
Peng C, Jian L, Zhiming L (2008) Solving 0-1 knapsack problems by a discrete binary version of differential evolution. In: Second international symposium on intelligent information technology application, 2008. IITA’08, vol 2. IEEE, pp 513–516
Reniers GL, Sörensen K (2013) An approach for optimal allocation of safety resources: Using the knapsack problem to take aggregated cost-efficient preventive measures. Risk Anal 33(11):2056–2067
Shi H (2006) Solution to 0/1 knapsack problem based on improved ant colony algorithm. In: 2006 IEEE international conference on information acquisition. IEEE, pp 1062–1066
Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Sundar S, Singh A, Rossi A (2010) An artificial bee colony algorithm for the 0–1 multidimensional knapsack problem. In: International conference on contemporary computing. Springer, pp 141–151
Tasgetiren MF, Pan QK, Liang YC, Suganthan PN (2007) A discrete differential evolution algorithm for the total earliness and tardiness penalties with a common due year on a single-machine. In: 2007 IEEE symposium on computational intelligence in scheduling. IEEE, pp 271–278
Tian N, Wang M, Gu Y (2016) An improved binary particle swarm optimization for 0-1 knapsack problem. ICIC Express Letters 10(8):1987–1994
Toth P (1980) Dynamic programming algorithms for the zero-one knapsack problem. Computing 25(1):29–45
Toumi S, Cheikh M, Jarboui B (2015) 0–1 quadratic knapsack problem solved with vns algorithm. Electron Notes Discrete Math 47:269–276
Tran DC, Wu Z (2014) New approaches of binary artificial bee colony algorithm for solving 0-1 knapsack problem. Adv Inf Sci Serv Sci 6(2):1
Tran DH, Cheng MY, Cao MT (2015) Hybrid multiple objective artificial bee colony with differential evolution for the time–cost–quality tradeoff problem. Knowl-Based Syst 74:176–186
Wei L, Ben N, Hanning C (2012) Binary artificial bee colony algorithm for solving 0-1 knapsack problem. Adv Inf Sci Serv Sci 4(22):464–470
Zhao J, Huang T, Pang F, Liu Y (2009) Genetic algorithm based on greedy strategy in the 0-1 knapsack problem. In: 3rd international conference on genetic and evolutionary computing, 2009. WGEC’09. IEEE, pp 105–107
Zhou Y, Bao Z, Luo Q, Zhang S (2016) A complex-valued encoding wind driven optimization for the 0-1 knapsack problem. Appl Intell, pp 1–19
Zhou Y, Chen X, Zhou G (2016) An improved monkey algorithm for a 0-1 knapsack problem. Appl Soft Comput 38:817–830
Zou D, Gao L, Li S, Wu J (2011) Solving 0–1 knapsack problem by a novel global harmony search algorithm. Appl Soft Comput 11(2):1556–1564
Acknowledgements
This work is supported in part by the National Natural Science Foundation of China under grant Nos. 61174124, 61233003, 61673361, in part by Research Fund for the Doctoral Program of Higher Education of China under grant No. 20123402110029, and supported by the Fundamental Research Funds for the Central Universities No. JZ2015HGBZ0493.
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This work is supported in part by the National Natural Science Foundation of China under grant Nos. 61174124, 61233003.
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Cao, J., Yin, B., Lu, X. et al. A modified artificial bee colony approach for the 0-1 knapsack problem. Appl Intell 48, 1582–1595 (2018). https://doi.org/10.1007/s10489-017-1025-x
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DOI: https://doi.org/10.1007/s10489-017-1025-x