Similar articles

Abstract: To address indeterminism in the bilevel knapsack problem, an uncertain bilevel knapsack problem (UBKP) model is proposed. Then, an uncertain solution for UBKP is proposed by defining the P_E Nash equilibrium and P_E Stackelberg–Nash equilibrium. To improve the computational efficiency of the uncertain solution, an evolutionary algorithm, the improved binary wolf pack algorithm, is constructed with one rule (wolf leader regulation), two operators (invert operator and move operator), and three intelligent behaviors (scouting behavior, intelligent hunting behavior, and upgrading). The UBKP model and the P_E uncertain solution are applied to an armament transportation problem as a case study.

求解不确定双层背包问题的改进二进制狼群算法

[1]Bai T, Wei J, Yang WW, et al., 2018. Multi-objective parameter estimation of improved Muskingum model by wolf pack algorithm and its application in upper Hanjiang River, China. Water, 10(10):1415.

[2]Brotcorne L, Hanafi S, Mansi R, 2013. One-level reformulation of the bilevel knapsack problem using dynamic programming. Dis Optim, 10(1):1-10.

[3]Caprara A, Carvalho M, Lodi A, et al., 2014. A study on the computational complexity of the bilevel knapsack problem. SIAM J Optim, 24(2):823-838.

[4]Carvalho M, Lodi A, Marcotte P, 2018. A polynomial algorithm for a continuous bilevel knapsack problem. Oper Res Lett, 46(2):185-188.

[5]Chih M, Lin CJ, Chern MS, et al., 2014. Particle swarm optimization with time-varying acceleration coefficients for the multidimensional knapsack problem. Appl Math Model, 38(4):1338-1350.

[6]Cohn AM, Barnhart C, 1998. The stochastic knapsack problem with random weights: a heuristic approach to robust transportation planning. Proc Triennial Symp on Transportation Analysis, p.1-13.

[7]Dempe S, Richter K, 2000. Bilevel programming with knapsack constraints. Centr Eur J Oper Res, 8(2):93-107.

[8]Gao F, Cui G, Wu ZB, et al., 2009. Virus-evolutionary particle swarm optimization algorithm for knapsack problem. J Harbin Inst Technol, 41(6):103-107 (in Chinese).

[9]Gao YJ, Zhang FM, Zhao Y, et al., 2019. A novel quantum- inspired binary wolf pack algorithm for difficult knapsack problem. Int J Wirel Mob Comput, 16(3):222-232.

[10]Gherboudj A, Layeb A, Chikhi S, 2012. Solving 0-1 knapsack problems by a discrete binary version of cuckoo search algorithm. Int J Bio-Inspir Comput, 4(4):229-236.

[11]Han ZH, Tian XT, Ma XF, et al., 2018. Scheduling for re-entrant hybrid flowshop based on wolf pack algorithm. IOP Conf Ser Mater Sci Eng, 382(3):032007.

[12]Li H, Zhang L, Jiao YC, 2014. Solution for integer linear bilevel programming problems using orthogonal genetic algorithm. J Syst Eng Electron, 25(3):443-451.

[13]Li H, Xiao RB, Wu HS, 2016. Modelling for combat task allocation problem of aerial swarm and its solution using wolf pack algorithm. Int J Innov Comput Appl, 7(1): 50-59.

[14]Liu B, 2009a. Some research problems in uncertainty theory. J Uncert Syst, 3(1):3-10.

[15]Liu B, 2009b. Theory and Practice of Uncertain Programming. Springer Verlag, Berlin, Germany.

[16]Liu B, 2010. Uncertainty Theory: a Branch of Mathematics for Modeling Human Uncertainty. Springer Verlag, Berlin, Germany.

[17]Liu B, 2016. Uncertainty Theory (5^th Ed.). Springer Verlag, Berlin, Germany.

[18]Liu JQ, He YC, Gu QQ, 2007. Solving knapsack problem based on discrete particle swarm optimization. Comput Eng Des, 28(13):3189-3191, 3204 (in Chinese).

[19]Özaltın OY, Prokopyev OA, Schaefer AJ, 2010. The bilevel knapsack problem with stochastic right-hand sides. Oper Res Lett, 38(4):328-333.

[20]Qian J, Zheng JG, 2012. Greedy quantum-inspired evolutionary algorithm for quadratic knapsack problem. Comput Integr Manuf Syst, 18(9):2003-2011 (in Chinese).

[21]Qiu X, Kern W, 2015. Improved approximation algorithms for a bilevel knapsack problem. Theor Comput Sci, 595(30): 120-129.

[22]Wang R, Guo N, Xiang FH, et al., 2012. An improved quantum genetic algorithm with mutation and its application to 0-1 knapsack problem. Proc Int Conf on Measurement, Information and Control, p.484-488.

[23]Wang ZT, Guo JS, Zheng MF, et al., 2015. A new approach for uncertain multiobjective programming problem based on _E principle. J Ind Manag Optim, 11(1):13-26.

[24]Wu HS, Zhang FM, Wu LS, 2013. New swarm intelligence algorithm―wolf pack algorithm. Syst Eng Electron, 35(11):2430-2438 (in Chinese).

[25]Xue JJ, Wang Y, Li H, et al., 2016. A smart wolf pack algorithm and its convergence analysis. Contr Dec, 31(12):2131-2139 (in Chinese).