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 \({\mathcal{P}_E}\) Nash equilibrium and \({\mathcal{P}_E}\) 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 \({\mathcal{P}_E}\) uncertain solution are applied to an armament transportation problem as a case study.
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Project supported by the National Science and Technology Innovation 2030 Major Project of the Ministry of Science and Technology of China (No. 2018AAA0101200), the National Natural Science Foundation of China (No. 61502534), the Natural Science Foundation of Shaanxi Province, China (No. 2020JQ-493), and the Domain Foundation of China (No. 61400010304)
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Ren-bin XIAO designed the research. Jun-jie XUE and Jin-qiang HU processed the data. Hu-sheng WU drafted the manuscript. Ren-bin XIAO helped organize the manuscript. Hu-sheng WU revised and finalized the paper.
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Hu-sheng WU, Jun-jie XUE, Ren-bin XIAO, and Jin-qiang HU declare that they have no conflict of interest.
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Wu, Hs., Xue, Jj., Xiao, Rb. et al. Uncertain bilevel knapsack problem based on an improved binary wolf pack algorithm. Front Inform Technol Electron Eng 21, 1356–1368 (2020). https://doi.org/10.1631/FITEE.1900437
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DOI: https://doi.org/10.1631/FITEE.1900437