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On-line Access: 2020-09-09

Received: 2019-08-26

Revision Accepted: 2019-12-02

Crosschecked: 2020-04-10

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Hu-sheng Wu


Ren-bin Xiao


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Frontiers of Information Technology & Electronic Engineering  2020 Vol.21 No.9 P.1356-1368


Uncertain bilevel knapsack problem based on an improved binary wolf pack algorithm

Author(s):  Hu-sheng Wu, Jun-jie Xue, Ren-bin Xiao, Jin-qiang Hu

Affiliation(s):  School of Equipment Management and Support, Armed Police Force Engineering University, Xi’an 710086, China; more

Corresponding email(s):   wuhusheng0421@163.com, 1019609875@qq.com, rbxiao@hust.edu.cn, hujinqiang002@163.com

Key Words:  Bilevel knapsack problem, Uncertainty, Improved binary wolf pack algorithm

Hu-sheng Wu, Jun-jie Xue, Ren-bin Xiao, Jin-qiang Hu. Uncertain bilevel knapsack problem based on an improved binary wolf pack algorithm[J]. Frontiers of Information Technology & Electronic Engineering, 2020, 21(9): 1356-1368.

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%A Hu-sheng Wu
%A Jun-jie Xue
%A Ren-bin Xiao
%A Jin-qiang Hu
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%DOI 10.1631/FITEE.1900437

T1 - Uncertain bilevel knapsack problem based on an improved binary wolf pack algorithm
A1 - Hu-sheng Wu
A1 - Jun-jie Xue
A1 - Ren-bin Xiao
A1 - Jin-qiang Hu
J0 - Frontiers of Information Technology & Electronic Engineering
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1900437

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 PE Nash equilibrium and PE 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 PE uncertain solution are applied to an armament transportation problem as a case study.



摘要:为解决双层背包问题中的不确定性,提出一种不确定双层背包问题(uncertain bilevel knapsack problem, UBKP)模型。通过定义期望值纳什均衡(PE Nash equilibrium)和期望值斯塔克尔伯格-纳什均衡(PE Stackelberg-Nashe quilibrium),给出UBKP问题的不确定解。为提高不确定解的计算效率,构造一种改进的二进制狼群算法。该算法由一个规则(头狼规则)、两个算子(反向算子和移动算子)和三种智能行为(游走、智能猎杀和种群更新行为)组成。以某装备运输问题为实例,验证了UBKP模型及/不确定解的有效性。


Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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