Uncertain multi-objective dynamic weapon-target allocation problem based on uncertainty theory

Guangjian Li; Guangjun He; Mingfa Zheng; Aoyu Zheng; Guangjian Li; Guangjun He; Mingfa Zheng; Aoyu Zheng

doi:10.3934/math.2023284

AIMS Mathematics

2023, Volume 8, Issue 3: 5639-5669. doi: 10.3934/math.2023284

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Uncertain multi-objective dynamic weapon-target allocation problem based on uncertainty theory

1.
Air Defense and Anti-missile School, Air Force Engineering University, Xi'an 710051, China
2.
Fundamentals Department, Air Force Engineering University, Xi'an 710051, China
3.
Equipment Management and Unmanned Aerial Vehicle Engineering School, Air Force Engineering University, Xi'an 710051, China

Received: 22 October 2022 Revised: 29 November 2022 Accepted: 12 December 2022 Published: 21 December 2022
MSC : 68U99

The weapon-target allocation (WTA) problem is a fundamental subject of defense-related applications research, and previous studies assume that the parameters in the model are determinate. For the real battlefield, asymmetric information usually leads to the failure of the above assumption, and there are uncertain factors whose frequency is hard to pinpoint. Based on uncertainty theory, we study a WTA problem in indeterminate battlefield in this paper. First, we analyze the uncertain factors in indeterminate battlefield and their influence on WTA problem. Then, considering the target threat value, the protected asset value and the extra cost of interception as uncertain variables, the uncertain multi-objective dynamic WTA (UMDWTA) model is established, where three indices including the value of destruction of targets, the value of surviving assets and the cost of operation are regarded as objective functions, and on this basis, an equivalent transformation is presented to convert the UMDWTA model into a determinate multi-objective programming (MOP) problem by expected value and standard deviation principle. To solve the proposed model efficiently, an improved multi-objective evolutionary algorithm based on decomposition (MOEA/D) is designed, which employs three new evolutionary operators and the weight vectors adaptation mechanism to improve the convergence and uniformity of the Pareto front obtained. Finally, a case of the UMDWTA problem is carried out to be solved by the designed algorithm, and the results verify the feasibility of the proposed model.
- uncertainty theory,
- weapon-target allocation,
- multi-objective programming,
- evolutionary algorithm
Citation: Guangjian Li, Guangjun He, Mingfa Zheng, Aoyu Zheng. Uncertain multi-objective dynamic weapon-target allocation problem based on uncertainty theory[J]. AIMS Mathematics, 2023, 8(3): 5639-5669. doi: 10.3934/math.2023284

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Abstract

The weapon-target allocation (WTA) problem is a fundamental subject of defense-related applications research, and previous studies assume that the parameters in the model are determinate. For the real battlefield, asymmetric information usually leads to the failure of the above assumption, and there are uncertain factors whose frequency is hard to pinpoint. Based on uncertainty theory, we study a WTA problem in indeterminate battlefield in this paper. First, we analyze the uncertain factors in indeterminate battlefield and their influence on WTA problem. Then, considering the target threat value, the protected asset value and the extra cost of interception as uncertain variables, the uncertain multi-objective dynamic WTA (UMDWTA) model is established, where three indices including the value of destruction of targets, the value of surviving assets and the cost of operation are regarded as objective functions, and on this basis, an equivalent transformation is presented to convert the UMDWTA model into a determinate multi-objective programming (MOP) problem by expected value and standard deviation principle. To solve the proposed model efficiently, an improved multi-objective evolutionary algorithm based on decomposition (MOEA/D) is designed, which employs three new evolutionary operators and the weight vectors adaptation mechanism to improve the convergence and uniformity of the Pareto front obtained. Finally, a case of the UMDWTA problem is carried out to be solved by the designed algorithm, and the results verify the feasibility of the proposed model.

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