基于正向解析式和多目标博弈优化算法的复杂装备体系优化设计方法

doi:10.12382/bgxb.2023.0031

摘要/Abstract

摘要：

针对复杂装备体系(Complex Equipment System-of-systems, CES)优化设计中指标变量多、仿真依赖性强、易陷入局部最优的问题,提出一种基于正向解析式和多目标博弈理论(Multi-Objective Game Theory, MOGT)优化算法的CES优化设计方法。为提升CES优化设计的可解释性,构建任务级—能力级—装备级的评估指标体系;在此基础上,基于装备机理和效用函数表征装备评估指标与作战能力之间的正向映射关系,并利用相邻优属度熵权法计算各指标权重;通过正向解析式与约束条件建立多目标优化模型,并采用MOGT优化算法获得最佳优化结果。以某作战推演平台中防空攻防想定为例,开展算例评估与验证分析。研究结果表明,该方法能够实现CES中最优设计方案的求解,可显著提高设计效率和降低设计成本,为下一代装备发展论证、设计评估和作战试验提供了基础性工作。

关键词: 复杂装备体系, 正向优化设计, 多目标博弈理论优化算法, 相邻优属度熵权, 作战推演仿真

Abstract:

For the problems of many index variables, strong simulation dependence and being easy to fall into local optimum in the optimization design of complex equipment system-of-systems (CES), an optimization design method of CES based on forward analytical formula and multi-objective game theory (MOGT) optimization algorithm is proposed. In order to improve the interpretability of the CES optimization design, evaluation index systems among task-level, capability-level and equipment-level are constructed. On this basis, the positive mapping relationship between the evaluation performance index and the combat capability is characterized based on the equipment mechanism and utility function, and the weight of each index is calculated by the adjacent priority degree entropy weight method. A multi-objective optimization model is established by using the forward analytical formulas and constraints, and the MOGT optimization algorithm is used to obtain the best optimization results.The air defense scenario in an operation deduction platform is taken as an example for the example evaluation and verification analysis. The results show that the proposed method can realize the solution of the optimal design scheme in the CES, which can significantly improve the design efficiency and reduce the design cost, and provide the basic work for the development demonstration, design evaluation and combat test of the next generation equipment.

Key words: complex equipment system-of-systems, forward optimization design, multi-objective game theory optimization algorithm, adjacent priority entropy weight, operation deduction simulation

中图分类号:

TJ301

丁伟, 明振军, 王国新, 阎艳, 禹磊. 基于正向解析式和多目标博弈优化算法的复杂装备体系优化设计方法[J]. 兵工学报, 2024, 45(6): 1974-1990.

DING Wei, MING Zhenjun, WANG Guoxin, YAN Yan, YU Lei. Optimization Design Method of Complex Equipment System-of-systems Based on Forward Analytical Formula and MOGT Optimization Algorithm[J]. Acta Armamentarii, 2024, 45(6): 1974-1990.

图/表 18

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作战能力	评估指标	主观权重	客观权重	综合权重
	目标发现概率ω_1,1	0.426	0.401	0.417
目标侦察能力y₁	目标识别精度ω_1,2	0.304	0.339	0.326
	目标单位密度ω_1,3	0.270	0.260	0.257
持续探测能力y₂	搜索率ω_2,1	0.475	0.498	0.481
	发现率ω_2,2	0.525	0.502	0.519
抗干扰能力y₃	发现概率ω_3,1	0.550	0.537	0.539
	探测距离ω_3,2	0.450	0.463	0.461

作战能力	评估指标	主观权重	客观权重	综合权重
	目标发现概率ω_1,1	0.426	0.401	0.417
目标侦察能力y₁	目标识别精度ω_1,2	0.304	0.339	0.326
	目标单位密度ω_1,3	0.270	0.260	0.257
持续探测能力y₂	搜索率ω_2,1	0.475	0.498	0.481
	发现率ω_2,2	0.525	0.502	0.519
抗干扰能力y₃	发现概率ω_3,1	0.550	0.537	0.539
	探测距离ω_3,2	0.450	0.463	0.461

作战能力	评估指标	主观权重	客观权重	综合权重
	通讯覆盖范围ω_4,1	0.455	0.431	0.440
指挥通讯能力y₄	通讯目标数量ω_4,2	0.318	0.348	0.341
	通讯传输时延ω_4,3	0.227	0.221	0.219
	信息处理时间ω_5,1	0.391	0.369	0.388
信息处理能力y₅	信息存储空间ω_5,2	0.388	0.380	0.412
	信息处理延误率ω_5,3	0.221	0.251	0.200
	战场评估耗时ω_6,1	0.238	0.256	0.231
战场决策能力y₆	决策响应时长ω_6,2	0.317	0.328	0.340
	决策正确率ω_6,3	0.445	0.416	0.429

作战能力	评估指标	主观权重	客观权重	综合权重
	通讯覆盖范围ω_4,1	0.455	0.431	0.440
指挥通讯能力y₄	通讯目标数量ω_4,2	0.318	0.348	0.341
	通讯传输时延ω_4,3	0.227	0.221	0.219
	信息处理时间ω_5,1	0.391	0.369	0.388
信息处理能力y₅	信息存储空间ω_5,2	0.388	0.380	0.412
	信息处理延误率ω_5,3	0.221	0.251	0.200
	战场评估耗时ω_6,1	0.238	0.256	0.231
战场决策能力y₆	决策响应时长ω_6,2	0.317	0.328	0.340
	决策正确率ω_6,3	0.445	0.416	0.429

作战能力	评估指标	主观权重	客观权重	综合权重
	技术准备时间ω_7,1	0.287	0.293	0.310
快速反应能力y₇	波次响应周期ω_7,2	0.359	0.405	0.364
	波次打击耗时ω_7,3	0.354	0.302	0.326
	目标定位精度ω_8,1	0.165	0.177	0.174
	命中精度ω_8,2	0.206	0.192	0.191
精准打击能力y₈	打击角度ω_8,3	0.183	0.186	0.188
	打击距离ω_8,4	0.217	0.204	0.213
	战斗部威力ω_8,5	0.229	0.241	0.234
	突防概率ω_9,1	0.436	0.395	0.382
有效突防能力y₉	环境适应性水平ω_9,2	0.340	0.351	0.345
	隐蔽伪装水平ω_9,3	0.224	0.254	0.273
	波次打击数量ω_10,1	0.317	0.304	0.311
持续投送能力y₁₀	弹药装填耗时ω_10,2	0.329	0.295	0.301
	备件数量满足率ω_10,3	0.185	0.188	0.199
	技术人员专业性ω_10,4	0.169	0.213	0.189