兵工学报 ›› 2023, Vol. 44 ›› Issue (11): 3516-3528.doi: 10.12382/bgxb.2022.1276
所属专题: 群体协同与自主技术
收稿日期:
2022-12-22
上线日期:
2023-05-04
通讯作者:
基金资助:
ZHAO Wenfei1,*(), CHEN Jian1, WANG Yan2, TENG Kenan1
Received:
2022-12-22
Online:
2023-05-04
摘要:
针对海上要地群协同防空作战动态火力分配问题,综合分析海上要地防空作战过程的特点,建立基于马尔可夫决策模型的动态火力分配问题,构建以海上要地毁伤期望、拦截成本为指标的优化模型。考虑到马尔可夫决策模型求解易陷入维数灾难的问题,提出利用近似动态规划方法来探究解的有效性,并给出基于强化学习的最小二乘时序差分算法来求解该问题。通过4种典型的攻防场景共80个案例仿真结果表明,相比传统的匹配算法、遗传算法和粒子群优化算法,新构建的模型和算法更加科学合理有效,可为海上要地群协同防空作战火力分配提供一定的理论依据。
中图分类号:
赵文飞, 陈健, 王, 滕克难. 基于强化学习的海上要地群协同防空动态火力分配[J]. 兵工学报, 2023, 44(11): 3516-3528.
ZHAO Wenfei, CHEN Jian, WANG Yan, TENG Kenan. Dynamic Firepower Allocation for Cooperative Air Defense of Strategic Locations on the Sea Based on Reinforcement Learning[J]. Acta Armamentarii, 2023, 44(11): 3516-3528.
场景 | 要地导弹数量/发 | 要地价值系数 |
---|---|---|
场景1 | (30,20,15) | (15,20,10) |
场景2 | (10,10,10) | (15,20,10) |
场景3 | (30,20,15) | (15,10,20) |
场景4 | (10,10,10) | (15,10,20) |
表1 四类典型案例场景参数
Table 1 Scenario parameters of four typical cases
场景 | 要地导弹数量/发 | 要地价值系数 |
---|---|---|
场景1 | (30,20,15) | (15,20,10) |
场景2 | (10,10,10) | (15,20,10) |
场景3 | (30,20,15) | (15,10,20) |
场景4 | (10,10,10) | (15,10,20) |
φ(S) | Φ0(S) | Φ1(S) | Φ2(S) | Φ3(S) | Φ4(S) | Φ5(S) |
---|---|---|---|---|---|---|
1 | 1 | At | ||||
2 | 1 | At | ||||
3 | 1 |
表2 特征函数
Table 2 Characteristic functions
φ(S) | Φ0(S) | Φ1(S) | Φ2(S) | Φ3(S) | Φ4(S) | Φ5(S) |
---|---|---|---|---|---|---|
1 | 1 | At | ||||
2 | 1 | At | ||||
3 | 1 |
仿真情形 | N | K | φ(S) | α |
---|---|---|---|---|
1 | 10 | 500 | 1 | 0.01 |
2 | 50 | 1000 | 2 | 0.3 |
3 | 100 | 1500 | 3 | 0.8 |
表3 仿真参数
Table 3 Simulation parameters
仿真情形 | N | K | φ(S) | α |
---|---|---|---|---|
1 | 10 | 500 | 1 | 0.01 |
2 | 50 | 1000 | 2 | 0.3 |
3 | 100 | 1500 | 3 | 0.8 |
攻击向量 | LSTD算法 | GA | PSO算法 | LSTD算法最优值vL | GA最优值vG | PSO算法最优值vP | JLG/% | JLP/% |
---|---|---|---|---|---|---|---|---|
(1, 0, 0) | (2, 0, 0) | (3, 0, 0) | (3, 0, 0) | 0.868 | 0.769 | 0.769 | -12.87 | -12.87 |
(0, 1, 0) | (1, 1, 0) | (2, 3, 0) | (2, 2, 0) | 1.341 | 1.271 | 1.436 | -5.51 | 6.62 |
(0, 0, 1) | (1, 0,1) | (2, 0, 3) | (2, 0, 2) | 1.540 | 2.055 | 2.201 | 25.06 | 30.03 |
(2, 0, 0) | (4, 0, 0) | (6, 0, 0) | (6, 0, 0) | 1.713 | 1.538 | 1.538 | -11.38 | -11.38 |
(0, 2, 0) | (0, 4, 0) | (4, 6, 0) | (4, 4, 0) | 2.087 | 2.540 | 2.861 | 17.83 | 27.05 |
(0, 0, 2) | (2, 0, 4) | (3, 0, 6) | (3, 0, 4) | 2.604 | 4.064 | 4.320 | 35.93 | 39.72 |
(1, 1, 0) | (2, 1, 0) | (5, 3, 0) | (5, 2, 0) | 2.312 | 2.040 | 2.204 | -13.33 | -4.90 |
(1, 0, 1) | (3, 0, 2) | (5, 0,3) | (5, 0, 2) | 2.512 | 2.823 | 2.970 | 11.02 | 15.42 |
(1, 1, 1) | (2, 1, 2) | (7, 3, 3) | (7, 2, 2) | 3.936 | 4.094 | 4.406 | 3.86 | 10.67 |
(1, 2, 1) | (5, 4, 2) | (9, 6, 3) | (9, 4, 2) | 5.215 | 5.363 | 5.831 | 2.76 | 10.56 |
(1, 1, 2) | (5, 2, 4) | (8, 3,6) | (8, 2, 4) | 5.257 | 6.104 | 6.525 | 13.88 | 19.43 |
(2, 1, 1) | (4, 2, 2) | (10 3,3) | (9, 2, 2) | 4.675 | 4.863 | 5.312 | 3.87 | 11.99 |
(2, 2, 1) | (5, 3, 1) | (12, 6,3) | (11, 4, 2) | 6.158 | 6.132 | 6.737 | -0.42 | 8.59 |
(1, 2, 2) | (6, 4, 4) | (10, 6, 6) | (10, 4, 4) | 6.453 | 7.373 | 7.950 | 12.48 | 18.83 |
(1, 2, 1) | (4, 2, 2) | (9, 6, 3) | (9, 4, 2) | 5.185 | 5.363 | 5.831 | 3.32 | 11.08 |
(3, 0, 0) | (6, 0, 0) | (9, 0, 0) | (9, 0, 0) | 2.396 | 2.306 | 2.306 | -3.90 | -3.90 |
(3, 1, 1) | (8, 2, 2) | (13, 3, 3) | (11, 2, 2) | 4.447 | 5.632 | 6.306 | 21.04 | 29.48 |
(1, 3, 1) | (5, 6, 2) | (11, 8, 3) | (11, 6, 2) | 6.491 | 6.620 | 7.246 | 1.95 | 10.42 |
(1, 3, 3) | (7, 6, 6) | (14, 8, 8) | (13, 6, 6) | 7.871 | 10.615 | 11.455 | 25.85 | 31.29 |
(2, 4, 1) | (4, 7, 2) | (17, 11, 3) | (15, 8, 2) | 8.551 | 8.635 | 9.557 | 0.97 | 10.53 |
表4 Rt=(30,20,15), Ct=(15,20,10)仿真结果对比
Table 4 Comparison of simulated results in the case of Rt=(30,20,15), Ct=(15,20,10)
攻击向量 | LSTD算法 | GA | PSO算法 | LSTD算法最优值vL | GA最优值vG | PSO算法最优值vP | JLG/% | JLP/% |
---|---|---|---|---|---|---|---|---|
(1, 0, 0) | (2, 0, 0) | (3, 0, 0) | (3, 0, 0) | 0.868 | 0.769 | 0.769 | -12.87 | -12.87 |
(0, 1, 0) | (1, 1, 0) | (2, 3, 0) | (2, 2, 0) | 1.341 | 1.271 | 1.436 | -5.51 | 6.62 |
(0, 0, 1) | (1, 0,1) | (2, 0, 3) | (2, 0, 2) | 1.540 | 2.055 | 2.201 | 25.06 | 30.03 |
(2, 0, 0) | (4, 0, 0) | (6, 0, 0) | (6, 0, 0) | 1.713 | 1.538 | 1.538 | -11.38 | -11.38 |
(0, 2, 0) | (0, 4, 0) | (4, 6, 0) | (4, 4, 0) | 2.087 | 2.540 | 2.861 | 17.83 | 27.05 |
(0, 0, 2) | (2, 0, 4) | (3, 0, 6) | (3, 0, 4) | 2.604 | 4.064 | 4.320 | 35.93 | 39.72 |
(1, 1, 0) | (2, 1, 0) | (5, 3, 0) | (5, 2, 0) | 2.312 | 2.040 | 2.204 | -13.33 | -4.90 |
(1, 0, 1) | (3, 0, 2) | (5, 0,3) | (5, 0, 2) | 2.512 | 2.823 | 2.970 | 11.02 | 15.42 |
(1, 1, 1) | (2, 1, 2) | (7, 3, 3) | (7, 2, 2) | 3.936 | 4.094 | 4.406 | 3.86 | 10.67 |
(1, 2, 1) | (5, 4, 2) | (9, 6, 3) | (9, 4, 2) | 5.215 | 5.363 | 5.831 | 2.76 | 10.56 |
(1, 1, 2) | (5, 2, 4) | (8, 3,6) | (8, 2, 4) | 5.257 | 6.104 | 6.525 | 13.88 | 19.43 |
(2, 1, 1) | (4, 2, 2) | (10 3,3) | (9, 2, 2) | 4.675 | 4.863 | 5.312 | 3.87 | 11.99 |
(2, 2, 1) | (5, 3, 1) | (12, 6,3) | (11, 4, 2) | 6.158 | 6.132 | 6.737 | -0.42 | 8.59 |
(1, 2, 2) | (6, 4, 4) | (10, 6, 6) | (10, 4, 4) | 6.453 | 7.373 | 7.950 | 12.48 | 18.83 |
(1, 2, 1) | (4, 2, 2) | (9, 6, 3) | (9, 4, 2) | 5.185 | 5.363 | 5.831 | 3.32 | 11.08 |
(3, 0, 0) | (6, 0, 0) | (9, 0, 0) | (9, 0, 0) | 2.396 | 2.306 | 2.306 | -3.90 | -3.90 |
(3, 1, 1) | (8, 2, 2) | (13, 3, 3) | (11, 2, 2) | 4.447 | 5.632 | 6.306 | 21.04 | 29.48 |
(1, 3, 1) | (5, 6, 2) | (11, 8, 3) | (11, 6, 2) | 6.491 | 6.620 | 7.246 | 1.95 | 10.42 |
(1, 3, 3) | (7, 6, 6) | (14, 8, 8) | (13, 6, 6) | 7.871 | 10.615 | 11.455 | 25.85 | 31.29 |
(2, 4, 1) | (4, 7, 2) | (17, 11, 3) | (15, 8, 2) | 8.551 | 8.635 | 9.557 | 0.97 | 10.53 |
攻击向量 | LSTD算法 | GA | PSO算法 | LSTD最优值vL | GA最优值vG | PSO最优值vP | JLG/% | JLP/% |
---|---|---|---|---|---|---|---|---|
(1, 0, 0) | (2, 0, 0) | (3, 0, 0) | (3, 0, 0) | 0.868 | 0.769 | 0.769 | -12.87 | -12.87 |
(0, 1, 0) | (1, 1, 0) | (2, 3, 0) | (2, 2, 0) | 1.341 | 1.271 | 1.436 | -5.51 | 6.62 |
(0, 0, 1) | (1, 0,1) | (2, 0, 3) | (2, 0, 2) | 1.54 | 2.055 | 2.201 | 25.06 | 30.03 |
(2, 0, 0) | (4, 0, 0) | (6, 0, 0) | (6, 0, 0) | 1.713 | 1.538 | 1.538 | -11.38 | -11.38 |
(0, 2, 0) | (1, 2, 0) | (4, 6, 0) | (4, 4, 0) | 2.534 | 2.54 | 2.861 | 0.24 | 11.43 |
(0, 0, 2) | (2, 0, 4) | (3, 0, 6) | (3, 0, 4) | 2.604 | 4.064 | 4.32 | 35.93 | 39.72 |
(1, 1, 0) | (2, 1, 0) | (5, 3, 0) | (5, 2, 0) | 2.312 | 2.04 | 2.204 | -13.33 | -4.90 |
(1, 0, 1) | (2, 0, 2) | (5, 0,3) | (5, 0, 2) | 2.631 | 2.823 | 2.97 | 6.80 | 11.41 |
(1, 1, 1) | (2, 1, 2) | (7, 3, 3) | (7, 2, 2) | 3.936 | 4.094 | 4.406 | 3.86 | 10.67 |
(1, 2, 1) | (2, 4, 2) | (9, 6, 3) | (9, 4, 2) | 5.243 | 5.363 | 5.831 | 2.24 | 10.08 |
(1, 1, 2) | (5, 2, 4) | (8, 3,6) | (8, 2, 4) | 5.257 | 6.104 | 6.525 | 13.88 | 19.43 |
(2, 1, 1) | (2, 2, 1) | (10,3,3) | (9, 4, 2) | 4.745 | 4.863 | 5.312 | 2.43 | 10.67 |
(2, 2, 1) | (5, 3, 1) | (10, 6,3) | (8, 4, 2) | 6.158 | 6.327 | 6.821 | 2.67 | 9.72 |
(1, 2, 2) | (1, 3, 4) | (10, 6, 6) | (10, 4, 4) | 6.542 | 7.373 | 7.95 | 11.27 | 17.71 |
(1, 2, 1) | (2, 2, 2) | (9, 6, 3) | (9, 4, 2) | 5.213 | 5.363 | 5.831 | 2.80 | 10.60 |
(3, 0, 0) | (6, 0, 0) | (9, 0, 0) | (9, 0, 0) | 2.396 | 2.306 | 2.306 | -3.90 | -3.90 |
(3, 1, 1) | (5, 1, 2) | (10, 3, 3) | (9, 2, 2) | 4.812 | 6.059 | 6.403 | 20.58 | 24.85 |
(1, 3, 1) | (3, 3, 2) | (10, 8, 3) | (8, 6, 2) | 6.621 | 6.678 | 7.681 | 0.85 | 13.80 |
(1, 3, 3) | (7, 6, 6) | (10, 8, 8) | (8, 6, 6) | 7.871 | 11.14 | 11.851 | 29.34 | 33.58 |
(2, 4, 1) | (6, 4, 2) | (10, 10, 4) | (9, 8, 2) | 8.887 | 9.98 | 10.134 | 10.95 | 12.31 |
表5 Rt=(10,10,10), Ct=(15,20,10)仿真结果对比
Table 5 Comparison of simulated results in the case of Rt=(10,10,10), Ct=(15,20,10)
攻击向量 | LSTD算法 | GA | PSO算法 | LSTD最优值vL | GA最优值vG | PSO最优值vP | JLG/% | JLP/% |
---|---|---|---|---|---|---|---|---|
(1, 0, 0) | (2, 0, 0) | (3, 0, 0) | (3, 0, 0) | 0.868 | 0.769 | 0.769 | -12.87 | -12.87 |
(0, 1, 0) | (1, 1, 0) | (2, 3, 0) | (2, 2, 0) | 1.341 | 1.271 | 1.436 | -5.51 | 6.62 |
(0, 0, 1) | (1, 0,1) | (2, 0, 3) | (2, 0, 2) | 1.54 | 2.055 | 2.201 | 25.06 | 30.03 |
(2, 0, 0) | (4, 0, 0) | (6, 0, 0) | (6, 0, 0) | 1.713 | 1.538 | 1.538 | -11.38 | -11.38 |
(0, 2, 0) | (1, 2, 0) | (4, 6, 0) | (4, 4, 0) | 2.534 | 2.54 | 2.861 | 0.24 | 11.43 |
(0, 0, 2) | (2, 0, 4) | (3, 0, 6) | (3, 0, 4) | 2.604 | 4.064 | 4.32 | 35.93 | 39.72 |
(1, 1, 0) | (2, 1, 0) | (5, 3, 0) | (5, 2, 0) | 2.312 | 2.04 | 2.204 | -13.33 | -4.90 |
(1, 0, 1) | (2, 0, 2) | (5, 0,3) | (5, 0, 2) | 2.631 | 2.823 | 2.97 | 6.80 | 11.41 |
(1, 1, 1) | (2, 1, 2) | (7, 3, 3) | (7, 2, 2) | 3.936 | 4.094 | 4.406 | 3.86 | 10.67 |
(1, 2, 1) | (2, 4, 2) | (9, 6, 3) | (9, 4, 2) | 5.243 | 5.363 | 5.831 | 2.24 | 10.08 |
(1, 1, 2) | (5, 2, 4) | (8, 3,6) | (8, 2, 4) | 5.257 | 6.104 | 6.525 | 13.88 | 19.43 |
(2, 1, 1) | (2, 2, 1) | (10,3,3) | (9, 4, 2) | 4.745 | 4.863 | 5.312 | 2.43 | 10.67 |
(2, 2, 1) | (5, 3, 1) | (10, 6,3) | (8, 4, 2) | 6.158 | 6.327 | 6.821 | 2.67 | 9.72 |
(1, 2, 2) | (1, 3, 4) | (10, 6, 6) | (10, 4, 4) | 6.542 | 7.373 | 7.95 | 11.27 | 17.71 |
(1, 2, 1) | (2, 2, 2) | (9, 6, 3) | (9, 4, 2) | 5.213 | 5.363 | 5.831 | 2.80 | 10.60 |
(3, 0, 0) | (6, 0, 0) | (9, 0, 0) | (9, 0, 0) | 2.396 | 2.306 | 2.306 | -3.90 | -3.90 |
(3, 1, 1) | (5, 1, 2) | (10, 3, 3) | (9, 2, 2) | 4.812 | 6.059 | 6.403 | 20.58 | 24.85 |
(1, 3, 1) | (3, 3, 2) | (10, 8, 3) | (8, 6, 2) | 6.621 | 6.678 | 7.681 | 0.85 | 13.80 |
(1, 3, 3) | (7, 6, 6) | (10, 8, 8) | (8, 6, 6) | 7.871 | 11.14 | 11.851 | 29.34 | 33.58 |
(2, 4, 1) | (6, 4, 2) | (10, 10, 4) | (9, 8, 2) | 8.887 | 9.98 | 10.134 | 10.95 | 12.31 |
攻击向量 | LSTD算法 | GA | PSO算法 | LSTD最优值vL | GA最优值vG | PSO最优值vP | JLG/% | JLP/% |
---|---|---|---|---|---|---|---|---|
(1, 0, 0) | (2, 0, 0) | (3, 0, 0) | (3, 0, 0) | 0.891 | 0.769 | 0.769 | -15.86 | -15.86 |
(0, 1, 0) | (0, 1, 0) | (2, 2, 0) | (1, 1, 0) | 0.791 | 1.118 | 1.436 | 29.25 | 44.92 |
(0, 0, 1) | (1, 0,2) | (2, 0, 4) | (1, 0, 2) | 1.483 | 1.672 | 2.055 | 11.30 | 27.83 |
(2, 0, 0) | (4, 0, 0) | (3, 0, 0) | (3, 0, 0) | 1.495 | 1.538 | 1.538 | 2.80 | 2.80 |
(0, 2, 0) | (1, 2, 0) | (3, 5, 0) | (2, 3, 0) | 1.25 | 2.157 | 3.208 | 42.05 | 61.03 |
(0, 0, 2) | (2, 0, 4) | (4, 0, 9) | (2, 0, 4) | 4.033 | 3.325 | 4.073 | -21.29 | 0.98 |
(1, 1, 0) | (2, 1, 0) | (5, 2, 0) | (4, 1, 0) | 1.8 | 1.887 | 2.377 | 4.61 | 24.27 |
(1, 0, 1) | (2, 0, 2) | (5, 0,4) | (3, 0, 2) | 2.492 | 2.44 | 2.823 | -2.13 | 11.73 |
(1, 1, 1) | (4,2, 2) | (7, 2, 4) | (4, 2, 2) | 4.372 | 4.558 | 4.489 | 4.08 | 2.61 |
(1, 2, 1) | (3, 2, 2) | (8, 5, 4) | (5, 4, 2) | 5.28 | 4.597 | 6.217 | -14.86 | 15.07 |
(1, 1, 2) | (5, 2, 4) | (9, 2,9) | (5, 2, 4) | 4.081 | 5.211 | 6.469 | 21.68 | 36.91 |
(2, 1, 1) | (4, 1, 1) | (10,2,4) | (6, 2, 2) | 5.199 | 5.327 | 5.213 | 2.40 | 0.27 |
(2, 2, 1) | (5, 3, 2) | (11, 5,4) | (7, 4, 2) | 5.264 | 5.366 | 7.128 | 1.90 | 26.15 |
(1, 2, 2) | (1, 3, 4) | (10, 5, 9) | (4, 4, 5) | 6.751 | 7.25 | 7.88 | 6.88 | 14.33 |
(1, 2, 1) | (2, 2, 2) | (8,5, 4) | (8, 4, 2) | 5.304 | 4.597 | 5.722 | -15.38 | 7.31 |
(3, 0, 0) | (4, 0, 0) | (9, 0, 0) | (6, 0, 0) | 2.47 | 2.506 | 2.601 | 1.44 | 5.04 |
(3, 1, 1) | (6, 2, 2) | (13, 2, 4) | (6, 2, 2) | 5.824 | 5.996 | 6.154 | 2.87 | 5.36 |
(1, 3, 1) | (3, 6, 2) | (10, 7, 4) | (7, 5, 2) | 6.055 | 5.652 | 7.031 | -7.13 | 13.88 |
(1, 3, 3) | (8, 4, 6) | (14, 7, 13) | (8, 6,8) | 9.134 | 9.650 | 9.698 | 5.35 | 5.82 |
(2, 4, 1) | (6, 4, 2) | (14, 9, 4) | (9, 8, 2) | 7.437 | 7.490 | 10.191 | 0.71 | 27.02 |
表6 Rt=(30,20,15), Ct=(15,10,20)仿真结果对比
Table 6 Comparison of simulated results in the case of Rt=(30,20,15), Ct=(15,10,20)
攻击向量 | LSTD算法 | GA | PSO算法 | LSTD最优值vL | GA最优值vG | PSO最优值vP | JLG/% | JLP/% |
---|---|---|---|---|---|---|---|---|
(1, 0, 0) | (2, 0, 0) | (3, 0, 0) | (3, 0, 0) | 0.891 | 0.769 | 0.769 | -15.86 | -15.86 |
(0, 1, 0) | (0, 1, 0) | (2, 2, 0) | (1, 1, 0) | 0.791 | 1.118 | 1.436 | 29.25 | 44.92 |
(0, 0, 1) | (1, 0,2) | (2, 0, 4) | (1, 0, 2) | 1.483 | 1.672 | 2.055 | 11.30 | 27.83 |
(2, 0, 0) | (4, 0, 0) | (3, 0, 0) | (3, 0, 0) | 1.495 | 1.538 | 1.538 | 2.80 | 2.80 |
(0, 2, 0) | (1, 2, 0) | (3, 5, 0) | (2, 3, 0) | 1.25 | 2.157 | 3.208 | 42.05 | 61.03 |
(0, 0, 2) | (2, 0, 4) | (4, 0, 9) | (2, 0, 4) | 4.033 | 3.325 | 4.073 | -21.29 | 0.98 |
(1, 1, 0) | (2, 1, 0) | (5, 2, 0) | (4, 1, 0) | 1.8 | 1.887 | 2.377 | 4.61 | 24.27 |
(1, 0, 1) | (2, 0, 2) | (5, 0,4) | (3, 0, 2) | 2.492 | 2.44 | 2.823 | -2.13 | 11.73 |
(1, 1, 1) | (4,2, 2) | (7, 2, 4) | (4, 2, 2) | 4.372 | 4.558 | 4.489 | 4.08 | 2.61 |
(1, 2, 1) | (3, 2, 2) | (8, 5, 4) | (5, 4, 2) | 5.28 | 4.597 | 6.217 | -14.86 | 15.07 |
(1, 1, 2) | (5, 2, 4) | (9, 2,9) | (5, 2, 4) | 4.081 | 5.211 | 6.469 | 21.68 | 36.91 |
(2, 1, 1) | (4, 1, 1) | (10,2,4) | (6, 2, 2) | 5.199 | 5.327 | 5.213 | 2.40 | 0.27 |
(2, 2, 1) | (5, 3, 2) | (11, 5,4) | (7, 4, 2) | 5.264 | 5.366 | 7.128 | 1.90 | 26.15 |
(1, 2, 2) | (1, 3, 4) | (10, 5, 9) | (4, 4, 5) | 6.751 | 7.25 | 7.88 | 6.88 | 14.33 |
(1, 2, 1) | (2, 2, 2) | (8,5, 4) | (8, 4, 2) | 5.304 | 4.597 | 5.722 | -15.38 | 7.31 |
(3, 0, 0) | (4, 0, 0) | (9, 0, 0) | (6, 0, 0) | 2.47 | 2.506 | 2.601 | 1.44 | 5.04 |
(3, 1, 1) | (6, 2, 2) | (13, 2, 4) | (6, 2, 2) | 5.824 | 5.996 | 6.154 | 2.87 | 5.36 |
(1, 3, 1) | (3, 6, 2) | (10, 7, 4) | (7, 5, 2) | 6.055 | 5.652 | 7.031 | -7.13 | 13.88 |
(1, 3, 3) | (8, 4, 6) | (14, 7, 13) | (8, 6,8) | 9.134 | 9.650 | 9.698 | 5.35 | 5.82 |
(2, 4, 1) | (6, 4, 2) | (14, 9, 4) | (9, 8, 2) | 7.437 | 7.490 | 10.191 | 0.71 | 27.02 |
攻击向量 | LSTD算法 | GA | PSO算法 | LSTD最优值vL | GA最优值vG | PSO最优值vP | JLG/% | JLP/% |
---|---|---|---|---|---|---|---|---|
(1, 0, 0) | (1, 0, 0) | (3, 0, 0) | (3, 0, 0) | 0.94 | 0.769 | 0.769 | -22.24 | -22.24 |
(0, 1, 0) | (0, 2, 0) | (2, 2, 0) | (1, 1, 0) | 0.846 | 1.118 | 1.436 | 24.33 | 41.09 |
(0, 0, 1) | (1, 0,2) | (2, 0, 4) | (1, 0, 2) | 2.485 | 1.672 | 2.055 | -48.62 | -20.92 |
(2, 0, 0) | (3, 0, 0) | (3, 0, 0) | (3, 0, 0) | 1.7 | 1.538 | 1.538 | -10.53 | -10.53 |
(0, 2, 0) | (0,2, 0) | (3, 5, 0) | (2, 3, 0) | 1.472 | 2.157 | 3.208 | 31.76 | 54.11 |
(0, 0, 2) | (2, 0, 4) | (4, 0, 9) | (2, 0, 4) | 4.025 | 3.325 | 4.073 | -21.05 | 1.18 |
(1, 1, 0) | (1, 1, 0) | (5, 2, 0) | (4, 1, 0) | 1.783 | 1.887 | 2.377 | 5.51 | 24.99 |
(1, 0, 1) | (1, 0, 2) | (5, 0,4) | (3, 0, 2) | 2.438 | 2.44 | 2.823 | 0.08 | 13.64 |
(1, 1, 1) | (2,2, 2) | (7, 2, 4) | (4, 2, 2) | 3.48 | 3.558 | 4.489 | 2.19 | 22.48 |
(1, 2, 1) | (3,4, 1) | (8, 5, 4) | (5, 4, 2) | 4.1 | 4.597 | 6.217 | 10.81 | 34.05 |
(1, 1, 2) | (2, 2, 4) | (9, 2,9) | (5, 2, 4) | 4.506 | 5.211 | 6.469 | 13.53 | 30.34 |
(2, 1, 1) | (6, 2, 2) | (10,2,4) | (6, 2, 2) | 4.735 | 4.327 | 5.213 | -9.43 | 9.17 |
(2, 2, 1) | (5, 3, 2) | (10, 5,4) | (7, 4, 2) | 4.364 | 5.503 | 7.128 | 20.70 | 38.78 |
(1, 2, 2) | (3, 3,2) | (10, 5, 9) | (4, 4, 5) | 5.972 | 6.25 | 7.88 | 4.45 | 24.21 |
(1, 2, 1) | (2, 2, 2) | (8,5, 4) | (8, 4, 2) | 3.529 | 4.597 | 5.722 | 23.23 | 38.33 |
(3, 0, 0) | (3, 0, 0) | (9, 0, 0) | (6, 0, 0) | 2.634 | 2.306 | 2.306 | -14.22 | -14.22 |
(3, 1, 1) | (6, 1, 2) | (10, 2, 4) | (6, 2, 2) | 4.33 | 5.527 | 6.154 | 21.66 | 29.64 |
(1, 3, 1) | (2, 6, 2) | (10, 7, 4) | (7, 5, 2) | 4.694 | 5.652 | 7.031 | 16.95 | 33.24 |
(1, 3, 3) | (5, 6, 8) | (10, 7, 10) | (8, 6,8) | 9.767 | 9.850 | 9.898 | 0.84 | 1.32 |
(2, 4, 1) | (5, 6, 2) | (10, 9, 4) | (9, 8, 2) | 7.481 | 8.222 | 10.191 | 9.01 | 26.59 |
表7 Rt=(10,10,10),Ct=(15,10,20)仿真结果对比
Table 7 Comparison of simulated results in the case of Rt=(10,10,10), Ct=(15,10,20)
攻击向量 | LSTD算法 | GA | PSO算法 | LSTD最优值vL | GA最优值vG | PSO最优值vP | JLG/% | JLP/% |
---|---|---|---|---|---|---|---|---|
(1, 0, 0) | (1, 0, 0) | (3, 0, 0) | (3, 0, 0) | 0.94 | 0.769 | 0.769 | -22.24 | -22.24 |
(0, 1, 0) | (0, 2, 0) | (2, 2, 0) | (1, 1, 0) | 0.846 | 1.118 | 1.436 | 24.33 | 41.09 |
(0, 0, 1) | (1, 0,2) | (2, 0, 4) | (1, 0, 2) | 2.485 | 1.672 | 2.055 | -48.62 | -20.92 |
(2, 0, 0) | (3, 0, 0) | (3, 0, 0) | (3, 0, 0) | 1.7 | 1.538 | 1.538 | -10.53 | -10.53 |
(0, 2, 0) | (0,2, 0) | (3, 5, 0) | (2, 3, 0) | 1.472 | 2.157 | 3.208 | 31.76 | 54.11 |
(0, 0, 2) | (2, 0, 4) | (4, 0, 9) | (2, 0, 4) | 4.025 | 3.325 | 4.073 | -21.05 | 1.18 |
(1, 1, 0) | (1, 1, 0) | (5, 2, 0) | (4, 1, 0) | 1.783 | 1.887 | 2.377 | 5.51 | 24.99 |
(1, 0, 1) | (1, 0, 2) | (5, 0,4) | (3, 0, 2) | 2.438 | 2.44 | 2.823 | 0.08 | 13.64 |
(1, 1, 1) | (2,2, 2) | (7, 2, 4) | (4, 2, 2) | 3.48 | 3.558 | 4.489 | 2.19 | 22.48 |
(1, 2, 1) | (3,4, 1) | (8, 5, 4) | (5, 4, 2) | 4.1 | 4.597 | 6.217 | 10.81 | 34.05 |
(1, 1, 2) | (2, 2, 4) | (9, 2,9) | (5, 2, 4) | 4.506 | 5.211 | 6.469 | 13.53 | 30.34 |
(2, 1, 1) | (6, 2, 2) | (10,2,4) | (6, 2, 2) | 4.735 | 4.327 | 5.213 | -9.43 | 9.17 |
(2, 2, 1) | (5, 3, 2) | (10, 5,4) | (7, 4, 2) | 4.364 | 5.503 | 7.128 | 20.70 | 38.78 |
(1, 2, 2) | (3, 3,2) | (10, 5, 9) | (4, 4, 5) | 5.972 | 6.25 | 7.88 | 4.45 | 24.21 |
(1, 2, 1) | (2, 2, 2) | (8,5, 4) | (8, 4, 2) | 3.529 | 4.597 | 5.722 | 23.23 | 38.33 |
(3, 0, 0) | (3, 0, 0) | (9, 0, 0) | (6, 0, 0) | 2.634 | 2.306 | 2.306 | -14.22 | -14.22 |
(3, 1, 1) | (6, 1, 2) | (10, 2, 4) | (6, 2, 2) | 4.33 | 5.527 | 6.154 | 21.66 | 29.64 |
(1, 3, 1) | (2, 6, 2) | (10, 7, 4) | (7, 5, 2) | 4.694 | 5.652 | 7.031 | 16.95 | 33.24 |
(1, 3, 3) | (5, 6, 8) | (10, 7, 10) | (8, 6,8) | 9.767 | 9.850 | 9.898 | 0.84 | 1.32 |
(2, 4, 1) | (5, 6, 2) | (10, 9, 4) | (9, 8, 2) | 7.481 | 8.222 | 10.191 | 9.01 | 26.59 |
仿真情形 | Rt=(30,20,15), Ct=(15,20,10) | Rt=(10,10,10), Ct=(15,20,10) | Rt=(30,20,15), Ct=(15,10,20) | Rt=(10,10,10), Ct=(15,10,20) |
---|---|---|---|---|
1 | 5.14 | 5.23 | 5.45 | 5.44 |
2 | 4.88 | 5.01 | 5.31 | 5.29 |
3 | 4.93 | 4.94 | 5.29 | 5.24 |
表8 LSTD算法在各类仿真参数得到的最优目标函数值
Table 8 Optimal objective function values obtained by LSTD algorithm in various simulation parameters
仿真情形 | Rt=(30,20,15), Ct=(15,20,10) | Rt=(10,10,10), Ct=(15,20,10) | Rt=(30,20,15), Ct=(15,10,20) | Rt=(10,10,10), Ct=(15,10,20) |
---|---|---|---|---|
1 | 5.14 | 5.23 | 5.45 | 5.44 |
2 | 4.88 | 5.01 | 5.31 | 5.29 |
3 | 4.93 | 4.94 | 5.29 | 5.24 |
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