多平台协同鲁棒团队形成问题与算法

doi:10.12305/j.issn.1001-506X.2026.08.14

摘要/Abstract

摘要：

随着装备智能化程度的提高，低成本的小型平台越来越受到青睐。任务规划者可对小型平台进行动态组合以满足任务需求，提升任务完成的经济性与灵活性，但面临更高的决策复杂度。针对平台选择面临的决策空间大、对抗性强、时效性要求高等挑战，研究多平台协同鲁棒团队形成问题，除了考虑平台的能力互补和使用成本之外，还考虑了团队鲁棒性和平台间的协同成本。针对这一非确定性多项式难问题，设计一种简单且高效的元启发式算法，能够在很短时间内得到高质量解。在不同规模的数据集上进行了计算实验，证明了所提算法的有效性。

关键词: 多平台协同, 团队形成, 鲁棒性, 元启发式算法

Abstract:

With the improvement of the intelligence level of equipment, small platforms with low cost are becoming more and more popular. Task planners can dynamically combine small platforms to meet task requirements, which improves the economy and flexibility of task completion, but it also faces higher decision-making complexity. Aiming at the challenges such as a large decision-making space, strong antagonism, and high requirements for timeliness in platform selection, the problem of multi-platform collaborative robust team formation is studied. In addition to considering the complementary capabilities and usage cost of platforms, the team robustness and the collaborative cost between platforms are also taken into account. For this non-deterministic polynomial-hard problem, a simple and efficient meta-heuristic algorithm is designed, which can obtain high-quality solutions in a very short time. Computational experiments are conducted on datasets of different scales, which proves the effectiveness of the proposed algorithm.

Key words: multi-platform collaboration, team formation, robustness, meta-heuristic algorithm

中图分类号:

O 22

汤罗浩, 雷洪涛, 石建迈, 刁博阳, 朱承. 多平台协同鲁棒团队形成问题与算法[J]. 系统工程与电子技术, 2026, 48(8): 2659-2668.

Luohao TANG, Hongtao LEI, Jianmai SHI, Boyang DIAO, Cheng ZHU. Multi-platform collaborative robust team formation problem and algorithm[J]. Systems Engineering and Electronics, 2026, 48(8): 2659-2668.

图/表 7

表1

Data-1数据集计算结果"

M	N	平均计算时间/s					平均目标值						GA Gap
M	N	SA	RLS	MRLS	GA	BF	SA	RLS	MRLS	GA	GAbest	BF	Gap1/%	Gap2/%
5	15	0.2	0.1	3.6	1.3	0.3	1437.9	2038.7	1229.7	1197.0	1197.0	1197.0	0.0	0.0
	17	0.2	0.1	3.2	1.1	2.5	1799.7	2305.9	1724.9	1671.0	1671.0	1671.0	0.0	0.0
	19	0.2	0.1	3.9	1.7	14.4	1921.0	2872.9	1772.0	1543.0	1543.0	1543.0	0.0	0.0
	21	0.2	0.1	4.2	0.9	80.1	1748.4	2529.5	1630.5	1580.5	1580.5	1580.5	0.0	0.0
	23	0.1	0.1	4.0	1.1	565.8	1930.1	2208.1	1740.5	1578.5	1578.5	1578.5	0.0	0.0
	25	0.2	0.1	5.3	1.1	1783.9	1023.8	1803.6	982.1	935.6	927.5	927.5	0.9	0.0
8	15	0.2	0.1	3.6	2.1	0.6	1835.2	2757.8	1903.9	1468.5	1468.5	1468.5	0.0	0.0
	17	0.2	0.1	4.2	2.2	2.2	2509.5	3364.7	2437.0	2256.0	2256.0	2256.0	0.0	0.0
	19	0.2	0.1	4.1	2.5	14.1	1934.6	3008.7	1994.4	1674.0	1674.0	1674.0	0.0	0.0
	21	0.2	0.1	3.5	1.2	146.3	2264.4	2994.8	2156.3	2148.0	2148.0	2148.0	0.0	0.0
	23	0.2	0.1	4.1	1.4	611.8	1077.1	1512.9	1051.6	998.5	998.5	998.5	0.0	0.0
	25	0.2	0.1	5.6	1.9	1454.6	1687.1	3234.7	1668.6	1231.5	1231.5	1231.5	0.0	0.0
11	15	0.3	0.0	2.1	1.9	0.4	2391.1	4054.1	2830.9	2065.5	2065.5	2065.5	0.0	0.0
	17	0.2	0.1	4.3	1.6	2.6	3146.3	3800.4	3014.6	2867.5	2867.5	2867.5	0.0	0.0
	19	0.3	0.1	5.0	2.1	9.5	2605.5	4271.1	2733.0	2158.0	2158.0	2158.0	0.0	0.0
	21	0.2	0.1	4.2	1.1	147.3	1813.9	2647.1	1681.7	1584.4	1576.0	1576.0	0.5	0.0
11	23	0.2	0.1	6.1	9.0	395.6	1835.7	3838.8	2157.5	1450.0	1450.0	1450.0	0.0	0.0
11	25	0.2	0.1	4.1	1.1	3604.1	1880.3	2198.6	1612.4	1433.9	1422.5	1422.5	0.8	0.0
14	15	0.2	0.1	2.4	0.9	0.3	1665.6	3117.2	1644.5	1560.5	1560.5	1560.5	0.0	0.0
	17	0.2	0.1	4.2	1.5	4.6	1932.7	3118.4	1937.9	1754.0	1740.5	1740.5	0.8	0.0
	19	0.3	0.0	3.0	1.6	2.9	3261.3	5220.2	3400.8	3110.0	3110.0	3110.0	0.0	0.0
	21	0.2	0.1	5.5	2.1	55.8	2317.5	4496.3	2394.3	2033.0	2033.0	2033.0	0.0	0.0
	23	0.2	0.1	4.3	1.4	863.7	2058.0	2583.0	1974.1	1857.4	1847.5	1847.5	0.5	0.0
	25	0.2	0.1	5.4	1.2	2512.1	1199.5	3337.2	1309.1	876.0	876.0	876.0	0.0	0.0
17	15	0.2	0.1	1.9	1.6	0.2	3462.9	4185.7	3309.5	3020.5	3020.5	3020.5	0.0	0.0
	17	0.3	0.0	3.0	1.4	1.5	1724.9	3944.5	1955.6	1487.5	1487.5	1487.5	0.0	0.0
	19	0.2	0.1	4.2	2.9	16.0	2269.3	3114.3	2285.4	2059.8	2057.5	2057.5	0.1	0.0
	21	0.2	0.1	4.0	2.0	105.2	1784.1	2305.1	1680.3	1510.5	1510.5	1510.5	0.0	0.0
	23	0.2	0.1	4.6	2.8	912.0	1667.3	2322.7	1593.1	1310.0	1310.0	1310.0	0.0	0.0
	25	0.2	0.1	6.7	4.5	1109.9	2561.9	5549.1	2885.0	2043.5	2043.5	2043.5	0.0	0.0
20	15	0.2	0.1	3.5	3.0	0.7	2953.2	3583.0	2492.9	2139.5	2139.5	2139.5	0.0	0.0
	17	0.2	0.1	2.3	1.2	1.9	3481.8	5246.8	3546.5	3064.0	3064.0	3064.0	0.0	0.0
	19	0.2	0.1	4.2	1.2	22.7	1461.2	2219.6	1098.7	935.0	935.0	935.0	0.0	0.0
	21	0.3	0.1	2.9	2.9	20.7	3282.5	6048.7	4039.1	3077.0	3077.0	3077.0	0.0	0.0
	23	0.2	0.1	4.7	1.8	934.9	2595.7	3626.5	2422.5	2258.2	2248.0	2248.0	0.5	0.0
	25	0.2	0.1	5.6	4.2	3957.4	2373.4	3976.0	2314.7	1985.0	1985.0	1985.0	0.0	0.0

表1

表2

Data-2数据集计算结果"

M	N	平均计算时间/s					平均目标值						GA Gap
M	N	SA	RLS	MRLS	GA	BF	SA	RLS	MRLS	GA	GAbest	BF	Gap1/%	Gap2/%
5	15	0.2	0.1	3.0	1.4	0.2	2350.7	3031.7	2164.0	2101.5	2098.0	2098.0	0.2	0.0
	17	0.2	0.1	3.4	1.8	1.7	2366.5	3853.5	2167.6	1987.5	1987.5	1987.5	0.0	0.0
	19	0.2	0.1	3.4	1.3	5.7	2244.4	5721.9	2904.3	2011.0	2011.0	2011.0	0.0	0.0
	21	0.1	0.1	3.4	0.8	76.9	1526.9	2264.5	1457.6	1334.0	1334.0	1334.0	0.0	0.0
	23	0.1	0.1	4.1	1.0	282.7	2233.0	3381.4	2194.2	2005.5	2005.5	2005.5	0.0	0.0
	25	0.2	0.1	4.6	1.7	1233.1	2918.6	3918.7	2729.8	2282.5	2282.5	2282.5	0.0	0.0
8	15	0.2	0.1	2.1	1.1	0.2	2565.2	3305.6	2413.8	2281.0	2281.0	2281.0	0.0	0.0
	17	0.2	0.0	2.4	1.2	0.9	2496.1	4369.6	2538.6	2270.0	2270.0	2270.0	0.0	0.0
	19	0.2	0.1	3.5	1.1	12.2	2332.1	3364.0	2033.8	1826.5	1826.5	1826.5	0.0	0.0
	21	0.2	0.1	4.0	1.1	51.9	1802.4	2919.5	1747.2	1615.3	1611.0	1611.0	0.3	0.0
	23	0.2	0.1	4.6	1.5	300.6	1960.7	4210.3	1833.7	1383.5	1383.5	1383.5	0.0	0.0
	25	0.2	0.1	4.5	1.3	1732.6	1724.0	3500.5	1647.4	1521.8	1465.0	1465.0	3.9	0.0
11	15	0.1	0.1	3.0	1.1	0.6	2152.8	2362.7	1725.5	1582.5	1582.5	1582.5	0.0	0.0
	17	0.2	0.1	3.9	1.0	1.7	3727.8	4413.8	3224.5	3018.5	3018.5	3018.5	0.0	0.0
	19	0.2	0.1	3.5	1.6	10.3	3056.1	4501.3	3084.8	2679.0	2679.0	2679.0	0.0	0.0
	21	0.2	0.1	3.5	1.1	100.5	2436.6	3316.3	2099.9	1950.5	1950.5	1950.5	0.0	0.0
	23	0.2	0.1	4.2	2.3	292.7	2966.9	4456.8	2558.6	2122.9	2120.0	2120.0	0.1	0.0
	25	0.2	0.1	6.9	4.5	492.2	2811.4	5771.5	3423.1	1950.0	1950.0	1950.0	0.0	0.0
14	15	0.2	0.0	1.8	1.4	0.2	3708.5	4595.4	3310.8	3124.5	3124.5	3124.5	0.0	0.0
	17	0.2	0.0	2.2	1.2	1.1	3994.9	5439.1	3764.7	3421.5	3421.5	3421.5	0.0	0.0
	19	0.3	0.1	3.3	3.5	2.4	3724.1	5282.1	3741.0	3252.1	3238.5	3238.5	0.4	0.0
	21	0.2	0.1	4.2	1.7	51.4	2729.6	3656.2	2425.3	2122.5	2122.5	2122.5	0.0	0.0
	23	0.2	0.1	4.7	5.0	290.6	3182.4	4161.3	2793.0	2250.0	2250.0	2250.0	0.0	0.0
	25	0.2	0.1	5.5	1.3	1582.2	2126.0	3904.1	2008.9	1606.5	1606.5	1606.5	0.0	0.0
17	15	0.2	0.1	2.5	2.0	0.3	3227.4	4127.8	3001.9	2846.5	2846.5	2846.5	0.0	0.0
	17	0.2	0.1	3.8	1.4	2.7	1843.0	3316.9	1776.8	1401.0	1401.0	1401.0	0.0	0.0
	19	0.3	0.1	4.8	2.1	4.6	3689.7	5494.2	3654.5	3045.0	3045.0	3045.0	0.0	0.0
	21	0.2	0.1	4.1	2.2	65.1	3012.5	7286.1	3692.2	2504.0	2504.0	2504.0	0.0	0.0
	23	0.2	0.1	5.7	1.7	314.6	2675.4	5007.7	2673.0	2019.0	2019.0	2019.0	0.0	0.0
	25	0.2	0.1	4.6	2.1	2233.0	2777.3	4463.6	2649.4	2165.5	2165.5	2165.5	0.0	0.0
20	15	0.2	0.1	3.4	2.8	0.4	2417.8	3454.8	2294.2	2021.5	2021.5	2021.5	0.0	0.0
	17	0.3	0.0	1.5	6.6	0.9	3898.7	5897.0	4253.1	3354.5	3354.5	3354.5	0.0	0.0
	19	0.3	0.1	4.4	2.4	11.8	3203.0	5761.1	3559.6	2609.0	2609.0	2609.0	0.0	0.0
	21	0.2	0.1	5.0	2.1	31.3	3125.2	5307.4	3458.2	2708.5	2708.5	2708.5	0.0	0.0
	23	0.7	0.0	3.0	5.9	36.6	4120.9	8345.1	5481.0	3548.6	3538.0	3538.0	0.3	0.0
	25	0.2	0.1	5.1	3.5	1405.7	2099.4	4089.3	2092.4	1462.5	1462.5	1462.5	0.0	0.0

表2

表3

Data-3数据集计算结果"

M	N	平均计算时间/s				平均目标值					Gap/%
M	N	SA	RLS	MRLS	GA	SA	RLS	MRLS	GA	GAbest	Gap/%
30	100	0.6	1.5	61.3	7.1	8822.7	16125.8	9930.0	5702.6	5664.0	0.7
	150	0.6	1.5	86.8	3.5	7680.8	17577.9	9647.8	4278.5	4259.5	0.4
	200	0.6	1.2	67.6	3.2	7781.0	11636.6	7389.8	4127.8	4060.0	1.7
	250	0.6	1.9	98.2	3.8	7435.2	13210.1	8046.1	3581.6	3515.0	1.9
	300	0.7	2.2	127.9	3.7	7893.0	13304.9	8734.5	3746.1	3711.0	0.9
	350	0.7	2.8	127.7	4.0	7482.4	14625.4	8605.2	3615.0	3593.0	0.6
40	100	0.6	0.8	45.4	3.3	7850.6	11273.3	8149.1	5515.5	5477.0	0.7
	150	0.7	1.6	91.4	5.0	9630.1	18664.2	11491.1	6277.2	6206.5	1.1
	200	0.6	2.6	97.6	3.9	8315.7	16122.4	8393.9	3622.4	3534.0	2.5
	250	0.7	2.7	126.0	4.6	8507.5	16362.6	9865.0	4536.7	4435.0	2.3
	300	0.6	2.4	107.7	3.6	7364.9	14579.8	8304.8	4053.6	3952.5	2.6
	350	0.7	2.6	135.7	3.8	8220.5	15315.2	8887.2	3643.3	3588.0	1.5
50	100	0.7	1.6	83.4	9.7	11251.8	20415.2	13010.9	7181.0	7100.5	1.1
	150	0.5	1.1	61.5	3.0	6638.7	11516.4	7419.4	3688.6	3664.0	0.7
	200	0.8	2.3	104.7	4.4	10427.0	18601.7	10698.5	5240.9	5159.5	1.6
	250	0.7	2.0	103.7	3.8	8344.9	14231.8	8147.5	4452.9	4431.5	0.5
	300	0.7	2.4	128.8	4.3	8666.4	17573.0	9832.8	4611.7	4563.0	1.1
	350	0.7	2.7	125.1	3.8	7863.7	13651.5	8040.1	3903.2	3862.5	1.1
60	100	0.7	1.4	65.2	4.0	9589.7	17934.3	11053.2	6364.9	6283.0	1.3
	150	0.7	2.3	100.2	3.7	9267.6	17284.4	10264.5	4628.2	4613.0	0.3
	200	0.7	1.7	99.8	5.1	9465.9	17529.2	11038.5	5413.6	5313.0	1.9
	250	0.6	2.5	113.3	4.0	7796.2	15922.7	9082.1	4337.2	4299.5	0.9
	300	0.7	3.1	134.2	4.9	8396.1	16674.2	10023.4	4206.2	4153.5	1.3
	350	0.8	2.2	113.5	4.5	8664.7	14877.1	8132.5	4398.8	4344.5	1.2
70	100	0.7	1.8	93.2	16.8	11111.9	21541.6	13900.9	6483.7	6459.0	0.4
	150	0.7	2.2	102.3	3.9	9000.0	18890.9	11436.8	4593.1	4586.0	0.2
	200	0.7	2.1	108.2	4.7	9033.8	16916.2	9941.4	4510.7	4420.5	2.0
	250	0.7	2.5	129.1	4.2	9012.8	15849.0	9836.1	4289.4	4151.5	3.3
	300	0.7	2.3	130.1	4.0	8138.9	13458.5	8338.9	3763.5	3682.0	2.2
	350	0.7	2.7	133.2	3.9	8639.6	13978.8	8611.1	3439.2	3384.5	1.6
80	100	0.8	1.7	78.5	7.2	10397.2	21516.4	13809.8	7257.2	7157.0	1.4
	150	0.6	1.6	69.0	3.6	7687.4	13974.1	8634.5	5033.9	4978.5	1.1
	200	0.6	2.1	90.4	3.4	7690.1	15612.8	8247.8	4367.4	4285.0	1.9
	250	0.7	3.0	111.2	4.1	7948.3	17441.3	8971.5	4283.3	4247.0	0.9
	300	0.7	2.5	128.6	4.3	8353.5	13961.1	8853.1	3846.2	3809.5	1.0
	350	0.7	2.7	146.2	4.2	8527.7	15566.9	9566.0	3781.9	3729.0	1.4

表3

图1

图2

图3

图4

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