A Lagrange Relaxation Method for Solving Weapon-Target Assignment Problem

Table 1

Numerical results of Lagrange relaxation method.

Dataset	Metrics (𝑊,𝑇)	Number of integral variables	Initial objective value	Best objective value	Improve rate	Computing time (sec)
						Initial solution	Best solution
1	𝑊=4,𝑇=7	28	3.37	4.1995	24.61%	0.002	0.005
2	𝑊=20,𝑇=30	600	11.7959	13.7753	16.78%	0.003	0.012
3	𝑊=30,𝑇=40	1200	14.6271	17.3206	18.41%	0.003	0.015
4	𝑊=40,𝑇=50	2000	18.7093	22.1186	18.22%	0.003	0.015
5	𝑊=40,𝑇=70	2800	30.0852	34.0953	13.33%	0.004	0.016
6	𝑊=40,𝑇=70	2800	25.6031	30.625	19.61%	0.004	0.018
7	𝑊=30,𝑇=100	3000	40.0767	45.1007	12.54%	0.007	0.015
8	𝑊=30,𝑇=100	3000	40.321	45.255	12.24%	0.006	0.016
9	𝑊=50,𝑇=100	5000	42.5188	47.0363	10.62%	0.008	0.038
10	𝑊=50,𝑇=100	5000	41.511	45.2753	9.07%	0.009	0.024
11	𝑊=100,𝑇=100	10000	40.6264	44.7785	10.22%	0.031	0.061
12	𝑊=100,𝑇=100	10000	45.0092	49.8157	10.68%	0.016	0.041
13	𝑊=100,𝑇=150	15000	62.9031	67.2282	6.88%	0.047	0.703
14	𝑊=100,𝑇=150	15000	67.0165	72.3343	7.94%	0.063	0.835
15	𝑊=150,𝑇=150	22500	69.5433	74.1215	6.58%	0.078	1.927
16	𝑊=150,𝑇=150	22500	68.9607	74.9836	8.73%	0.062	1.006
17	𝑊=100,𝑇=300	30000	122.0562	129.9045	6.43%	0.094	2.313
18	𝑊=100,𝑇=300	30000	133.6946	145.4427	8.79%	0.093	3.142
19	𝑊=200,𝑇=200	40000	92.3307	98.6923	6.89%	0.125	9.315
20	𝑊=200,𝑇=200	40000	96.3919	106.7961	10.79%	0.112	9.637