A Fuzzy Genetic Algorithm Based on Binary Encoding for Solving Multidimensional Knapsack Problems

Table 11

Computational results of FGA with heuristics and local search algorithms.

m	n	α	Benchmark	Heuristics and local search algorithms					FGA
				M&O	V&Z	MKHEUR	SA	GACB
5	100	0.25	24197.20	13.69	10.30	1.59	2.95	0.99	0.12
		0.50	43252.90	6.71	6.90	0.77	1.67	0.45	0.08
		0.75	60471.00	5.11	5.86	0.48	0.87	0.32	0.01
	250	0.25	60409.70	6.64	5.85	0.53	3.09	0.23	0.01
		0.50	109284.60	5.22	4.40	0.24	1.89	0.12	0.00
		0.75	151555.90	3.56	3.59	0.16	0.84	0.08	0.00
	500	0.25	120615.50	4.93	4.11	0.22	3.41	0.09	0.00
		0.50	219503.10	2.96	2.53	0.08	2.04	0.04	0.00
		0.75	302354.90	2.31	2.41	0.06	0.92	0.03	0.00
			Average	5.68	5.12	0.46	1.96	0.26	0.02
10	100	0.25	22601.90	15.88	15.55	3.43	3.93	1.56	0.23
		0.50	45659.10	10.41	10.72	1.84	2.09	0.79	0.11
		0.75	59555.60	6.07	5.67	1.06	1.06	0.48	0.02
	250	0.25	58993.90	11.73	10.53	1.07	3.21	0.51	0.02
		0.50	108706.40	6.83	5.92	0.57	2.14	0.25	0.01
		0.75	151330.40	4.42	3.77	0.33	1.01	0.15	0.00
	500	0.25	118565.50	8.81	7.90	0.52	3.67	0.24	0.00
		0.50	217274.60	5.71	4.14	0.22	2.50	0.11	0.00
		0.75	302556.00	3.62	2.93	0.14	1.17	0.07	0.00
			Average	8.16	7.46	1.02	2.31	0.46	0.04
30	100	0.25	21654.60	17.39	17.21	9.02	4.94	2.91	0.53
		0.50	41431.30	11.82	10.19	3.51	2.62	1.34	0.28
		0.75	59199.10	6.58	5.92	2.03	1.29	0.83	0.06
	250	0.25	56875.90	13.54	12.41	3.70	3.60	1.19	0.24
		0.50	106673.70	8.64	7.12	1.53	2.25	0.53	0.05
		0.75	150443.50	4.49	3.91	0.84	0.96	0.31	0.01
	500	0.25	115473.50	9.84	9.62	1.89	3.75	0.61	0.05
		0.50	216156.90	7.10	5.71	0.73	2.30	0.26	0.00
		0.75	302353.40	3.72	3.51	0.48	1.07	0.17	0.00
			Average	9.24	8.40	2.64	2.53	0.91	0.14
Average				7.69	6.99	1.37	2.27	0.54	0.07