A VNS Metaheuristic with Stochastic Steps for Max 3-Cut and Max 3-Section

Table 2

The numerical comparisons of 0.836-approximate algorithm with VNS metaheuristic.

Wnp	𝑚	Obj rsdp	0.836-algorithm		VNS
	s.v.		Obj GM	𝑡GM	Objvns-𝑘	𝑡vns-𝑘	𝜌𝑘%	Objvns-𝑡	𝜌𝑡%	∇𝜌%
W20.1	990	121	117	22.93	119	0.28	−1.65	119	−1.65	0
W20.3	570	232	225	25.58	228	0.29	−1.72	228	−1.72	0
W20.6		492	464	14.27	479	0.40	−2.65	479	−2.24	0.41
W30.1	2235	147	139	161.56	144	0.81	−2.04	144	−2.04	0
W30.3	1305	566	521	140.12	550	0.97	−2.83	550	−2.30	0.53
W30.6		1181	1101	94.93	1151	0.92	−2.54	1151	−2.03	0.51
W45.1	5040	675	594	202.48	605	0.92	−10.38	612	−9.33	1.05
W45.3	2970	1300	1147	211.72	1192	1.02	−8.31	1300	−7.15	1.16
W45.6		2441	2272	217.57	2313	1.02	−5.25	2350	−3.73	1.52
W60.1	8970	1069	918	256.35	965	2.14	−9.73	981	−8.23	1.50
W60.3	5310	2494	2228	256.57	2301	3.13	−7.74	2332	−6.50	1.24
W60.6		4403	4054	266.68	4213	2.48	−4.32	4307	−2.18	2.14
W80.1	15960	1567	1357	537.58	1415	5.82	−9.71	1438	−8.23	1.48
W80.3	9480	4094	3666	546.23	3801	7.35	−7.16	3912	−4.45	2.71
W80.6		7746	7328	495.34	7423	6.31	−4.17	7481	−3.42	0.75
W100.1	24950	2526	2149	893.52	2262	12.73	−10.46	2302	−8.87	1.60
W100.3	14850	6418	5814	882.73	6010	12.66	−6.36	6113	−4.75	1.61
W100.6		11956	11212	865.28	11391	11.99	−4.73	11422	−4.47	0.26
W120.1	33990	3746	3222	1476.54	3335	34.07	−10.98	3392	−9.45	1.53
W120.3	21420	9173	8266	1498.18	8575	35.41	−6.52	8623	−6.00	0.52
W120.6		16748	15596	1567.43	16056	43.80	−4.14	16114	−3.79	0.35
W150.1	56175	5821	5020	2618.11	5208	69.20	−10.54	5257	−9.69	0.85
W150.3	33525	14432	13209	3021.87	13543	70.60	−6.15	13607	−5.72	0.43
W150.6		26310	25076	3172.22	25405	74.46	−3.44	25517	−3.01	0.43
W180.05	80910	4303	3578	9043.25	3726	133.10	−13.41	3812	−11.41	1.20
W180.1	48330	7236	6328	10225.54	6481	130.07	−10.44	6547	−9.52	0.92
W180.3		20147	18436	9887.36	19031	132.14	−5.54	19213	−4.64	0.90
W180.6		37292	35386	10004.11	35949	102.77	−3.61	36124	−3.13	0.48
W200.05	99900	5174	4306	25872.33	4484	71.90	−13.40	4509	−12.85	0.55
W200.1	59700	9271	8092	29003.28	8799	149.50	−5.10	8853	−4.51	0.59
W200.5		38831	36481	28774.17	37477	200.16	−3.49	37552	−3.29	0.20