A Modified Artificial Bee Colony Algorithm for 𝑝-Center Problems

Table 1

Computational results for benchmark problems.

Problem	𝑛	𝑝	M-I	VNS	TS-1	TS-2	SS	BCOi	M-ABC
Pmed1	100	5	127	127	127	127	127	127	127
Pmed2	100	10	98	98	98	98	98	98	98
Pmed3	100	10	93	93	93	93	93	93	93
Pmed4	100	20	74	74	74	74	—	74	74
Pmed5	100	33	48	48	48	48	—	48	48
Pmed6	200	5	84	84	84	84	84	84	84
Pmed7	200	10	64	64	64	64	64	64	64
Pmed8	200	20	58	55	55	55	—	55	55
Pmed9	200	40	46	37	37	37	—	37	37
Pmed10	200	67	30	20	20	20	—	20	20
Pmed11	300	5	59	59	59	59	59	59	59
Pmed12	300	10	51	51	51	51	51	51	51
Pmed13	300	30	41	36	36	36	—	37	36
Pmed14	300	60	36	26	26	26	—	27	26
Pmed15	300	100	29	18	25	18	—	18	18
Pmed16	400	5	47	47	47	47	47	47	47
Pmed17	400	10	40	39	39	39	39	39	39
Pmed18	400	28	29	28	28	35.71	—	29	30
Pmed19	400	80	28	19	23	19	—	19	19
Pmed20	400	133	26	14	22	14	—	14	14
Pmed21	500	5	40	40	40	40	40	40	40
Pmed22	500	10	40	38	38	38	38	39	38
Pmed23	500	50	30	23	23	23	—	23	23
Pmed24	500	100	25	16	18	16	—	16	16
Pmed25	500	167	22	12	24	12	—	12	12
Pmed26	600	5	38	38	38	38	38	38	38
Pmed27	600	10	33	32	32	32	32	32	32
Pmed28	600	60	25	19	19	19	—	19	19
Pmed29	600	120	23	13	23	13	—	14	13
Pmed30	600	200	20	11	19	11	—	10	11
Pmed31	700	5	30	30	30	30	30	30	30
Pmed32	700	10	30	29	29	29	29	29	29
Pmed33	700	70	22	16	16	16	—	16	16
Pmed34	700	140	21	12	20	12	—	12	12
Pmed35	800	5	30	30	30	30	30	30	30
Pmed36	800	10	28	27	27	27	27	28	28
Pmed37	800	80	23	16	22	16	—	16	16
Pmed38	900	5	29	29	29	29	29	29	29
Pmed39	900	10	24	24	23	24	23	24	23
Pmed40	900	90	21	14	22	14	—	14	14
Best/total			15/40	38/40	31/40	37/40	19/19	33/40	37/40