Algorithmic Mechanism Design of Evolutionary Computation

Table 7

Number of function calls (NFC in (11)), success rate (SR in (12)), acceleration rate (AR in (13)), and fitness value to reach (VTR in (10)) of 5D benchmark function.

(a)

Function	DE-best		DE-rand			jDE-best			jDE-rand			Best-
	NFC	SR	NFC	SR	AR	NFC	SR	AR	NFC	SR	AR	NFC	SR	AR
	19022	0.37	19024	0.37	97.04	3132	0.90	219.20	3132	0.90	219.20	19018	0.37	113.83
	18021	0.40	17032	0.43	38.28	4160	0.86	157.48	4160	0.86	157.48	19012	0.37	148.01
	14025	0.53	17041	0.43	40.80	4077	0.86	238.19	4079	0.86	238.17	15022	0.50	153.89
	17037	0.43	15058	0.50	39.49	6195	0.79	127.66	5297	0.82	54.31	20021	0.33	46.58
	16019	0.47	22021	0.27	0.71	8115	0.73	88.14	8126	0.73	86.84	22009	0.27	74.67
	13014	0.57	15016	0.50	20.39	5058	0.83	218.61	5050	0.83	218.70	10015	0.67	171.82
	14022	0.53	17023	0.43	70.01	4094	0.86	205.57	4094	0.86	205.57	20004	0.33	83.92
	26007	0.13	26020	0.13	22.06	13248	0.56	63.47	12219	0.59	71.18	27016	0.10	10.02
	24009	0.20	27000	0.10	0.89	5158	0.83	161.35	5158	0.83	161.35	21010	0.30	130.37
	22005	0.27	22006	0.27	40.82	6112	0.80	171.47	7109	0.76	179.88	21006	0.30	100.82
	26003	0.13	25005	0.17	31.75	8302	0.72	137.37	7284	0.76	182.02	23010	0.23	77.98
	22001	0.27	17019	0.43	135.48	7138	0.76	140.67	7138	0.76	140.67	19007	0.37	142.09
	14008	0.53	16004	0.47	27.16	2072	0.93	193.09	2072	0.93	193.09	9016	0.70	237.42
	28006	0.07	29001	0.03	34.23	14184	0.53	182.18	14191	0.53	181.66	25013	0.17	105.53
Average	19514.21	0.35	20305.00	0.32	42.79	6503.21	0.78	164.60	6364.93	0.79	163.58	19298.50	0.36	114.07

(b)

Function	Rand-			Best-Cr			Rand-Cr			Mutation			Mixture
	NFC	SR	AR	NFC	SR	AR	NFC	SR	AR	NFC	SR	AR	NFC	SR	AR
	25015	0.17	0.72	3152	0.89	164.36	4177	0.86	107.04	19016	0.37	90.20	3367	0.89	208.62
	20016	0.33	71.13	6215	0.79	82.35	4539	0.85	76.96	19023	0.37	51.93	7137	0.76	170.13
	14030	0.53	112.95	1156	0.96	153.02	2783	0.91	54.13	15018	0.50	74.25	4159	0.86	149.96
	19046	0.37	26.03	10177	0.66	48.29	3978	0.87	45.09	22050	0.27	0.72	5513	0.82	97.85
	22021	0.27	45.04	4235	0.86	103.76	3255	0.89	98.19	17034	0.43	103.63	10295	0.66	73.34
	10032	0.67	116.85	5054	0.83	161.90	3103	0.90	148.66	13014	0.57	70.79	3143	0.90	158.03
	17020	0.43	59.56	2114	0.93	165.37	4128	0.86	160.04	13028	0.57	215.68	7142	0.76	151.00
	17075	0.43	109.19	4795	0.84	65.60	2236	0.93	98.39	26010	0.13	50.79	715	0.98	128.44
	15058	0.50	118.20	10177	0.66	100.23	4248	0.86	99.42	22010	0.27	96.46	1496	0.95	135.55
	15031	0.50	166.54	7174	0.76	102.39	3632	0.88	95.18	22014	0.27	34.09	5221	0.83	219.77
	16083	0.46	80.30	7441	0.75	132.90	4907	0.84	161.32	26001	0.13	37.96	2121	0.93	95.21
	17023	0.43	84.50	6358	0.79	110.48	3371	0.89	122.79	21009	0.30	20.43	1243	0.96	179.52
	8038	0.73	206.99	3072	0.90	217.49	1159	0.96	161.38	10040	0.67	152.20	2106	0.93	275.64
	22046	0.27	94.53	7069	0.76	72.58	4927	0.84	82.05	28009	0.07	5.75	3285	0.89	137.22
Average	16966.71	0.43	92.32	5584.93	0.81	120.05	3603.07	0.88	107.90	19519.71	0.35	71.78	4067.36	0.86	155.73