Composite Differential Evolution with Modified Oracle Penalty Method for Constrained Optimization Problems

Table 2

The comparison results of different methods.

(a)

Function	HEA-ACT [5]				ES-DE [8]
	Worst	Best	Mean	Std.	Worst	Best	Mean	Std.
	−8.8	−15	−11.9	2.57320	−13.0000	−15.0000	−14.8511
	−0.6066	−0.8036	−0.7405	0.04906	−0.530496	−0.803311	−0.738181
	0	−0.2864	−0.0169	0.06382	−1.0000	−1.0000	−1.0000
	−30665.5	−30665.5	−30665.5	0	−30665.54	−30665.54	−30665.54
	5126.4965	5126.4965	5126.4965	0	5129.420	5126.500	5127.290
	−6961.8	−6961.8	−6961.8	0	−6961.814	−6961.814	−6961.814
	29.0591	24.306	25.048	1.37164	24.3077	24.3062	24.3065
	−0.09582	−0.09582	−0.09582	0	−0.095825	−0.095825	−0.095825
	680.63	680.63	680.63	0	680.6301	680.6301	680.6301
	8832.12	7049.25	7290.75	379.12207	7050.22	7049.253	7049.418
	1	1	1	0	0.7500	0.7500	0.7500

(b)

Function	DUVDE + APM [9]				MOCoDE
	Worst	Best	Mean	Std.	Worst	Best	Mean	Std.
	−6	−15	−12.5	2.37254	−15	−15	−15
	−0.6709	−0.8036	−0.7688	0.03568	−0.79818	−0.80362	−0.80351	0.00076891
	−0	−1.0	−0.2015	0.34508	−0.066992	−1.0005	−0.77806	0.23028
	−30665.5	−30665.5	−30665.5	0	−30665.5387	−30665.5387	−30665.5387
	5126.4965	5126.4965	5126.4965	0	5191.2685	5126.4967	5131.5314	14.322
	−6961.8	−6961.8	−6961.8	0	−6961.8139	−6961.8139	−6961.8139
	121.747	24.306	30.404	21.56839	24.3062	24.3062	24.3062
	−0.09582	−0.09582	−0.09582	0	−0.095825	−0.095825	−0.095825
	680.63	680.63	680.63	0.00003	680.6301	680.6301	680.6301
	8332.12	7049.25	7351.17	525.62430	7049.248	7049.248	7049.248
	1	0.75	0.98749	0.05590	0.7499	0.7499	0.7499

Result in boldface indicates that a better result is reached.

(c)

Function	SAMO-GA [10]				SAMO-DE [10]
	Worst	Best	Mean	Std.	Worst	Best	Mean	Std.
	—	−15.0000	−15.0000		—	−15.0000	−15.0000
	—	−0.80359052	−0.79604769		—	−0.8036191	−0.79873521
	—	−1.0005	−1.0005		—	−1.0005	−1.0005
	—	−30665.5386	−30665.5386		—	−30665.5386	−30665.5386
	—	5126.497	5127.976432		—	5126.497	5126.497
	—	−6961.813875	−6961.813875		—	−6961.813875	−6961.813875
	—	24.3062	24.4113		—	24.3062	24.3096
	—	−0.09582504	−0.09582504		—	−0.09582504	−0.09582504
	—	680.630	680.634		—	680.630	680.630
	—	7049.248	7144.40311		—	7049.2481	7059.81345
	—	0.7499	0.7499		—	0.7499	0.7499