A Memetic Differential Evolution Algorithm Based on Dynamic Preference for Constrained Optimization Problems

Table 6

Statistical results obtained by MDE-DP over 30 independent runs with different upper bound values of the first component in weighting vector 𝜔 in stage two.

fcn/opt.	Status	𝜔1^max=0.4	𝜔1^max=0.45	𝜔1^max=0.5	𝜔1^max=0.6	𝜔1^max=0.7
g01/−15.0000	Best	−15	−15	−15	−15	−15
	Median	−15	−15	−15	−15	−15
	Mean	−15	−15	−15	−15	−15
	Worst	−15	−15	−15	−15	−15
	Std.	1.3𝐸−14	2.4𝐸−14	0	1.8𝐸−14	1.8𝐸−14
g02/−0.803619	Best	−0.794882	−0.803617	−0.803616	−0.803615	−0.803613
	Median	−0.757723	−0.771748	−0.763716	−0.771840	−0.773241
	Mean	−0.750477	−0.758338	−0.757713	−0.761655	−0.764268
	Worst	−0.640313	−0.590475	−0.616138	−0.601025	−0.647718
	Std.	4.0𝐸−02	4.4𝐸−02	1.9𝐸−02	3.8𝐸−02	3.5𝐸−02
g03/−1.0005	Best	−1.0005	−1.0005	−1.0005	−1.0005	−1.0005
	Median	−1.0005	−1.0005	−1.0005	−1.0005	−1.0005
	Mean	−1.0005	−1.0005	−1.0005	−1.0005	−1.0005
	Worst	−1.0005	−1.0005	−1.0005	−1.0005	−1.0005
	Std.	2.9𝐸−06	1.8𝐸−06	2.9𝐸−07	2.7𝐸−06	2.9𝐸−06
g04/30665.539	Best	30665.539	30665.539	30665.539	30665.539	30665.539
	Median	30665.539	30665.539	30665.539	30665.539	30665.539
	Mean	30665.539	30665.539	30665.539	30665.539	30665.539
	Worst	30665.539	30665.539	30665.539	30665.539	30665.539
	Std.	1.5𝐸−11	1.5𝐸−11	1.4𝐸−11	1.5𝐸−11	1.5𝐸−11
g05/5126.49671	Best	5126.49671	5126.49671	5126.49671	5126.49671	5126.49671
	Median	5126.49671	5126.49671	5126.49671	5126.49671	5126.49671
	Mean	5126.49671	5126.49671	5126.49671	5126.49671	5126.49671
	Worst	5126.49671	5126.49671	5126.49671	5126.49671	5126.49671
	Std.	4.7𝐸−12	4.0𝐸−12	3.0𝐸−12	4.0𝐸−12	4.8𝐸−12
g06/−6961.814	Best	−6961.814	−6961.814	−6961.814	−6961.814	−6961.814
	Median	−6961.814	−6961.814	−6961.814	−6961.814	−6961.814
	Mean	−6961.814	−6961.814	−6961.814	−6961.814	−6961.814
	Worst	−6961.814	−6952.814	−6961.814	−6961.814	−6961.814
	Std.	1.8𝐸−12	1.8𝐸−12	1.8𝐸−12	1.8𝐸−12	1.8𝐸−12
g07/24.306	Best	24.306	24.306	24.306	24.306	24.306
	Median	24.306	24.306	24.306	24.306	24.306
	Mean	24.306	24.306	24.306	24.306	24.306
	Worst	24.307	24.306	24.306	24.307	24.307
	Std.	1.2𝐸−04	8.5𝐸−06	4.6𝐸−06	6.1𝐸−05	1.4𝐸−04
g08/−0.095825	Best	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825
	Median	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825
	Mean	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825
	Worst	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825
	Std.	8.5𝐸−17	8.4𝐸−17	8.4𝐸−17	8.4𝐸−17	8.4𝐸−17
g09/680.630	Best	680.630	680.630	680.630	680.630	680.630
	Median	680.630	680.630	680.630	680.630	680.630
	Mean	680.630	680.630	680.630	680.630	680.630
	Worst	680.630	680.630	680.630	680.630	680.630
	Std.	1.7𝐸−12	1.2𝐸−12	3.6𝐸−10	6.2𝐸−12	1.1𝐸−08
g10/7049.248	Best	7049.260	7049.270	7049.249	7049.259	7049.257
	Median	7049.350	7049.364	7049.257	7049.328	7049.356
	Mean	7049.397	7049.410	7049.258	7049.360	7049.370
	Worst	7049.864	7049.954	7049.311	7049.703	7049.696
	Std.	1.3𝐸−02	1.4𝐸−01	1.1𝐸−02	9.6𝐸−02	7.4𝐸−02
g11/0.7499	Best	0.7499	0.7499	0.7499	0.7499	0.7499
	Median	0.7499	0.7499	0.7499	0.7499	0.7499
	Mean	0.7499	0.7499	0.7499	0.7499	0.7499
	Worst	0.7499	0.7499	0.7499	0.7499	0.7499
	Std.	3.4𝐸−16	3.4𝐸−16	3.4𝐸−16	3.4𝐸−16	3.4𝐸−16
g12/−1	Best	−1	−1	−1	−1	−1
	Median	−1	−1	−1	−1	−1
	Mean	−1	−1	−1	−1	−1
	Worst	−1	−1	−1	−1	−1
	Std.	0	0	0	0	0
g13/0.0539415	Best	0.05395415	0.05395415	0.05395415	0.05395415	0.05395415
	Median	0.05395415	0.05395415	0.05395415	0.05395415	0.05395415
	Mean	0.05395415	0.05395415	0.05395415	0.05395415	0.06163874
	Worst	0.05395415	0.05395415	0.05395415	0.05395415	0.43880261
	Std.	2.7𝐸−13	5.6𝐸−10	1.3𝐸−12	5.6𝐸−10	5.4𝐸−02