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

Table 1

Statistical results obtained by MDEDP over 30 independent runs and the comparison with Var2 [24], SAMSDE-2 [24], SR [2], ATMES [9], and BBO-DM [25]. The result in boldface indicates that the proposed MDEDP obtained the global optimum. The bold-face values mean they are optimal solutions. NA means not available in related reference.

fcn/opt.	Status	MDEDP	Var2 [24]	SAMSDE-2 [24]	SR [2]	ATMES [9]	BBO-DM [25]	DEDP
g01/−15.0000	Best	−15.000	−15.0000	−15.0000	−15.000	−15.000	−15	−14.9999
	Median	−15.000	−15.0000	−15.0000	−15.000	−15.000	NA	−14.9998
	Mean	−15.000	−15.0000	−15.0000	−15.000	−15.000	−15	−14.9999
	Worst	−15.000	−15.0000	−15.0000	−15.000	−15.000	−15	−14.9998
	Std.	0	0	0	0.0𝐸+00	1.6𝐸−14	8.2𝐸−14	3.9𝐸−05
g02/−0.803619	Best	−0.803616	−0.803616	−0.803619	−0.803515	−0.803388	−0.803557	−0.604182
	Median	−0.763716	−0.785259	−0.783053	−0.785800	−0.792420	NA	−0.554816
	Mean	−0.757713	−0.779414	−0.774917	−0.781975	−0.790148	−0.802774	−0.553601
	Worst	−0.616138	−0.729905	−0.729398	−0.726288	−0.756986	−0.792576	−0.511070
	Std.	1.9𝐸−02	1.9𝐸−02	2.5𝐸−02	2.0𝐸−02	1.3𝐸−02	2.7𝐸−03	2.0𝐸−02
g03/−1.0005	Best	−1.0005	−1.0005	−1.0005	−1.000	−1.000	−1.000	−1.0005
	Median	−1.0005	−1.0005	−1.0005	−1.000	−1.000	NA	−1.0005
	Mean	−1.0005	−1.0005	−1.0005	−1.000	−1.000	−1.000	−1.0005
	Worst	−1.0005	−1.0005	−1.0005	−1.000	−1.000	−1.000	−1.0005
	Std.	2.9𝐸−07	1.3𝐸−05	8.2𝐸−06	1.9𝐸−04	5.9𝐸−05	6.0𝐸−16	9.4𝐸−14
g04/−30665.53867	Best	−30665.53867	−30665.53867	−30665.53867	−30665.539	−30665.539	−30665.539	−30665.53867
	Median	−30665.53867	−30665.53867	−30665.53867	−30665.539	−30665.539	NA	−30665.53867
	Mean	−30665.53867	−30662.69876	−30665.53867	−30665.539	−30665.539	−30665.539	−30665.53867
	Worst	−30665.53867	−30634.93399	−30665.53867	−30665.539	−30665.539	−30665.539	−30665.53867
	Std.	1.4𝐸−11	8.7𝐸+00	0	2.0𝐸−05	4.6𝐸−13	1.7𝐸−11	1.1𝐸−11
g05/5126.49671	Best	5126.49671	5126.49674	5126.49671	5126.497	5126.498	5126.498	5126.49671
	Median	5126.49671	5126.98662	5126.49674	5127.372	5126.776	NA	5126.49671
	Mean	5126.49671	5133.70682	5126.63543	5128.881	5127.648	5126.498	5126.49671
	Worst	5126.49671	5217.94796	5128.80623	5142.472	5135.256	5126.498	5126.49671
	Std.	3.0𝐸−12	2.0𝐸+01	5.0𝐸−01	3.5𝐸+00	1.8𝐸+00	2.2𝐸−04	9.3𝐸−13
g06/−6961.814	Best	−6961.814	−6961.83188	−6961.83188	−6961.814	−6961.814	−6961.814	−6961.814
	Median	−6961.814	−6961.80882	−6961.83188	−6961.814	−6961.814	NA	−6961.814
	Mean	−6961.814	−6937.41732	−6961.83188	−6875.940	−6961.814	−6961.814	−6961.814
	Worst	−6961.814	−6804.36991	−6961.83188	−6350.262	−6961.814	−6961.814	−6961.814
	Std.	1.8𝐸−12	4.8𝐸+01	0	1.6𝐸+02	4.6𝐸−12	4.6𝐸−12	1.9𝐸−02
g07/24.306	Best	24.306	24.3069	24.3069	24.307	24.306	24.326	24.330
	Median	24.306	24.3205	24.3287	24.357	24.313	NA	24.340
	Mean	24.306	24.3289	24.3330	24.374	24.316	24.345	24.342
	Worst	24.306	24.4085	24.3881	24.642	24.359	24.378	24.360
	Std.	4.6𝐸−06	2.5𝐸−02	2.5𝐸−02	6.6𝐸−02	1.1𝐸−02	1.3𝐸−02	8.7𝐸−03
g08/−0.095825	Best	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825
	Median	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825	NA	−0.095825
	Mean	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825
	Worst	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825	−0.095825
	Std.	8.4𝐸−17	0	0	2.6𝐸−17	2.8𝐸−17	2.8𝐸−17	2.8𝐸−17
g09/680.630	Best	680.630	680.630	680.630	680.630	680.630	680.630	680.630
	Median	680.630	680.633	680.631	680.641	680.633	NA	680.630
	Mean	680.630	680.634	680.631	680.656	680.639	680.630	680.630
	Worst	680.630	680.646	680.632	680.763	680.673	680.630	680.630
	Std.	3.6𝐸−10	4.0𝐸−03	6.8𝐸−04	3.4𝐸−02	1.0𝐸−02	4.3𝐸−13	1.5𝐸−11
g10/7049.248	Best	7049.249	7049.570	7049.378	7054.316	7052.253	7059.802	7052.473
	Median	7049.257	7071.060	7105.992	7372.613	7215.357	NA	7054.639
	Mean	7049.258	7105.844	7112.012	7559.192	7250.437	7075.832	7054.623
	Worst	7049.311	7347.264	7191.295	8835.655	7560.224	7098.254	7058.081
	Std.	1.1𝐸−02	7.3𝐸+01	7.0𝐸+01	5.3𝐸+02	1.2𝐸+02	8.5𝐸+00	1.5𝐸+00
g11/0.7499	Best	0.7499	0.7499	0.7499	0.750	0.75	0.750	0.7499
	Median	0.7499	0.7499	0.7499	0.750	0.75	NA	0.7499
	Mean	0.7499	0.7499	0.7499	0.750	0.75	0.750	0.7499
	Worst	0.7499	0.7499	0.7499	0.750	0.75	0.750	0.7499
	Std.	3.4𝐸−16	0	0	8.0𝐸−05	3.4𝐸−04	0	1.0𝐸−16
g12/−1.000	Best	−1	−1.0000	−1.0000	−1.000000	−1.000	−1.000000	−1
	Median	−1	−1.0000	−1.0000	−1.000000	−1.000	NA	−1
	Mean	−1	−1.0000	−1.0000	−1.000000	−1.000	−1.000000	−1
	Worst	−1	−1.0000	−1.0000	−1.000000	−0.994	−1.000000	−1
	Std.	0	0	0	0.0𝐸+00	1.0𝐸−03	0	0
g13/0.0539415	Best	0.0539415	0.0539452	0.0539415	0.053957	0.053950	NA	0.0539415
	Median	0.0539415	0.0546893	0.0539415	0.057006	0.053952	NA	0.0588605
	Mean	0.0539415	0.0602843	0.0539417	0.067543	0.053959	NA	0.1586557
	Worst	0.0539415	0.0828200	0.0539428	0.216915	0.053999	NA	0.4461180
	Std.	1.3𝐸−12	9.9𝐸−03	3.0𝐸−07	3.1𝐸−02	1.3𝐸−05	NA	1.6𝐸−01