A generalized evolutionary metaheuristic (GEM) algorithm for engineering optimization

Figures & data

Figure 1. Analysis of algorithmic features such as components, mechanisms and stability.

Figure 2. Different perspectives for quantitative analysis of algorithms.

Table 1. Measured data for a vibration problem.

Time ti	1	2	3	4	5
$y(t_i)$	1.0706	1.3372	0.8277	0.9507	1.0848
Time ti	6	7	8	9	10
$y(t_i)$	0.9814	0.9769	1.0169	1.0012	0.9933

Table 2. Numerical experiments for ten test functions.

	Best ($f_{\mathrm{\text{min}}}$)	Worst	Mean ($f_{\mathrm{\text{min}}}$)	True $f_{\mathrm{\text{min}}}$
Fun 1	$+1.4073e-28$	$+1.3985e-27$	$+5.2722e-28$	0
Fun 2	$+1.0192e-26$	$+4.3595e-05$	$+4.3595e-06$	0
Fun 3	$+2.6645e-15$	$+2.3981e-14$	$+9.7700e-15$	0
Fun 4	$+9.8139e-27$	$+6.6667e-01$	$+2.0000e-01$	0
Fun 5	$-3.4560e+03$	$-3.4560e+03$	$-3.4560e+03$	−3456
Fun 6	$+3.1554e-30$	$+1.8302e-28$	$+7.9359e-29$	0
Fun 7	$-1.9209e+01$	$-1.6268e+01$	$-1.8620e+01$	−19.2085
Fun 8	$+1.9586e-29$	$+7.6207e-01$	$+7.6207e-02$	0
Fun 9	$-1.6000e+01$	$-1.6000e+01$	$-1.6000e+01$	−16
Fum 10	$+0.0000e+00$	$+1.9899e+00$	$+1.1940e+00$	0

Table 3. Pressure vessel design benchmarks.

	x1	x2	x3	x4	$f_{\mathrm{\text{min}}}$
Run 1	1.2500	0.6250	64.7668	11.9886	7332.8419
Run 2	0.7500	0.3750	38.8601	221.3657	5850.3851
Run 3	1.1875	0.6250	61.5285	26.9310	7273.5127
Run 4	1.0000	0.5000	51.8135	84.5785	6410.0869
Run 5	0.8750	0.4375	45.3367	140.2544	6090.5325
Run 6	0.8750	0.4375	45.3368	140.2538	6090.5262
Run 7	0.7500	0.3750	38.8601	221.3655	5850.3831
Run 8	1.0000	0.5625	51.8135	84.5785	6708.4337
Run 9	0.8125	0.4375	42.0984	176.6366	6059.7143
Run 10	0.7500	0.4375	38.8601	221.3655	6018.2036

Table 4. Results for the five design benchmarks.

	Best ($f_{\mathrm{\text{min}}}$)	Worst	Mean ($f_{\mathrm{\text{min}}}$)	Best so far
Spring design	$1.2665e-02$	$1.2873e-02$	$1.2729e-02$	$1.2665e-02$
Truss system	$2.6389e+02$	$2.6390e+02$	$2.6390e+02$	$2.6389e+02$
Beam design	$1.3400e+00$	$5.1657e+00$	$2.3158e+00$	$1.3400e+00$
Pressure vessel	$5.8504e+03$	$7.3328e+03$	$6.3685e+03$	$6.0597e+03$
ODE parameters	$6.9479e-09$	$1.5850e-02$	$3.1700e-03$	$6.8900e-09$