Two Strategies to Improve the Differential Evolution Algorithm for Optimizing Design of Truss Structures

Table 8

Performance comparison of the 942-bar truss.

Element group	Members	Cross–sectional areas (in^2)
		Hasancebi [47]	This work
		Adaptive ESs	DE	EDE	EDE-1	EDE-2	EDE-3	EDE-4
1	1, 2	1.020	5.503	1.867	1.177	1.805	1.527	1.351
2	3–10	1.037	3.807	0.325	0.108	0.130	0.246	0.239
3	11–18	2.943	3.738	3.533	4.120	3.730	3.657	2.752
4	19–34	1.920	2.442	1.982	2.248	1.870	1.870	1.923
5	35–46	1.025	11.269	10.283	9.062	10.473	11.110	11.668
6	47–58	14.961	10.952	10.717	10.379	10.717	10.027	10.362
7	59–82	3.074	10.436	9.427	9.878	9.378	10.401	10.465
8	83–86	6.780	8.689	4.620	4.464	2.708	2.808	5.141
9	87–94	18.580	6.797	8.100	9.911	7.250	6.362	6.107
10	95–98	2.415	23.975	23.242	22.531	23.263	21.361	29.080
11	99–106	6.584	8.455	7.191	5.441	7.568	7.317	7.038
12	107–122	6.291	4.776	5.839	5.761	5.615	5.001	4.661
13	123–130	15.383	12.470	15.171	16.285	16.669	17.421	17.639
14	131–162	2.100	1.998	2.056	2.139	2.038	2.128	2.139
15	163–170	6.021	2.646	4.374	3.360	3.977	4.023	3.667
16	171–186	1.022	0.100	0.104	0.222	0.100	0.363	0.524
17	187–194	23.099	21.578	22.630	21.533	22.433	21.486	21.802
18	195–226	2.889	2.529	2.323	2.528	2.515	2.486	2.331
19	227–234	7.960	6.817	7.478	8.255	7.111	7.515	7.643
20	235–258	1.008	0.644	0.551	0.779	0.448	0.543	0.379
21	259–270	28.548	32.349	27.738	26.512	28.049	27.327	29.069
22	271–318	3.349	3.304	2.959	2.931	2.776	2.894	2.895
23	319–330	16.144	17.146	15.878	15.792	15.216	15.574	16.259
24	331–338	24.822	22.083	24.093	23.860	22.865	21.512	22.837
25	339–342	38.401	52.242	35.819	34.526	34.530	34.837	29.940
26	343–350	3.787	1.786	1.717	3.466	4.145	1.520	2.794
27	351–358	12.320	19.338	11.374	9.421	9.966	12.545	9.453
28	359–366	17.036	13.275	14.507	12.802	13.606	15.593	13.035
29	367–382	14.733	15.048	12.021	13.493	13.284	13.351	13.338
30	383–390	15.031	12.601	15.345	14.397	14.915	14.688	15.111
31	391–398	38.597	26.285	34.848	35.191	36.275	36.871	36.072
32	399–430	3.511	3.564	3.145	3.099	2.947	3.235	2.926
33	431–446	2.997	5.679	2.083	1.803	2.368	2.216	1.968
34	447–462	3.060	5.278	2.340	2.349	2.565	2.539	2.410
35	463–486	1.086	1.602	0.123	0.185	0.100	0.190	0.227
36	487–498	1.462	0.990	0.213	0.356	0.421	0.100	0.117
37	499–510	59.433	52.600	55.823	56.099	52.331	52.739	53.967
38	511–558	3.632	2.594	2.963	2.928	3.036	3.266	3.046
39	559–582	1.887	2.196	2.320	2.323	2.188	2.317	2.320
40	583–606	4.072	3.954	2.892	2.854	2.953	2.615	2.787
41	607–630	1.595	0.979	0.244	0.121	0.267	0.257	0.104
42	631–642	3.671	0.911	1.134	1.841	1.382	1.284	0.815
43	643–654	79.511	74.845	73.370	76.727	73.712	72.484	72.741
44	655–702	3.394	3.735	3.076	3.041	3.114	2.884	2.907
45	703–726	1.581	1.843	2.076	2.093	1.946	2.006	2.079
46	727–750	4.204	2.666	3.074	3.079	3.313	3.419	3.300
47	751–774	1.329	1.317	0.308	0.725	0.417	0.416	0.483
48	775–786	2.242	0.100	0.277	0.451	0.577	0.553	0.256
49	787–798	96.886	78.724	86.644	86.760	84.354	86.335	88.369
50	799–846	3.710	3.145	3.107	3.195	3.130	3.142	3.619
51	847–870	1.055	8.557	2.075	0.658	2.384	2.469	2.599
52	871–894	4.566	4.121	3.539	2.949	3.452	3.830	3.869
53	895–902	9.606	30.069	9.719	7.361	12.883	9.837	10.473
54	903–906	2.984	12.180	8.382	7.519	8.500	8.553	10.070
55	907–910	45.917	54.295	40.526	40.681	40.973	43.239	39.841
56	911–918	1.000	0.535	0.129	0.201	0.271	0.171	0.132
57	919–926	62.426	31.736	56.362	59.574	55.438	53.716	52.565
58	927–934	2.977	4.960	4.725	2.888	3.893	5.330	4.996
59	935–942	1.000	8.553	0.122	0.225	2.893	0.763	0.335
Weightbest (lb)		141241	142,436	132,441	132,529	132,713	132,658	132,905
Weightworst (lb)		—	151,351	134,404	135,764	135,694	134,170	135,632
Weightmean (lb)		—	145,986	133,153	133,386	133,436	133,243	133,942
Weightmedian (lb)		—	145,639	133,018	133,279	133,280	133,161	133,698
Weightstdev (lb)		—	2292.7	483.1	613.0	709.5	396.9	652.3
Nanalyses		150,000	100,000	100,000	100,000	100,000	100,000	100,000