Solving Constrained Global Optimization Problems by Using Hybrid Evolutionary Computing and Artificial Life Approaches

Table 9

Comparison of the numerical results of the proposed RGA-PSO and AIA-PSO algorithms and those of the published individual AIA and RGA for TPs 5–13.

TP number	Global optimum	Methods	Best	Mean	Median	Worst	MAPE%
5	1227.1978	AIA-2 [10]	1227.3191	1228.6097	1227.8216	1239.5205	1.15𝐸−01
		GA-3 [9]	1228.5118	1279.3825	1263.2589	1481.3710	4.266
		The proposed RGA-PSO	1227.2321	1228.8471	1228.3935	1231.6003	1.34𝐸−01
		The proposed AIA-PSO	1227.1598	1228.1800	1227.9762	1229.6590	8.02𝐸−02
6	3.9511	AIA-2 [10]	3.9518	4.1005	4.0460	4.2997	3.781
		GA-3 [9]	3.9697	4.1440	4.1358	4.3743	4.881
		The proposed RGA-PSO	3.9521	3.9577	3.9566	3.9722	1.67𝐸−01
		The proposed AIA-PSO	3.9516	3.9581	3.9569	3.9735	1.77𝐸−01
7	−5.7398	AIA-2 [10]	−5.7398	−5.7398	−5.7398	−5.7396	6.03𝐸−04
		GA-3 [9]	−5.7398	−5.7375	−5.7383	−5.7316	3.98𝐸−02
		The proposed RGA-PSO	−5.7398	−5.7398	−5.7398	−5.7398	2.54𝐸−04
		The proposed AIA-PSO	−5.7398	−5.7398	−5.7398	−5.7398	2.42𝐸−04
8	−83.254	AIA-2 [10]	−83.2504	−83.2499	−83.2499	−83.2496	4.93𝐸−03
		GA-3 [9]	−83.2497	−83.2490	−83.2494	−83.2461	6.06𝐸−03
		The proposed RGA-PSO	−83.2497	−83.2497	−83.2497	−83.2497	5.13𝐸−03
		The proposed AIA-PSO	−83.2497	−83.2497	−83.2497	−83.2497	5.13𝐸−03
9	−6.0482	AIA-2 [10]	−6.0471	−5.9795	−6.0138	−5.7159	1.136
		GA-3 [9]	−6.0417	−5.8602	−5.8772	−5.6815	3.108
		The proposed RGA-PSO	−6.0441	−5.9883	−5.9968	−5.8051	0.991
		The proposed AIA-PSO	−6.0466	−5.9808	−5.9969	−5.8274	1.082
10	6300	AIA-2 [10]	6299.8232	6299.8388	6299.8403	6299.8494	2.56𝐸−03
		GA-3 [9]	6299.8399	6299.8546	6299.8453	6299.9407	2.31𝐸−03
		The proposed RGA-PSO	6299.8374	6299.8412	6299.8419	6299.8428	2.52𝐸−03
		The proposed AIA-PSO	6299.8395	6299.8420	6299.8423	6299.8425	2.51𝐸−03
11	10122.6964	AIA-2 [10]	10122.4343	10122.5014	10122.5023	10122.6271	1.93𝐸−03
		GA-3 [9]	10122.4809	10125.2441	10123.9791	10155.1349	2.58𝐸−04
		The proposed RGA-PSO	10122.4732	10122.4925	10122.4925	10122.6444	2.01𝐸−03
		The proposed AIA-PSO	10122.4852	10122.4920	10122.4927	10122.4931	2.02𝐸−03
12	—	AIA-2 [10]	0.012665	0.012703	0.012719	0.012725	—
		GA-3 [9]	0.012665	0.012739	0.012717	0.013471	—
		The proposed RGA-PSO	0.012692	0.012724	0.012721	0.012784	—
		The proposed AIA-PSO	0.012667	0.012715	0.012719	0.012778	—
13	—	AIA-2 [10]	5885.5312	5900.4860	5894.7929	6014.2198	—
		GA-3 [9]	5885.3076	5943.4714	5897.2904	6289.7314	—
		The proposed RGA-PSO	5885.3018	5895.0381	5885.3326	6005.4351	—
		The proposed AIA-PSO	5885.3310	5886.5426	5885.3323	5906.7404	—

(The “—” denotes unavailable information.)