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

Table 7

Comparison of the results of the proposed RGA-PSO and AIA-PSO algorithms and those of the published individual GA and AIA approaches for TPs 1–4.

TP number	Global optimum	Methods	Best	Mean	Median	Worst	MAPE%
		GA-1 [20]	24.690	—	29.258	36.060	—
		GA-2 [21]	24.372	—	24.409	25.075	—
		GA-3 [9]	24.935	27.314	27.194	33.160	12.377
1	24.306	AIA-1 [22]	24.506	25.417	—	26.422	—
		AIA-2 [10]	24.377	24.669	24.663	24.988	1.495
		The proposed RGA-PSO	24.323	24.568	24.521	24.831	1.078
		The proposed AIA-PSO	24.358	24.579	24.564	24.809	1.125
		GA-1 [20]	—	—	—	—	—
		GA-2 [21]	—	—	—	—	—
		GA-3 [9]	−30665.526	−30662.922	−30664.709	−30632.445	8.53𝐸−03
2	−30665.539	AIA-1 [22]	−30665.539	−30665.539	—	−30665.539	—
		AIA-2 [10]	−30665.539	−30665.526	−30665.527	−30665.506	4.20𝐸−05
		The proposed RGA-PSO	−30665.539	−30665.539	−30665.539	−30665.534	1.34𝐸−06
		The proposed AIA-PSO	−30665.539	−30665.539	−30665.539	−30665.539	9.95𝐸−07
		GA-1 [20]	680.642	—	680.718	680.955	—
		GA-2 [21]	680.634	—	680.642	680.651	—
		GA-3 [9]	680.641	680.815	680.768	681.395	2.72𝐸−02
3	680.630	AIA-1 [22]	680.631	680.652	—	680.697	—
		AIA-2 [10]	680.634	680.653	680.650	680.681	3.45𝐸−03
		The proposed RGA-PSO	680.632	680.640	680.639	680.658	1.46𝐸−03
		The proposed AIA-PSO	680.633	680.640	680.640	680.657	1.50𝐸−03
		GA-1 [20]	−15	−15	−15	−15	—
		GA-2 [21]	—	—	—	—	—
		GA-3 [9]	−13.885	−12.331	−12.267	−10.467	17.795
4	−15	AIA-1 [22]	−14.987	−14.726	—	−12.917	—
		AIA-2 [10]	−14.998	−14.992	−14.992	−14.988	5.08𝐸−02
		The proposed RGA-PSO	−15	−15	−15	−15	1.27𝐸−06
		The proposed AIA-PSO	−15	−15	−15	−15	1.20𝐸−10

(The “—” denotes unavailable information.)