An Effective Hybrid Self-Adapting Differential Evolution Algorithm for the Joint Replenishment and Location-Inventory Problem in a Three-Level Supply Chain

Table 2

Benchmark functions.

Test functions	L	M	Global optimum (f min)
𝑓1(𝑥)=∑^𝐿𝑙=1𝑥^2𝑙	10, 30	[−100,100]^𝐿	0
𝑓2(𝑥)=∑^𝐿𝑙=1𝑥𝑙+∏^𝐿𝑙=1𝑥𝑙	10, 30	[−10,10]^𝐿	0
𝑓3(𝑥)=∑^𝐿𝑙=1(∑^𝑙𝑔=1𝑥𝑔)^2	10, 30	[−100,100]^𝐿	0
𝑓4(𝑥)=∑^𝐿𝑙=1(𝑥𝑙+0.5)^2	10, 30	[−100,100]^𝐿	0
𝑓5(𝑥)=∑^𝐿𝑙=1−𝑥𝑙sin𝑥𝑙	10, 30	[−500,500]^𝐿	−12569.5
𝑓6(𝑥)=−20exp−0.2∑^𝐿𝑙=1𝑥^2𝑙()∑/𝐿−exp1/𝐿^𝐿𝑙=1cos2𝜋𝑥𝑙+20+𝑒	10, 30	[−32,32]^𝐿	0
𝑓7(𝑥)=(1/4000)∑^𝐿𝑙=1𝑥^2𝑙−∏^𝐿𝑙=1cos𝑥𝑙/√𝑙+1	10, 30	[−600,600]^𝐿	0