Smallest-Small-World Cellular Harmony Search for Optimization of Unconstrained Benchmark Problems

Table 4

Definitions and specification of 30D benchmark problems.

Functions	Definition
Step function	Minimize  𝑓(𝑥)=∑^𝑛𝑖=1𝑥𝑖+0.5^2−30≤𝑥𝑖≤30; min𝑓=𝑓(0,…,0)=0
The Rastrigin function	Minimize   𝑓(𝑥)=10𝑛+∑^𝑛𝑖=1𝑥^2𝑖−10cos(2𝜋𝑥𝑖)−5.12≤𝑥𝑖≤5.12 min𝑓=𝑓(0,…,0)=0
The Griewank function	Minimize  𝑓(𝑥)=(1/4000)∑^𝑛𝑖=1𝑥^2𝑖−∏^𝑛𝑖=1cos𝑥𝑖/√𝑖+1−600≤𝑥𝑖≤600; min𝑓=𝑓(0,…,0)=0
The Ackley function	Minimize  𝑓(𝑥)=−𝑎exp−𝑏(1/𝑛)∑^𝑛𝑖=1𝑥^2𝑖)−exp(1/𝑛)∑^𝑛𝑖=1cos𝑐𝑥𝑖+𝑎+exp(1); 𝑎=20,𝑏=0.2,𝑐=2𝜋−32.768≤𝑥𝑖≤32.768; min𝑓=𝑓(0,…,0)=0