The base functions that are used to form the separable and non-separable subcomponents are: Sphere,
Elliptic, Rastrigin’s, Ackley’s, Schwefel’s, and Rosenbrock’s functions. These functions which are classi-
cal examples of benchmark functions in many continuous optimization test suites [
13, 40, 41] are mathe-
matically defined in Section 4.1. Based on the major four categories described above and the aforemen-
tioned six base functions, the following 15 large-scale functions are proposed in this report:
1. Fully-separable Functions
(a) f
1
: Elliptic Function
(b) f
2
: Rastrigin Function
(c) f
3
: Ackley Function
2. Partially Additively Separable Functions
• Functions with a separable subcomponent:
(a) f
4
: Elliptic Function
(b) f
5
: Rastrigin Function
(c) f
6
: Ackley Function
(d) f
7
: Schwefels Problem 1.2
• Functions with no separable subcomponents:
(a) f
8
: Elliptic Function
(b) f
9
: Rastrigin Function
(c) f
10
: Ackley Function
(d) f
11
: Schwefels Problem 1.2
3. Overlapping Functions
(a) f
12
: Rosenbrock’s Function
(b) f
13
: Schwefels Function with Conforming Overlapping Subcomponents
(c) f
14
: Schwefels Function with Conflicting Overlapping Subcomponents
4. Non-separable Functions
(a) f
15
: Schwefels Problem 1.2
The high-level design of these four major categories is explained in Section
4.2.
5