The decision variables of the specific optimisation problem p take values from a finite set of problem specific values. The solution space of p, S, consists of the direct problem solutions s for p. In GCOP, each s is obtained by a corresponding configuration c, i.e. c → s. The objective function f(s) → R evaluates the quality of s for p, s ∈ S.

Let M be a mapping function M: f(s) → F(c). The objective of GCOP is to search in C for the optimal c* which maps to the optimal s* for p, so that F(c*) is optimised as defined in Objective (1). Without loss of generality, we assume p is a minimisation problem. 

Obj: F(c* | c* → s*, c* ∈ C) ← f(s*) = min{f(s), s ∈ S}                        (1)

Terminologies:

• • Problem GCOP: a COP, whose decision variables take discrete values from a finite domain A of algorithmic components a, a ∈ A.

  • Domain A for decision variables in GCOP: algorithmic components a ∈ A, including operators with heuristic strategies, their parameter settings, and acceptance criteria. A can be extended with user defined components. Examples of the most common basic a in the literature shown in Table 1.

  • Search space C of GCOP: consists of solutions c for GCOP, i.e. algorithmic compositions c upon a ∈ A. Each c is used to produce a solution s for problem p, i.e. c → s.

  • Objective function F for GCOP: F(c) → R measures GCOP solutions c ∈ C. The objective is to find the optimal c which produces optimal s* for p, i.e. c* → s*. 

  • Problem p: an optimisation problem under consideration, whose decision variables are problem-specific.

  • Objective function f for p: f(s) → R evaluates solutions s for p, s ∈ S, obtained using algorithmic compositions c ∈ C.

  • Mapping function M: F(c) → f(s): maps each algorithmic composition c for GCOP to a solution s for p, i.e. c → s, thus the s produced reflects the performance of c.