A well-known approach to investigating and comparing the multiextremal optimization algorithms is based on testing these methods by solving a set of problems, chosen randomly from some specially designed class. It is supposed, that a constrained global optimization problem can be presented in the following form:
min{φ(y): y ∈ D, gi(y) ≤ 0, 1 ≤ i ≤ m} D = {y ∈ RN: aj ≤ yj ≤ bj, 1 ≤ j ≤ N}.
where the objective function φ(y) (henceforth denoted by g(m+1)(y)) is N-dimensional function and gi(y), 1 ≤ i ≤ m, are constraints. The functions gi(y), 1 ≤ i ≤ m + 1, are supposed to satisfy the Lipschitz condition with a priory unknown constants Li, i.e.
|gi(y1) - gi(y2)| ≤ Li‖y1 - y2‖, 1 ≤ i ≤ m + 1.
GCGen generator can use only functions with known global minimizer as an objective function.
When generating the test problems:
- the necessary number of constraints and the desired fraction of the feasible domain relative to the whole search domain D can be specified;
- the unconditional global minimizer of the objective function can be out of the feasible domain;
- the constrained minimizer can be located at the boundary of the feasible domain;
- the number of constraints active at the optimum point can be controlled.