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, g_i(y) ≤ 0, 1 ≤ i ≤ m} D = {y ∈ R^N: a_j ≤ y_j ≤ b_j, 1 ≤ j ≤ N}.

where the objective function φ(y) (henceforth denoted by g_(m+1)(y)) is N-dimensional function and g_i(y), 1 ≤ i ≤ m, are constraints. The functions g_i(y), 1 ≤ i ≤ m + 1, are supposed to satisfy the Lipschitz condition with a priory unknown constants L_i, i.e.

|g_i(y₁) - g_i(y₂)| ≤ L_i‖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.