Test problem generator for unconstrained global optimization

We develop in this paper a high performance test problem generator for generating analytic and highly multimodal test problems for benchmarking unconstrained global optimization algorithms. More specifically, we propose in this research a novel and computationally efficient procedure for generating nonlinear nonconvex not separable unconstrained test problems with (i) analytic test functions, (ii) known local minimizers that are distributed uniformly in the interior of a compact box, among which only one is the global solution, and (iii) controllable difficulty levels. A standard set of test problems with different sizes and different difficulty levels is produced for both MATLAB and GAMS and is available for downloading. Numerical experiments have demonstrated the stability of the generating process and the difficulty of solving the standard test problems.