A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization is presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically distorted by polynomials in order to introduce local minima. To determine a class, the user defines the following parameters: (i) problem dimension, (ii) number of local minima, (iii) value of the global minimum, (iv) radius of the attraction region of the global minimizer, (v) distance from the global minimizer to the vertex of the quadratic function. Then, all other necessary parameters are generated randomly for all 100 functions of the class. Full information about each test function including locations and values of all local minima is supplied to the user. Partial derivatives are also generated where possible.

Global optimization problems where evaluation of the objective function is an expensive operation arise frequently in engineering, decision making, optimal control, etc. There exist two huge but almost completely disjoint communities (they have different journals, different conferences, different test functions, etc.) solving these problems: a broad community of practitioners using stochastic nature-inspired metaheuristics and people from academia studying deterministic mathematical programming methods. In order to bridge the gap between these communities we propose a visual technique for a systematic comparison of global optimization algorithms having different nature. Results of more than 800,000 runs on 800 randomly generated tests show that both stochastic nature-inspired metaheuristics and deterministic global optimization methods are competitive and surpass one another in dependence on the available budget of function evaluations.

In the paper, the global optimization problem of a multidimensional "black-box" function satisfying the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant is considered. A new efficient algorithm for solving this problem is presented. At each iteration of the method a number of possible Lipschitz constants are chosen from a set of values varying from zero to infinity. This idea is unified with an efficient diagonal partition strategy. A novel technique balancing usage of local and global information during partitioning is proposed. A new procedure for finding lower bounds of the objective function over hyperintervals is also considered. It is demonstrated by extensive numerical experiments performed on more than 1600 multidimensional test functions that the new algorithm shows a very promising performance.