Developers: S. Kucherenko, O. Zaccheus

Solution of nonconvex global optimization problems is one of the hardest fields of optimization, presenting many challenges in both practical and theoretical aspects. There are two types kinds of commonly used techniques for solving such problems: deterministic and stochastic. Deterministic methods guarantee convergence to a global solution. However, for large-scale problems these methods require prohibitively large CPU-time.

Stochastic search methods yield an asymptotic (in a limit N going to infinity, where N are randomly chosen points) guarantee of convergence. But as in reality problems can be solved with limited sets of sample points N, convergence to a global solution is not guaranteed. However, stochastic methods have already shown their efficiency and usefulness in solving large scale practical problems.

We developed a novel method, which combines advantages of deterministic and stochastic methods. It is based on application of Quasi Monte Carlo (QMC) methods based on Sobol’ sequences [1] and multi-level linkage methods [2]. In comparison with pure stochastic methods employing random numbers application of QMC sampling generally significantly decreases the number of points N required to achieve the same tolerance of finding the global minimum [3].

SobolOpt is a general purpose global optimization solver which is based on the developed method. It is linked with modeling system GAMS and MATLAB. This solver is capable of solving complex constrained global optimization problems with continuous or mixed-integer variables.

1. Sobol’, D. Asotsky, A. Kreinin, S. Kucherenko. Construction and Comparison of High-Dimensional Sobol’ Generators, 2011, Wilmott Journal (2012) 64-79,
2. Kucherenko S., Sytsko Yu. Application of deterministic low-discrepancy sequences to nonlinear global optimization problems. Comp Optimization and Applications, 30, 3 (2005)  287-318.
3. Liberty L., Kucherenko S. Comparison of deterministic and stochastic approaches to global optimization, Int. Transactions in Operational Research, 12 (2005) 263-285.

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