Application of threshold accepting to the evaluation of the discrepancy of a set of points

Efficient routines for multidimensional numerical integration are provided by quasi-Monte Carlo methods. These methods are based on evaluating the integrand at a set of representative points of the integration area. A set may be called representative if it shows a low discrepancy. However, in dimensions higher than two and for a large number of points the evaluation of discrepancy becomes infeasible. The use of the efficient multiple purpose heuristic Threshold Accepting offers a possibility to obtain at least good approximations to the discrepancy of a given set of points. This paper presents an implementation of Threshold Accepting, an assessment of its performance for some small examples and results for larger sets of points with unknown discrepancy.