Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points
SIAM Journal on Numerical Analysis
A generalized discrepancy and quadrature error bound
Mathematics of Computation
A scatter search approach to unconstrained quadratic binary programs
New ideas in optimization
Greedy and Local Search Heuristics for Unconstrained Binary Quadratic Programming
Journal of Heuristics
Convex Optimization
Design and Modeling for Computer Experiments (Computer Science & Data Analysis)
Design and Modeling for Computer Experiments (Computer Science & Data Analysis)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Global optimality conditions for quadratic 0-1 optimization problems
Journal of Global Optimization
Construction of uniform designs without replications
Journal of Complexity
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In this paper, the wrap-around L"2-discrepancy (WD) of asymmetrical design is represented as a quadratic form, thus the problem of constructing a uniform design becomes a quadratic integer programming problem. By the theory of optimization, some theoretic properties are obtained. Algorithms for constructing uniform designs are then studied. When the number of runs n is smaller than the number of all level-combinations m, the construction problem can be transferred to a zero-one quadratic integer programming problem, and an efficient algorithm based on the simulated annealing is proposed. When n=m, another algorithm is proposed. Empirical study shows that when n is large, the proposed algorithms can generate designs with lower WD compared to many existing methods. Moreover, these algorithms are suitable for constructing both symmetrical and asymmetrical designs.