Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Computing the discrepancy with applications to supersampling patterns
ACM Transactions on Graphics (TOG)
AllelesLociand the Traveling Salesman Problem
Proceedings of the 1st International Conference on Genetic Algorithms
Optimizing low-discrepancy sequences with an evolutionary algorithm
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
Algorithmic construction of low-discrepancy point sets via dependent randomized rounding
Journal of Complexity
Evolutionary optimization of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Hardness of discrepancy computation and ε-net verification in high dimension
Journal of Complexity
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
A New Randomized Algorithm to Approximate the Star Discrepancy Based on Threshold Accepting
SIAM Journal on Numerical Analysis
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Geometric discrepancies are standard measures to quantify the irregularity of distributions. They are an important notion in numerical integration. One of the most important discrepancy notions is the so-called star discrepancy. Roughly speaking, a point set of low star discrepancy value allows for a small approximation error in quasi-Monte Carlo integration. It is thus the most studied discrepancy notion. In this work we present a new algorithm to compute point sets of low star discrepancy. The two components of the algorithm (for the optimization and the evaluation, respectively) are based on evolutionary principles. Our algorithm clearly outperforms existing approaches. To the best of our knowledge, it is also the first algorithm which can be adapted easily to optimize inverse star discrepancies.