Abstract. Low-discrepancy sequences provide a way to generate quasi-random numbers of high dimensionality with a very high level of uniformity. The nearly orthogonal Latin hypercube and the generalized Halton sequence are two popular methods when it comes to generate low-discrepancy sequences. In this article, we propose to use evolutionary algorithms in order to find optimized solutions to the combinatorial problem of configuring generators of these sequences. Experimental results show that the optimized sequence generators behave at least as well as generators from the literature for the Halton sequence and significantly better for the nearly orthogonal Latin hypercube.

DEAP (Distributed Evolutionary Algorithms in Python) is a novel evolutionary computation framework for rapid prototyping and testing of ideas. Its design departs from most other existing frameworks in that it seeks to make algorithms explicit and data structures transparent, as opposed to the more common black box type of frameworks. It also incorporates easy parallelism where users need not concern themselves with gory implementation details like synchronization and load balancing, only functional decomposition. Several examples illustrate the multiple properties of DEAP.

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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.

This paper proposes a complete system for robotic sensor placement in initially unknown arbitrary threedimensional environments. The system uses a novel approach for computing the quality of acquisition of a mobile sensor group in such environments. The quality of acquisition is based on a geometric model of a camera which allows accurate sensor models and simple occlusion computation. The proposed system combines this new metric with a global derivative-free optimization algorithm to find simultaneously the number of sensors and their configuration to sense accordingly the environment. The presented framework compares favourably with current techniques working in two-dimensional environments. Furthermore, simulation and experimental results demonstrate the ability of the system to cope with full three-dimensional environments, a domain still unexplored by previous methods.