Testing Nelder-Mead based repulsion algorithms for multiple roots of nonlinear systems via a two-level factorial design of experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.Fundação para a Ciência e Tecnologia (FCT

Assortment optimization under the Sequential Multinomial Logit Model

We study the assortment optimization problem under the Sequential Multinomial Logit (SML), a discrete choice model that generalizes the Multinomial Logit (MNL). Under the SML model, products are partitioned into two levels, to capture differences in attractiveness, brand awareness and, or visibility of the products in the market. When a consumer is presented with an assortment of products, she first considers products in the first level and, if none of them is purchased, products in the second level are considered. This model is a special case of the Perception-Adjusted Luce Model (PALM) recently proposed by Echenique et al. (2018). It can explain many behavioral phenomena such as the attraction, compromise, similarity effects and choice overload which cannot be explained by the MNL model or any discrete choice model based on random utility. In particular, the SML model allows violations to regularity which states that the probability of choosing a product cannot increase if the offer set is enlarged. This paper shows that the seminal concept of revenue-ordered assortment sets, which contain an optimal assortment under the MNL model, can be generalized to the SML model. More precisely, the paper proves that all optimal assortments under the SML are revenue-ordered by level, a natural generalization of revenue-ordered assortments that contains, at most, a quadratic number of assortments. As a corollary, assortment optimization under the SML is polynomial-time solvable

Heterogeneity-aware resource allocation in HPC systems

In their march towards exascale performance, HPC systems are becoming increasingly more heterogeneous in an effort to keep power consumption at bay. Exploiting accelerators such as GPUs and MICs together with traditional processors to their fullest requires heterogeneous HPC systems to employ intelligent job dispatchers that go beyond the capabilities of those that have been developed for homogeneous systems. In this paper, we propose three new heterogeneity-aware resource allocation algorithms suitable for building job dispatchers for any HPC system. We use real workload traces extracted from the Eurora HPC system to analyze the performance of our allocators when they are coupled with different schedulers. Our experimental results show that significant improvements can be obtained in job response times and system throughput over solutions developed for homogeneous systems. Our study also helps to characterize the operating conditions in which heterogeneity-aware resource allocation becomes crucial for heterogeneous HPC systems

Meta-heuristics and Artificial Intelligence

International audienceMeta-heuristics are generic search methods that are used to solve challenging combinatorial problems. We describe these methods and highlight their common features and differences by grouping them in two main kinds of approaches: Pertur-bative meta-heuristics that build new combinations by modifying existing combinations (such as, for example, genetic algorithms and local search), and Constructive meta-heuristics that generate new combinations in an incremental way by using a stochastic model (such as, for example, estimation of distribution algorithms and ant colony optimization). These approaches may be hybridised, and we describe some classical hybrid schemes. We also introduce the notions of diversification (ex-ploration) and intensification (exploitation), which are shared by all these meta-heuristics: diversification aims at ensuring a good sampling of the search space and, therefore, at reducing the risk of ignoring a promising sub-area which actually contains high-quality solutions, whereas intensification aims at locating the best combinations within a limited region of the search space. Finally, we describe two applications of meta-heuristics to typical artificial intelligence problems: satisfiability of Boolean formulas, and constraint satisfaction problems