Efficient Hill Climber for Constrained Pseudo-Boolean Optimization Problems

Efficient hill climbers have been recently proposed for single- and multi-objective pseudo-Boolean optimization problems. For $k$-bounded pseudo-Boolean functions where each variable appears in at most a constant number of subfunctions, it has been theoretically proven that the neighborhood of a solution can be explored in constant time. These hill climbers, combined with a high-level exploration strategy, have shown to improve state of the art methods in experimental studies and open the door to the so-called Gray Box Optimization, where part, but not all, of the details of the objective functions are used to better explore the search space. One important limitation of all the previous proposals is that they can only be applied to unconstrained pseudo-Boolean optimization problems. In this work, we address the constrained case for multi-objective $k$-bounded pseudo-Boolean optimization problems. We find that adding constraints to the pseudo-Boolean problem has a linear computational cost in the hill climber.

Combination of Evolutionary Algorithms with Experimental Design, Traditional Optimization and Machine Learning

Evolutionary algorithms alone cannot solve optimization problems very efficiently since there are many random (not very rational) decisions in these algorithms. Combination of evolutionary algorithms and other techniques have been proven to be an efficient optimization methodology. In this talk, I will explain the basic ideas of our three algorithms along this line (1): Orthogonal genetic algorithm which treats crossover/mutation as an experimental design problem, (2) Multiobjective evolutionary algorithm based on decomposition (MOEA/D) which uses decomposition techniques from traditional mathematical programming in multiobjective optimization evolutionary algorithm, and (3) Regular model based multiobjective estimation of distribution algorithms (RM-MEDA) which uses the regular property and machine learning methods for improving multiobjective evolutionary algorithms.

Dynamic Multi-Objective Optimization With jMetal and Spark: a Case Study

Technologies for Big Data and Data Science are receiving increasing research interest nowadays. This paper introduces the prototyping architecture of a tool aimed to solve Big Data Optimization problems. Our tool combines the jMetal framework for multi-objective optimization with Apache Spark, a technology that is gaining momentum. In particular, we make use of the streaming facilities of Spark to feed an optimization problem with data from different sources. We demonstrate the use of our tool by solving a dynamic bi-objective instance of the Traveling Salesman Problem (TSP) based on near real-time traffic data from New York City, which is updated several times per minute. Our experiment shows that both jMetal and Spark can be integrated providing a software platform to deal with dynamic multi-optimization problems.

Phylogenetic inference's algorithms

Phylogenetic inference consist in the search of an evolutionary tree to explain the best way possible genealogical relationships of a set of species. Phylogenetic analysis has a large number of applications in areas such as biology, ecology, paleontology, etc. There are several criterias which has been defined in order to infer phylogenies, among which are the maximum parsimony and maximum likelihood. The first one tries to find the phylogenetic tree that minimizes the number of evolutionary steps needed to describe the evolutionary history among species, while the second tries to find the tree that has the highest probability of produce the observed data according to an evolutionary model. The search of a phylogenetic tree can be formulated as a multi-objective optimization problem, which aims to find trees which satisfy simultaneously (and as much as possible) both criteria of parsimony and likelihood. Due to the fact that these criteria are different there won't be a single optimal solution (a single tree), but a set of compromise solutions. The solutions of this set are called "Pareto Optimal". To find this solutions, evolutionary algorithms are being used with success nowadays.This algorithms are a family of techniques, which aren’t exact, inspired by the process of natural selection. They usually find great quality solutions in order to resolve convoluted optimization problems. The way this algorithms works is based on the handling of a set of trial solutions (trees in the phylogeny case) using operators, some of them exchanges information between solutions, simulating DNA crossing, and others apply aleatory modifications, simulating a mutation. The result of this algorithms is an approximation to the set of the “Pareto Optimal” which can be shown in a graph with in order that the expert in the problem (the biologist when we talk about inference) can choose the solution of the commitment which produces the higher interest. In the case of optimization multi-objective applied to phylogenetic inference, there is open source software tool, called MO-Phylogenetics, which is designed for the purpose of resolving inference problems with classic evolutionary algorithms and last generation algorithms. REFERENCES [1] C.A. Coello Coello, G.B. Lamont, D.A. van Veldhuizen. Evolutionary algorithms for solving multi-objective problems. Spring. Agosto 2007 [2] C. Zambrano-Vega, A.J. Nebro, J.F Aldana-Montes. MO-Phylogenetics: a phylogenetic inference software tool with multi-objective evolutionary metaheuristics. Methods in Ecology and Evolution. En prensa. Febrero 2016.

Quantitative phase Analisis: A comparative study of Mo and Cu strictly monochromatic radiations

A comparison of the Rietveld quantitative phase analyses (RQPA) obtained using Cu-Kα1, Mo-Kα1, and synchrotron strictly monochromatic radiations is presented. The main aim is to test a simple hypothesis: high energy Mo-radiation, combined with high resolution laboratory X-ray powder diffraction optics, could yield more accurate RQPA, for challenging samples, than well-established Cu-radiation procedure(s). In order to do so, three set of mixtures with increasing amounts of a given phase (spiking-method) were prepared and the corresponding RQPA results have been evaluated. Firstly, a series of crystalline inorganic phase mixtures with increasing amounts of an analyte was studied in order to determine if Mo-Kα1 methodology is as robust as the well-established Cu-Kα1 one. Secondly, a series of crystalline organic phase mixtures with increasing amounts of an organic compound was analyzed. This type of mixture can result in transparency problems in reflection and inhomogeneous loading in narrow capillaries for transmission studies. Finally, a third series with variable amorphous content was studied. Limit of detection in Cu-patterns, ~0.2 wt%, are slightly lower than those derived from Mo-patterns, ~0.3 wt%, for similar recording times and limit of quantification for a well crystallized inorganic phase using laboratory powder diffraction was established ~0.10 wt%. However, the accuracy was comprised as relative errors were ~100%. Contents higher than 1.0 wt% yielded analyses with relative errors lower than 20%. From the obtained results it is inferred that RQPA from Mo-Kα1 radiation have slightly better accuracies than those obtained from Cu-Kα1. This behavior has been established with the calibration graphics obtained through the spiking method and also from Kullback-Leibler distance statistic studies. We explain this outcome, in spite of the lower diffraction power for Mo-radiation (compared to Cu-radiation), due to the larger volume tested with Mo, also because higher energy minimize pattern systematic errors and the microabsorption effect.

The use of mo and cu monochromatic radiations for quantitative phase analysis: study of the accuracy

Cement hydration is a very complex process in which crystalline phases are dissolving in water and after supersaturation hydrated crystalline and amorphous phases precipitate. Great efforts are being made to develop analytical tools to accurately quantify these processes and X-ray Powder Diffraction (XRPD) combined with Rietveld methodology is a suitable tool to quantify these complex mixtures and their time evolutions. However, some problems/drawbacks should be overcome to fully apply it to cement pastes characterization in order to get accurate phase analyses. In order to tackle this issue, a comparison of the Rietveld quantitative phase analyses (RQPA) obtained using Cu-Kα1, Mo-Kα1, and synchrotron strictly monochromatic radiations of three set of mixtures with increasing amounts of a given phase (spiking-method) is presented. The main aim is to test a simple hypothesis: high energy Mo-radiation, combined with high resolution laboratory X-ray powder diffraction optics, could yield more accurate RQPA, for challenging samples, than well-established Cu-radiation procedure(s). Firstly, a series of crystalline inorganic phase mixtures with increasing amounts of an analyte was studied in order to determine if Mo-Kα1 methodology is as robust as the well-established Cu-Kα1 one. Secondly, a series of crystalline organic phase mixtures with increasing amounts of an organic compound was analyzed. This type of mixture can result in transparency problems in reflection and inhomogeneous loading in narrow capillaries for transmission studies. Finally, a third series with variable amorphous content was studied. Limit of detection in Cu-patterns, ~0.2 wt%, are slightly lower than those derived from Mo-patterns, ~0.3 wt%, for similar recording times and limit of quantification for a well crystallized inorganic phase using laboratory powder diffraction was established ~0.10 wt%. From the obtained results it is inferred that RQPA from Mo-Kα1 radiation have slightly better accuracies than those obtained from Cu-Kα1. The results obtained in the previous comparison have been taken into account to obtain accurate RQPA, including the amorphous component with internal standard methodology, of hydrating cement pastes. The final goal of this second study was understanding the early-stage hydration mechanisms of a variety of cementing systems (Ordinary Portland Cement or Belite Alite Ye’elimite cement) as a function of water content, superplasticizer additives and type and content of sulfate source. In order to do so, X-ray powder diffraction data were taken in-situ with the humidity chamber coupled to the Mo-Kα1 powder diffractometer. Some results of this ongoing investigation will be reported and discussed.