Multi-objective optimization in graphical models

Many real-life optimization problems are combinatorial, i.e. they concern a choice of the best solution from a finite but exponentially large set of alternatives. Besides, the solution quality of many of these problems can often be evaluated from several points of view (a.k.a. criteria). In that case, each criterion may be described by a different objective function. Some important and well-known multicriteria scenarios are: · In investment optimization one wants to minimize risk and maximize benefits. · In travel scheduling one wants to minimize time and cost. · In circuit design one wants to minimize circuit area, energy consumption and maximize speed. · In knapsack problems one wants to minimize load weight and/or volume and maximize its economical value. The previous examples illustrate that, in many cases, these multiple criteria are incommensurate (i.e., it is difficult or impossible to combine them into a single criterion) and conflicting (i.e., solutions that are good with respect one criterion are likely to be bad with respect to another). Taking into account simultaneously the different criteria is not trivial and several notions of optimality have been proposed. Independently of the chosen notion of optimality, computing optimal solutions represents an important current research challenge. Graphical models are a knowledge representation tool widely used in the Artificial Intelligence field. They seem to be specially suitable for combinatorial problems. Roughly, graphical models are graphs in which nodes represent variables and the (lack of) arcs represent conditional independence assumptions. In addition to the graph structure, it is necessary to specify its micro-structure which tells how particular combinations of instantiations of interdependent variables interact. The graphical model framework provides a unifying way to model a broad spectrum of systems and a collection of general algorithms to efficiently solve them. In this Thesis we integrate multi-objective optimization problems into the graphical model paradigm and study how algorithmic techniques developed in the graphical model context can be extended to multi-objective optimization problems. As we show, multiobjective optimization problems can be formalized as a particular case of graphical models using the semiring-based framework. It is, to the best of our knowledge, the first time that graphical models in general, and semiring-based problems in particular are used to model an optimization problem in which the objective function is partially ordered. Moreover, we show that most of the solving techniques for mono-objective optimization problems can be naturally extended to the multi-objective context. The result of our work is the mathematical formalization of multi-objective optimization problems and the development of a set of multiobjective solving algorithms that have been proved to be efficient in a number of benchmarks.Muchos problemas reales de optimización son combinatorios, es decir, requieren de la elección de la mejor solución (o solución óptima) dentro de un conjunto finito pero exponencialmente grande de alternativas. Además, la mejor solución de muchos de estos problemas es, a menudo, evaluada desde varios puntos de vista (también llamados criterios). Es este caso, cada criterio puede ser descrito por una función objetivo. Algunos escenarios multi-objetivo importantes y bien conocidos son los siguientes: · En optimización de inversiones se pretende minimizar los riesgos y maximizar los beneficios. · En la programación de viajes se quiere reducir el tiempo de viaje y los costes. · En el diseño de circuitos se quiere reducir al mínimo la zona ocupada del circuito, el consumo de energía y maximizar la velocidad. · En los problemas de la mochila se quiere minimizar el peso de la carga y/o el volumen y maximizar su valor económico. Los ejemplos anteriores muestran que, en muchos casos, estos criterios son inconmensurables (es decir, es difícil o imposible combinar todos ellos en un único criterio) y están en conflicto (es decir, soluciones que son buenas con respecto a un criterio es probable que sean malas con respecto a otra). Tener en cuenta de forma simultánea todos estos criterios no es trivial y para ello se han propuesto diferentes nociones de optimalidad. Independientemente del concepto de optimalidad elegido, el cómputo de soluciones óptimas representa un importante desafío para la investigación actual. Los modelos gráficos son una herramienta para la represetanción del conocimiento ampliamente utilizados en el campo de la Inteligencia Artificial que parecen especialmente indicados en problemas combinatorios. A grandes rasgos, los modelos gráficos son grafos en los que los nodos representan variables y la (falta de) arcos representa la interdepencia entre variables. Además de la estructura gráfica, es necesario especificar su (micro-estructura) que indica cómo interactúan instanciaciones concretas de variables interdependientes. Los modelos gráficos proporcionan un marco capaz de unificar el modelado de un espectro amplio de sistemas y un conjunto de algoritmos generales capaces de resolverlos eficientemente. En esta tesis integramos problemas de optimización multi-objetivo en el contexto de los modelos gráficos y estudiamos cómo diversas técnicas algorítmicas desarrolladas dentro del marco de los modelos gráficos se pueden extender a problemas de optimización multi-objetivo. Como mostramos, este tipo de problemas se pueden formalizar como un caso particular de modelo gráfico usando el paradigma basado en semi-anillos (SCSP). Desde nuestro conocimiento, ésta es la primera vez que los modelos gráficos en general, y el paradigma basado en semi-anillos en particular, se usan para modelar un problema de optimización cuya función objetivo está parcialmente ordenada. Además, mostramos que la mayoría de técnicas para resolver problemas monoobjetivo se pueden extender de forma natural al contexto multi-objetivo. El resultado de nuestro trabajo es la formalización matemática de problemas de optimización multi-objetivo y el desarrollo de un conjunto de algoritmos capaces de resolver este tipo de problemas. Además, demostramos que estos algoritmos son eficientes en un conjunto determinado de benchmarks

RG limit cycles

In this review we consider the concept of limit cycles in the renormalization group flows. The examples of this phenomena in the quantum mechanics and field theory will be presented.Comment: 35 pages, 3 figures; Contribution to the "Pomeranchuk-100" Volum

Critical Team Composition Issues for Long-Distance and Long-Duration Space Exploration: A Literature Review, an Operational Assessment, and Recommendations for Practice and Research

Prevailing team effectiveness models suggest that teams are best positioned for success when certain enabling conditions are in place (Hackman, 1987; Hackman, 2012; Mathieu, Maynard, Rapp, & Gilson, 2008; Wageman, Hackman, & Lehman, 2005). Team composition, or the configuration of member attributes, is an enabling structure key to fostering competent teamwork (Hackman, 2002; Wageman et al., 2005). A vast body of research supports the importance of team composition in team design (Bell, 2007). For example, team composition is empirically linked to outcomes such as cooperation (Eby & Dobbins, 1997), social integration (Harrison, Price, Gavin, & Florey, 2002), shared cognition (Fisher, Bell, Dierdorff, & Belohlav, 2012), information sharing (Randall, Resick, & DeChurch, 2011), adaptability (LePine, 2005), and team performance (e.g., Bell, 2007). As such, NASA has identified team composition as a potentially powerful means for mitigating the risk of performance decrements due to inadequate crew cooperation, coordination, communication, and psychosocial adaptation in future space exploration missions. Much of what is known about effective team composition is drawn from research conducted in conventional workplaces (e.g., corporate offices, production plants). Quantitative reviews of the team composition literature (e.g., Bell, 2007; Bell, Villado, Lukasik, Belau, & Briggs, 2011) are based primarily on traditional teams. Less is known about how composition affects teams operating in extreme environments such as those that will be experienced by crews of future space exploration missions. For example, long-distance and long-duration space exploration (LDSE) crews are expected to live and work in isolated and confined environments (ICEs) for up to 30 months. Crews will also experience communication time delays from mission control, which will require crews to work more autonomously (see Appendix A for more detailed information regarding the LDSE context). Given the unique context within which LDSE crews will operate, NASA identified both a gap in knowledge related to the effective composition of autonomous, LDSE crews, and the need to identify psychological and psychosocial factors, measures, and combinations thereof that can be used to compose highly effective crews (Team Gap 8). As an initial step to address Team Gap 8, we conducted a focused literature review and operational assessment related to team composition issues for LDSE. The objectives of our research were to: (1) identify critical team composition issues and their effects on team functioning in LDSE-analogous environments with a focus on key composition factors that will most likely have the strongest influence on team performance and well-being, and 1 Astronaut diary entry in regards to group interaction aboard the ISS (p.22; Stuster, 2010) 2 (2) identify and evaluate methods used to compose teams with a focus on methods used in analogous environments. The remainder of the report includes the following components: (a) literature review methodology, (b) review of team composition theory and research, (c) methods for composing teams, (d) operational assessment results, and (e) recommendations

Eurolanguages-2010: Innovations and Development

Збірник наукових студентських робіт по підсумкам 8 Міжнародної конференції "Євромови-2010