5 research outputs found
Dynamic Backtracking
Because of their occasional need to return to shallow points in a search
tree, existing backtracking methods can sometimes erase meaningful progress
toward solving a search problem. In this paper, we present a method by which
backtrack points can be moved deeper in the search space, thereby avoiding this
difficulty. The technique developed is a variant of dependency-directed
backtracking that uses only polynomial space while still providing useful
control information and retaining the completeness guarantees provided by
earlier approaches.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning
The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques
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:
路 In investment optimization one wants to minimize risk and maximize benefits.
路 In travel scheduling one wants to minimize time and cost.
路 In circuit design one wants to minimize circuit area, energy consumption and maximize speed.
路 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 optimizaci贸n son combinatorios, es decir, requieren de la elecci贸n de la mejor soluci贸n (o soluci贸n
贸ptima) dentro de un conjunto finito pero exponencialmente grande de alternativas. Adem谩s, la mejor soluci贸n de muchos de estos
problemas es, a menudo, evaluada desde varios puntos de vista (tambi茅n llamados criterios). Es este caso, cada criterio puede ser
descrito por una funci贸n objetivo. Algunos escenarios multi-objetivo importantes y bien conocidos son los siguientes:
路 En optimizaci贸n de inversiones se pretende minimizar los riesgos y maximizar los beneficios.
路 En la programaci贸n de viajes se quiere reducir el tiempo de viaje y los costes.
路 En el dise帽o de circuitos se quiere reducir al m铆nimo la zona ocupada del circuito, el consumo de energ铆a y maximizar la
velocidad.
路 En los problemas de la mochila se quiere minimizar el peso de la carga y/o el volumen y maximizar su valor econ贸mico.
Los ejemplos anteriores muestran que, en muchos casos, estos criterios son inconmensurables (es decir, es dif铆cil o imposible
combinar todos ellos en un 煤nico criterio) y est谩n 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 simult谩nea todos estos criterios no es trivial y para ello se
han propuesto diferentes nociones de optimalidad. Independientemente del concepto de optimalidad elegido, el c贸mputo de
soluciones 贸ptimas representa un importante desaf铆o para la investigaci贸n actual.
Los modelos gr谩ficos son una herramienta para la represetanci贸n del conocimiento ampliamente utilizados en el campo de la
Inteligencia Artificial que parecen especialmente indicados en problemas combinatorios. A grandes rasgos, los modelos gr谩ficos son
grafos en los que los nodos representan variables y la (falta de) arcos representa la interdepencia entre variables. Adem谩s de la
estructura gr谩fica, es necesario especificar su (micro-estructura) que indica c贸mo interact煤an instanciaciones concretas de variables
interdependientes. Los modelos gr谩ficos 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 optimizaci贸n multi-objetivo en el contexto de los modelos gr谩ficos y estudiamos c贸mo
diversas t茅cnicas algor铆tmicas desarrolladas dentro del marco de los modelos gr谩ficos se pueden extender a problemas de
optimizaci贸n multi-objetivo. Como mostramos, este tipo de problemas se pueden formalizar como un caso particular de modelo
gr谩fico usando el paradigma basado en semi-anillos (SCSP). Desde nuestro conocimiento, 茅sta es la primera vez que los modelos
gr谩ficos en general, y el paradigma basado en semi-anillos en particular, se usan para modelar un problema de optimizaci贸n cuya
funci贸n objetivo est谩 parcialmente ordenada. Adem谩s, mostramos que la mayor铆a de t茅cnicas para resolver problemas monoobjetivo
se pueden extender de forma natural al contexto multi-objetivo. El resultado de nuestro trabajo es la formalizaci贸n
matem谩tica de problemas de optimizaci贸n multi-objetivo y el desarrollo de un conjunto de algoritmos capaces de resolver este tipo
de problemas. Adem谩s, demostramos que estos algoritmos son eficientes en un conjunto determinado de benchmarks