Automated planning and scheduling

Automated planning and scheduling, sometimes denoted as simply AI planning, is a branch of artificial intelligence that concerns the realization of strategies or action sequences, typically for execution by intelligent agents, autonomous robots and unmanned vehicles. Unlike classical control and classification problems, the solutions are complex and must be discovered and optimized in multidimensional space. Planning is also related to decision theory. In known environments with available models, planning can be done offline. Solutions can be found and evaluated prior to execution. In dynamically unknown environments, the strategy often needs to be revised online. Models and policies must be adapted. Solutions usually resort to iterative trial and error processes commonly seen in artificial intelligence. These include dynamic programming, reinforcement learning and combinatorial optimization. Languages used to describe planning and scheduling are often called action languages. Given a description of the possible initial states of the world, a description of the desired goals, and a description of a set of possible actions, the planning problem is to synthesize a plan that is guaranteed (when applied to any of the initial states) to generate a state which contains the desired goals (such a state is called a goal state). The difficulty of planning is dependent on the simplifying assumptions employed. Several classes of planning problems can be identified depending on the properties the problems have in several dimensions. Are the actions deterministic or non-deterministic? For nondeterministic actions, are the associated probabilities available? Are the state variables discrete or continuous? If they are discrete, do they have only a finite number of possible values? Can the current state be observed unambiguously? There can be full observability and partial observability.

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Logic programming

Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic programming language families include Prolog, answer set programming (ASP) and Datalog. In all of these languages, rules are written in the form of clauses: H :- B1, ..., Bn. and are read declaratively as logical implications: H if B1 and ... and Bn. H is called the head of the rule and B1, .

Constraint programming

Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables. Constraints differ from the common primitives of imperative programming languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found.

Constraint satisfaction problem

Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families.

Constraint Satisfaction: Formulation and Algorithms CS-330: Artificial intelligence

Covers the formulation of constraint satisfaction problems and systematic algorithms for solving them efficiently.

Distributed Multiagent Systems: Coordination and Learning CS-430: Intelligent agents

Explores coordination and learning in distributed multiagent systems, covering social laws, task exchange, constraint satisfaction, and coordination algorithms.

Calculus of Variations and Euler's Elastica

Covers variational methods, equilibrium shapes, Euler's Elastica, and numerical and analytical methods for solving Euler's Elastica.

Rigorous solution techniques for numerical constraint satisfaction problems

Xuan-Ha Vu

A constraint satisfaction problem (e.g., a system of equations and inequalities) consists of a finite set of constraints specifying which value combinations from given variable domains are admitted. It is called numerical if its variable domains are continuous. Such problems arise in many applications, but form a difficult problem class since they are NP-hard. Solving a constraint satisfaction problem is to find one or more value combinations satisfying all its constraints. Numerical computations on floating-point numbers in computers often suffer from rounding errors. The rigorous control of rounding errors during numerical computations is highly desired in many applications because it would benefit the quality and reliability of the decisions based on the solutions found by the computations. Various aspects of rigorous numerical computations in solving constraint satisfaction problems are addressed in this thesis: search, constraint propagation, combination of inclusion techniques, and post-processing. The solution of a constraint satisfaction problem is essentially performed by a search. In this thesis, we propose a new complete search technique (i.e., it can find all solutions within a predetermined tolerance) for numerical constraint satisfaction problems. This technique is general and can be used in place of branching steps in most branch-and-prune methods. Moreover, this new technique speeds up the most recent general search strategy (often by an order of magnitude) and provides a concise representation of solutions. To make a constraint satisfaction problem easier to solve, a major approach, called constraint propagation, in the constraint programming1 field is often used to reduce the variable domains (by discarding redundant value combinations from the domains). Basing on directed acyclic graphs, we propose a new constraint propagation technique and a method for coordinating constraint propagation and search. More importantly, we propose a novel generic scheme for combining multiple inclusion techniques2 in numerical constraint propagation. This scheme allows bringing into the constraint propagation framework the strengths of various techniques coming from different fields. To illustrate the flexibility and efficiency of the generic scheme, we base on this scheme and devise several specific combination strategies for rigorous numerical constraint propagation using interval constraint propagation, interval arithmetic, affine arithmetic, and linear programming. Our experiments show that the new propagation techniques outperform previously available methods by 1 to 4 orders of magnitude or more in speed. We also propose several post-processing techniques for the representation of continuums of solutions. Based on connectedness, they allow grouping each cluster of connected solution subsets into a larger subset, thus allowing getting additional grouping information. Potentially, these techniques enable interval-based solution techniques to be alternatives to bounding-volume techniques in applications such as collision detection and interactive graphics. __________________________________________________ 1 Constraint programming is an approach to programming that relies on both reasoning and computing. 2 An inclusion technique is to include a set of interest into enclosures. It is also called an enclosure technique.

EPFL2005

Integrating problem solving and information gathering using constraint satisfaction

Santiago Macho Gonzalez

EPFL2004

Scalable intelligent electronic catalogs

Marc Torrens Arnal

The world today is full of information systems which make huge quantities of information available. This incredible amount of information is clearly overwhelming Internet endusers. As a consequence, intelligent tools to identify worthwhile information are needed, in order to fully assist people in finding the right information. Moreover, most systems are ultimately used, not just to provide information, but also to solve problems. Encouraged by the growing popular success of Internet and the enormous business potential of electronic commerce, e-catalogs have been consolidated as one of the most relevant types of information systems. Nearly all currently available electronic catalogs are offering tools for extracting product information based on key-attribute filtering methods. The most advanced electronic catalogs are implemented as recommender systems using collaborative filtering techniques. This dissertation focuses on strategies for coping with the difficulty of building intelligent catalogs which fully support the user in his purchase decision-making process, while maintaining the scalability of the whole system. The contributions of this thesis lie on a mixed-initiative system which is inspired by observations on traditional commerce activities. Such a conversational model consists basically of a dialog between the customer and the system, where the user criticizes proposed products and the catalog suggests new products accordingly. Constraint satisfaction techniques are analyzed in order to provide a uniform framework for modeling electronic catalogs for configurable products. Within the same framework, user preferences and optimization constraints are also easily modeled. Searching strategies for proposing the adequate products according to criteria are described in detail. Another dimension of this dissertation faces the problem of scalability, i.e., the problem of supporting hundreds, or thousands of users simultaneously using intelligent electronic catalogs. Traditional wisdom would presume that in order to provide full assistance to users in complex tasks, the business logic of the system must be complex, thus preventing scalability. SmartClient is a software architectural model that uses constraint satisfaction problems for representing solution spaces, instead of traditional models which represent solution spaces by collections of single solutions. This main idea is supported by the fact that constraint solvers are extreme in their compactness and simplicity, while providing sophisticated business logic. Different SmartClient architecture configurations are provided for different uses and architectural requirements. In order to illustrate the use of constraint satisfaction techniques for complex electronic catalogs with the SmartClient architecture, a commercial Internet-based application for travel planning, called reality, has been successfully developed. Travel planning is a particularly appropriate domain for validating the results of this research, since travel information is dynamic, travel planning problems are combinatorial, and moreover, complex user preferences and optimization constraints must be taken into consideration.

EPFL2003

High-level programming languages

In computer science, a high-level programming language is a programming language with strong abstraction from the details of the computer. In contrast to low-level programming languages, it may use natural language elements, be easier to use, or may automate (or even hide entirely) significant areas of computing systems (e.g. memory management), making the process of developing a program simpler and more understandable than when using a lower-level language. The amount of abstraction provided defines how "high-level" a programming language is.

Combinatorial optimization

Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead.

First-order logic

First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable.