We investigate the solution of constraint-based configuration problems in which the preference function over outcomes is unknown or incompletely specified. The aim is to configure a system, such as a personal computer, so that it will be optimal for a given user. The goal of this project is to develop algorithms that generate the most preferred feasible configuration by posing preference queries to the user. In order to minimize the number and the complexity of preference queries posed to the user, the algorithm reasons about the user’s preferences while taking into account constraints over the set of feasible configurations. We assume that the user can structure their preferences in a particular way that, while natural in many settings, can be exploited during the optimization process. We also address in a preliminary fashion the trade-offs between computational effort in the solution of a problem and the degree of interaction with the user. 1

. This paper presents a Tabu Search (TS) algorithm for solving maximal constraint satisfaction problems. The algorithm was tested on a wide range of random instances (up to 500 variables and 30 values) . Comparisons were carried out with a min-conflicts+random-walk (MCRW) algorithm. Empirical evidence shows that the TS algorithm finds results which are better than that of the MCRW algorithm.the TS algorithm is 3 to 5 times faster than the MCRW algorithm to find solutions of the same quality. Keywords: Tabu search, constraint solving, combinatorial optimization. 1 Introduction A finite Constraint Network (CN) is composed of a finite set X of variables, a set D of finite domains and a set C of constraints over subsets of X. A constraint is a subset of the Cartesian product of the domains of the variables involved that specifies which combinations of values are compatible. A CN is said to be binary if all the constraints have 2 variables. Given a CN, the Constraint Satisfaction Problem ...

Abstract. We propose a new method for solving Valued Constraint Satisfaction Problems based both on backtracking techniques- branch and bound- and the notion of tree-decomposition of valued constraint networks. This mixed method aims to benefit from the practical efficiency of enumerative algorithms while providing a warranty of a bounded time complexity. Indeed the time complexity of our method is O(d w+ +1) with w + an approximation of the tree-width of the constraint network and d the maximum size of domains. Such a complexity is obtained by exploiting optimal bounds on the subproblems defined from the tree-decomposition. These bounds associated to some partial assignments are called ”structural valued goods”. Recording and exploiting these goods may allow our method to save some time and space with respect to ones required by classical dynamic programming methods. Finally, this method is a natural extension of the BTD algorithm [1] proposed in the classical CSP framework. 1

In the frame of classical Constraint Satisfaction Problems (CSPs), the backtrack tree search, combined with learning methods, presents a double advantage : for static solving, it improves the search speed by avoiding redundant explorations; for dynamic solving (after a slight change of the problem), it reuses the previous searches to build a new solution quickly. Backtrack reasoning concludes the reject of certain combinatorial choices. Nogood Recording memorizes these choices in order not to reproduce. We aim to use NogoodRecording in the wider scope of the Valued CSP framework(VCSP) to enhance the branch and bound algorithm. Therefore, nogoods are used to increase the lower bound used by the branch and bound to prune the search. This issue leads to the definition of the "Valued Nogoods" and their use. This study focuses particularly on penalty and dynamic VCSPs which require special developments. However, our results give an extension of the Nogood Recording to the general VCSP frame...

We summarize existing approaches to model and solve overconstrained problems. These problems are usually formulated as combinatorial optimization problems, and different specific and generic formalisms are discussed, including the special case of multi-objective optimization. Regarding solving methods, both systematic and local search approaches are considered. Finally we revise a number of case studies on overconstrained problems taken from the specialized literature.

The Multiagent Agreement Problem (MAP) is a special form of Distributed Constraint Optimization (DCOP) that requires agents to choose values for variables to satisfy not only their own constraints, but also equality constraints with other agents. For solving MAPs, we introduce the AdoptMVA algorithm which is an extension of the existing Adopt algorithm designed to take advantage of the partial centralization that exists in MAP domains where agents control multiple variables. Second, while existing solution approaches to DCOP require variables to be prioritized in some fashion in order to guarantee optimality, it is unclear how to order variables effectively when agents own multiple variables. We investigate a hierarchical approach which leverages known ordering techniques from the sequential constraint satisfaction literature by combining ordering at the agent level with orderings at the variable level to obtain efficient global orderings. Finally, we identify a promising technique for converting known effective variable orderings into effective agent orderings and identify an intra-agent variable ordering heuristic for MAP that is the most efficient of the ones tested. While the contributions presented in this paper are applicable to general DCOPs, we focus our discussion on MAPs because we feel it is a significant problem class worthy of specific attention. 1.

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(DARPA), or the Department of Interior-National Business Center (DOI-NBC).

In this paper, we present an experimental study of local search for constraint solving. For this purpose, we experiment with two algorithms based on Simulated Annealing (SA) and Tabu Search (TS) for solving the maximal constraint satisfaction problem. These two algorithms were tested on various large random instances going from 100 to 300 variables with 10 to 30 values per variable. Experimental results show that the TS algorithm dominates the SA algorithm on all the tested instances in terms of solution quality and solving speed. We propose empirical arguments to explain the difference of performances. Keywords: Local Search, Simulated Annealing, Tabu Search, Constraint Solving. 1 Introduction Constraint solving either for satisfaction or optimization purpose occupies a very important place in Artificial Intelligence (AI) and Mathematics. Informally, constraint solving consists in finding assignment of values to variables while respecting some constraints and eventually optimizing a...

This paper describes our experience for introducing Constraint Programming in operational systems of THALES . Many of them are on-board and real-time systems. We give the requirements of a technology for developing real-time systems with combinatorial optimization capabilities. We present the constraint technology that has the ability to fulfill most of the requirements.