. A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed. 1 Introduction Constraint satisfaction involves finding values for problem variables subject to constraints on acceptable combinations of values. Constraint satisfaction has wide application in artificial intelligence, in areas ranging from temporal r...

4, and Toby Walsh 5

Search algorithms on distributed constraints satisfaction problems, DisCSPs, are composed of agents performing computations concurrently. The most common abstract performance measurement that has been universally adopted for centralized CSPs algorithms is the number of constraints checks performed. However, when it comes to distributed search, constraints checks are performed concurrently by all agents on the network and therefore a simple measurement of constraints checks is not adequate any more. In order to be able to compare the behavior of different algorithms, there is a need for a new distributed method to measure the search effort of a DisCSP algorithm.

Abstract. Many problems in multi-agent systems can be described as distributed Constraint Satisfaction Problems (distributed CSPs), where the goal is to nd a set of assignments to variables that satis es all constraints among agents. However, when real problems are formalized as distributed CSPs, they are often over-constrained and have no solution that satis es all constraints. This paper provides the Distributed Partial Constraint Satisfaction Problem (DPCSP) as a new framework for dealing with over-constrained situations. We also present new algorithms for solving Distributed Maximal Constraint Satisfaction Problems (DM-CSPs), which belong to an important class of DPCSP. The algorithms are called the Synchronous Branch and Bound (SBB) and the Iterative Distributed Breakout (IDB). Both algorithms were tested on hard classes of over-constrained random binary distributed CSPs. The results can be summarized as SBB is preferable when we are mainly concerned with the optimality ofasolution, while IDB is preferable when we want to get a nearly optimal solution quickly. 1

In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satis able to a region where almost all problems are unsatis able do exist for Model RB as the number of variables approaches in nity. Moreover, the critical values at which the phase transitions occur are also known exactly. By relating the hardness of Model RB to Model B, it is shown that there exist a lot of hard instances in Model RB.

Solving constraint optimization problems is computationally so expensive that it is often impossible to provide a guaranteed optimal solution, either when the problem is too large, or when time is bounded. In these cases, local search algorithms usually provide good solutions. However, and even if an optimality proof is unreachable, it is often desirable to have some guarantee on the quality of the solution found, in order to decide if it is worthwile to spend more time on the problem. This paper is dedicated to the production of intervals, that bound as precisely as possible the optimum of Valued Constraint Satisfaction Problems (VCSP). Such intervals provide an upper bound on the distance of the best available solution to the optimum i.e., on the quality of the optimization performed. Experimental results on random VCSPs and real problems are given. Motivations The Constraint Satisfaction Problem framework is very convenient for representing and solving various problems, related t...

A new search algorithm for solving distributed constraint optimization problems (DisCOPs) is presented. Agents assign variables sequentially and propagate their assignments asynchronously. The asynchronous forward-bounding algorithm (AFB) is a distributed optimization search algorithm that keeps one consistent partial assignment at all times. Forward bounding propagates the bounds on the cost of solutions by sending copies of the partial assignment to all unassigned agents concurrently. The algorithm is described in detail and its correctness proven. Experimental evaluation of AFB on random Max-DisCSPs reveals a phase transition as the tightness of the problem increases. This effect is analogous to the phase transition of Max-CSP when local consistency maintenance is applied [3]. AFB outperforms Synchronous Branch & Bound (SBB) as well as the asynchronous state-of-the-art ADOPT algorithm, for the harder problem instances. Both asynchronous algorithms outperform SBB by a large factor. 1

Constraint Violation Minimization Problems arise when dealing with over-constrained CSPs. Unfortunately, experiments and practice show that they quickly become too large and too difficult to be optimally solved. In this context, multiple methods (limited tree search, heuristic or stochastic local search) are available to produce non-optimal, but good quality solutions, and thus to provide the user with anytime upper bounds of the problem optimum. On the other hand, few methods are available to produce anytime lower bounds of this optimum.

Abstract. We present an approach to the bid-evaluation problem in a system for multi-agent contract negotiation, called MAGNET. The MAGNET market infrastructure provides support for a variety oftypes of transactions, from simple buying and selling of goods and services to complex multi-agent contract negotiations. In the latter case, MAGNET is designed to negotiate contracts based on temporal and precedence constraints, and includes facilities for dealing with time-based contingencies. One responsibility of a customer agent in the MAGNET system is to select an optimal bid combination. We present an e cient anytime algorithm for a customer agent to select bids submitted by supplier agents in response to a call for bids. Bids might include combinations of subtasks and might include discounts for combinations. In an experimental study we explore the behavior of the algorithm based on the interactions of factors such as bid prices, number of bids, and number of subtasks. The results of experiments we present show that the algorithm is extremely e cient even for large number of bids. 1

Abstract. When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an election by misreporting their preferences. Fortunately, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NPhardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. To address this issue, I suggest studying empirically if computational complexity is in practice a barrier to manipulation. The basic tool used in my investigations is the identification of computational “phase transitions”. Such an approach has been fruitful in identifying hard instances of propositional satisfiability and other NP-hard problems. I show that phase transition behaviour gives insight into the hardness of manipulating voting rules, increasing concern that computational complexity is indeed any sort of barrier. Finally, I look at the problem of computing manipulation of other, related problems like stable marriage and tournament problems. 1