Bounds on Weighted CSPs Using Constraint Propagation and Super-Reparametrizations

We propose a framework for computing upper bounds on the optimal value of the (maximization version of) Weighted CSP (WCSP) using super-reparametrizations, which are changes of the weights that keep or increase the WCSP objective for every assignment. We show that it is in principle possible to employ arbitrary (under certain technical conditions) constraint propagation rules to improve the bound. For arc consistency in particular, the method reduces to the known Virtual AC (VAC) algorithm. Newly, we implemented the method for singleton arc consistency (SAC) and compared it to other strong local consistencies in WCSPs on a public benchmark. The results show that the bounds obtained from SAC are superior for many instance groups

Applications of CSP solving in computer games (camera control)

While camera control systems of commercial 3D games have improved greatly in recent years, they are not as fully developed as are other game components such as graphics and physics engines. Bourne and Sattar (2006) have proposed a reactive constraint based third person perspective camera control system. We have extended the capability of their system to handle occlusion while following the main character, and have used camera cuts to find appropriate camera positions for a few difficult situations. We have developed a reactive constraint based third person perspective chase camera control system to follow a character in a 3D environment. The camera follows the character from (near) optimal positions defined by a camera profile. The desired values of the height and distance constraints of the camera profile are changed appropriately whenever the character enters a semi-enclosed or an enclosed area, and the desired value of the orientation constraint of the camera profile is changed incrementally whenever theoptimal camera view is obstructed. Camera cuts are used whenever the main character backs up to a wall or any other obstructions, or comes out of a semi-enclosed or an enclosed area. Two auxiliary cameras to observe the main camera positions from top and side views have been added. The chase camera control system achieved real-time performance while following the main character in a typical 3D environment, and maintained an optimal view based on a user specified/selected camera profile

Revisiting the Linear Programming Relaxation Approach to Gibbs Energy Minimization and Weighted Constraint Satisfaction

We present a number of contributions to the LP relaxation approach to weighted constraint satisfaction (= Gibbs energy minimization). We link this approach to many works from constraint programming, which relation has so far been ignored in machine vision and learning. While the approach has been mostly considered only for binary constraints, we generalize it to n-ary constraints in a simple and natural way. This includes a simple algorithm to minimize the LP-based upper bound, n-ary max-sum diffusion – however, we consider using other bound-optimizing algorithms as well. The diffusion iteration is tractable for a certain class of higharity constraints represented as a black-box, which is analogical to propagators for global constraints CSP. Diffusion exactly solves permuted n-ary supermodular problems. A hierarchy of gradually tighter LP relaxations is obtained simply by adding various zero constraints and coupling them in various ways to existing constraints. Zero constraints can be added incrementally, which leads to a cutting plane algorithm. The separation problem is formulated as finding an unsatisfiable subproblem of a CSP

Empirical evaluation of Soft Arc Consistency algorithms for solving Constraint Optimization Problems

A large number of problems in Artificial Intelligence and other areas of science can be viewed as special cases of constraint satisfaction or optimization problems. Various approaches have been widely studied, including search, propagation, and heuristics. There are still challenging real-world COPs that cannot be solved using current methods. We implemented and compared several consistency propagation algorithms, which include W-AC*2001, EDAC, VAC, and xAC. Consistency propagation is a classical method to reduce the search space in CSPs, and has been adapted to COPs. We compared several consistency propagation algorithms, based on the resemblance between the optimal value ordering and the approximate value ordering generated by them. The results showed that xAC generated value orderings of higher quality than W-AC*2001 and EDAC. We evaluated some novel hybrid methods for solving COPs. Hybrid methods combine consistency propagation and search in order to reach a good solution as soon as possible and prune the search space as much as possible. We showed that the hybrid method which combines the variant TP+OnOff and branch-and-bound search performed fewer constraint checks and searched fewer nodes than others in solving random and real-world COPs

Adaptive and Opportunistic Exploitation of Tree-decompositions for Weighted CSPs

International audienceWhen solving weighted constraint satisfaction problems , methods based on tree-decompositions constitute an interesting approach depending on the nature of the considered instances. The exploited decompositions often aim to reduce the maximal size of the clusters, which is known as the width of the decomposition. Indeed, the interest of this parameter is related to its importance with respect to the theoretical complexity of these methods. However, its practical interest for the solving of instances remains limited if we consider its multiple drawbacks, notably due to the restrictions imposed on the freedom of the variable ordering heuristic. So, we first propose to exploit new decompositions for solving the constraint optimization problem. These decompositions aim to take into account criteria allowing to increase the solving efficiency. Secondly, we propose to use these decompositions in a more dynamic manner in the sense that the solving of a subprob-lem would be based on the decomposition, totally or locally, only when it seems to be useful. The performed experiments show the practical interest of these new decompositions and the benefit of their dynamic exploitation

A distributed optimization method for the geographically distributed data centres problem

The geographically distributed data centres problem (GDDC) is a naturally distributed resource allocation problem. The problem involves allocating a set of virtual machines (VM) amongst the data centres (DC) in each time period of an operating horizon. The goal is to optimize the allocation of workload across a set of DCs such that the energy cost is minimized, while respecting limitations on data centre capacities, migrations of VMs, etc. In this paper, we propose a distributed optimization method for GDDC using the distributed constraint optimization (DCOP) framework. First, we develop a new model of the GDDC as a DCOP where each DC operator is represented by an agent. Secondly, since traditional DCOP approaches are unsuited to these types of large-scale problem with multiple variables per agent and global constraints, we introduce a novel semi-asynchronous distributed algorithm for solving such DCOPs. Preliminary results illustrate the benefits of the new method