Solving the Weighted Constraint Satisfaction Problems Via the Neural Network Approach

A wide variety of real world optimization problems can be modelled as Weighted Constraint Satisfaction Problems (WCSPs). In this paper, we model this problem in terms of in original 0-1 quadratic programming subject to leaner constraints. View it performance, we use the continuous Hopfield network to solve the obtained model basing on original energy function. To validate our model, we solve several instance of benchmarking WCSP. In this regard, our approach recognizes the optimal solution of the said instances

Supply chain coordination using an adaptive distributed search strategy

A tree search strategy is said to be adaptive when it dynamically identifies which areas of the tree are likely to contain good solutions, using information that is gathered during the search process. This study shows how an adaptive approach can be used to enhance the efficiency of the coordination process of an industrial supply chain. The result is a new adaptive method (called the adaptive discrepancy search), intended for search in nonbinary trees, and that is exploitable in a distributed optimization context. For the industrial case studied (a supply chain in the forest products industry), this allowed reducing nearly half the time needed to obtain the best solution in comparison with a standard nonadaptive method. The method has also been evaluated for use with synthesized problems in order to validate the results that are obtained and to illustrate different properties of the algorith

Quantified weighted constraint satisfaction problems.

Mak, Wai Keung Terrence.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 100-104).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Constraint Satisfaction Problems --- p.1Chapter 1.2 --- Weighted Constraint Satisfaction Problems --- p.2Chapter 1.3 --- Quantified Constraint Satisfaction Problems --- p.3Chapter 1.4 --- Motivation and Goal --- p.4Chapter 1.5 --- Outline of the Thesis --- p.6Chapter 2 --- Background --- p.7Chapter 2.1 --- Constraint Satisfaction Problems --- p.7Chapter 2.1.1 --- Backtracking Tree Search --- p.9Chapter 2.1.2 --- Local Consistencies for solving CSPs --- p.11Node Consistency (NC) --- p.13Arc Consistency (AC) --- p.14Searching by Maintaining Arc Consistency --- p.16Chapter 2.1.3 --- Constraint Optimization Problems --- p.17Chapter 2.2 --- Weighted Constraint Satisfaction Problems --- p.19Chapter 2.2.1 --- Branch and Bound Search (B&B) --- p.23Chapter 2.2.2 --- Local Consistencies for WCSPs --- p.25Node Consistency --- p.26Arc Consistency --- p.28Chapter 2.3 --- Quantified Constraint Satisfaction Problems --- p.32Chapter 2.3.1 --- Backtracking Free search --- p.37Chapter 2.3.2 --- Consistencies for QCSPs --- p.38Chapter 2.3.3 --- Look Ahead for QCSPs --- p.45Chapter 3 --- Quantified Weighted CSPs --- p.48Chapter 4 --- Branch & Bound with Consistency Techniques --- p.54Chapter 4.1 --- Alpha-Beta Pruning --- p.54Chapter 4.2 --- Consistency Techniques --- p.57Chapter 4.2.1 --- Node Consistency --- p.62Overview --- p.62Lower Bound of A-Cost --- p.62Upper Bound of A-Cost --- p.66Projecting Unary Costs to Cθ --- p.67Chapter 4.2.2 --- Enforcing Algorithm for NC --- p.68Projection Phase --- p.69Pruning Phase --- p.69Time Complexity --- p.71Chapter 4.2.3 --- Arc Consistency --- p.73Overview --- p.73Lower Bound of A-Cost --- p.73Upper Bound of A-Cost --- p.75Projecting Binary Costs to Unary Constraint --- p.75Chapter 4.2.4 --- Enforcing Algorithm for AC --- p.76Projection Phase --- p.77Pruning Phase --- p.77Time complexity --- p.79Chapter 5 --- Performance Evaluation --- p.83Chapter 5.1 --- Definitions of QCOP/QCOP+ --- p.83Chapter 5.2 --- Transforming QWCSPs into QCOPs --- p.90Chapter 5.3 --- Empirical Evaluation --- p.91Chapter 5.3.1 --- Random Generated Problems --- p.92Chapter 5.3.2 --- Graph Coloring Game --- p.92Chapter 5.3.3 --- Min-Max Resource Allocation Problem --- p.93Chapter 5.3.4 --- Value Ordering Heuristics --- p.94Chapter 6 --- Concluding Remarks --- p.96Chapter 6.1 --- Contributions --- p.96Chapter 6.2 --- Limitations and Related Works --- p.97Chapter 6.3 --- Future Works --- p.99Bibliography --- p.10

Algorithmes pour la prise de décision distribuée en contexte hiérarchique

RÉSUMÉ Cette thèse a pour objet la coordination entre entités autonomes. De manière plus précise, nous nous intéressons à la coordination dans un contexte hiérarchique. Les problèmes étudiés montrent les caractéristiques suivantes : (1) il s’agit de problèmes d’optimisation distribués, (2) le problème est naturellement décomposé en sousproblèmes, (3) il existe a priori une séquence selon laquelle les sous-problèmes doivent être résolus, (4) les sous-problèmes sont sous la responsabilité de différentes entités et (5) chaque sous-problème est défini en fonction des solutions retenues pour les sousproblèmes précédents. Parmi les principaux domaines d’application, on trouve les systèmes d’aide à la décision organisationnels et les problèmes de synchronisation dans les chaînes logistiques industrielles. Ce dernier domaine sert de fil conducteur dans cette thèse : le travail de plusieurs unités de production est nécessaire pour fabriquer et livrer les commandes des clients. Différentes alternatives sont possibles en ce qui a trait aux pièces à utiliser, au choix des processus de fabrication, à l’ordonnancement des opérations et au transport. Chaque partenaire désire établir son plan de production (quoi faire, où et quand le faire), mais il est nécessaire pour eux de coordonner leurs activités. Les méthodes utilisées en pratique industrielle peuvent être qualifiées d’heuristiques de coordination. À l’opposé, il existe des algorithmes d’optimisation distribués et exacts, notamment les techniques de raisonnement sur contraintes distribuées (Distributed Constraint Optimization Problems, ou DCOP). Cependant, ces derniers algorithmes s’accommodent mal de la nature hiérarchique des problèmes étudiés et pourraient difficilement être utilisés en pratique. Les forces et les faiblesses des méthodes heuristiques et exactes nous ont donc amené à proposer de nouvelles approches.---------- ABSTRACT This thesis concerns multiagent coordination in hierarchical settings. These are distributed optimization problems showing the following characteristics: (1) the global problem is naturally decomposed into subproblems, (2) a sequence, defined a priori, exists in which the subproblems must be solved, (3) various agents are responsible for the subproblems, and (4) each subproblem is defined according to the solutions adopted for the preceding subproblems. Organizational distributed decision making and Supply chain coordination are among the main application domains. The latter case is more thoroughly studied in this thesis. In this kind of problem, the cooperation of several facilities is needed to produce and deliver the products ordered by external customers. However, different alternatives are possible regarding the parts to use, the manufacturing processes to follow, the scheduling of operations and the choice of transportation. Therefore, supply chain partners must coordinate their local decisions (e.g. what to do, where and when), with the common objective of delivering the ordered products with the least possible delay. The most commonly used coordination mechanisms can be described as heuristics. In contrast, some generic and complete distributed algorithms exist – researchers in Distributed Artificial Intelligence (DAI) have proposed a generic framework called Distributed Constraint Optimization Problem (DCOP). However, there are certain difficulties in mapping the actual business context (which is highly hierarchical) into the DCOP framework. Thus, based on the strengths and weaknesses of both the complete and heuristic approaches, we propose new approaches