Hybrid algorithms for distributed constraint satisfaction.

A Distributed Constraint Satisfaction Problem (DisCSP) is a CSP which is divided into several inter-related complex local problems, each assigned to a different agent. Thus, each agent has knowledge of the variables and corresponding domains of its local problem together with the constraints relating its own variables (intra-agent constraints) and the constraints linking its local problem to other local problems (inter-agent constraints). DisCSPs have a variety of practical applications including, for example, meeting scheduling and sensor networks. Existing approaches to Distributed Constraint Satisfaction can be mainly classified into two families of algorithms: systematic search and local search. Systematic search algorithms are complete but may take exponential time. Local search algorithms often converge quicker to a solution for large problems but are incomplete. Problem solving could be improved through using hybrid algorithms combining the completeness of systematic search with the speed of local search. This thesis explores hybrid (systematic + local search) algorithms which cooperate to solve DisCSPs. Three new hybrid approaches which combine both systematic and local search for Distributed Constraint Satisfaction are presented: (i) DisHyb; (ii) Multi-Hyb and; (iii) Multi-HDCS. These approaches use distributed local search to gather information about difficult variables and best values in the problem. Distributed systematic search is run with a variable and value ordering determined by the knowledge learnt through local search. Two implementations of each of the three approaches are presented: (i) using penalties as the distributed local search strategy and; (ii) using breakout as the distributed local search strategy. The three approaches are evaluated on several problem classes. The empirical evaluation shows these distributed hybrid approaches to significantly outperform both systematic and local search DisCSP algorithms. DisHyb, Multi-Hyb and Multi-HDCS are shown to substantially speed-up distributed problem solving with distributed systematic search taking less time to run by using the information learnt by distributed local search. As a consequence, larger problems can now be solved in a more practical timeframe

A hybrid approach to solving coarse-grained DisCSPs.

A coarse-grained Distributed Constraint Satisfaction Problem (DisCSP) consists of several loosely connected constraint satisfaction subproblems, each assigned to an individual agent. We present Multi-Hyb, a two-phase concurrent hybrid approach for solving DisCSPs. In the first phase, each agents subproblem is solved using systematic search which generates the key partial solutions to the global problem. Concurrently, a penalty-based local search algorithm attempts to find a global solution from these partial solutions. If phase 1 fails to find a solution, a phase 2 systematic search algorithm solves the problem using the knowledge gained from phase 1. We show that our approach is highly competitive in comparison with other coarse-grained DisCSP algorithms

A Multilevel Genetic Algorithm for the Maximum Satisfaction Problem

Genetic algorithms (GA) which belongs to the class of evolutionary algorithms are regarded as highly successful algorithms when applied to a broad range of discrete as well continuous optimization problems. This chapter introduces a hybrid approach combining genetic algorithm with the multilevel paradigm for solving the maximum constraint satisfaction problem (Max-CSP). The multilevel paradigm refers to the process of dividing large and complex problems into smaller ones, which are hopefully much easier to solve, and then work backward toward the solution of the original problem, using the solution reached from a child level as a starting solution for the parent level. The promising performances achieved by the proposed approach are demonstrated by comparisons made to solve conventional random benchmark problems

Гибридный алгоритм решения задачи удовлетворения ограничений

Представлен гибридный алгоритм improved Guided Local and Systematic Search для решения распределенной задачи удовлетворения ограничений. Алгоритм объединяет компоненты локального и конструктивного поиска. Доказаны полнота и корректность алгоритма. Приведены результаты его экспериментальной оценки на модельной задаче о ферзях и проведено сравнение его производительности с производительностью алгоритмов Dis-GLS и iGL.The improved Guided Local and Systematic Search hybrid algorithm is presented for solving the Distributed Constraint Satisfaction Problem, which combines two local and one systematic search methods. The completeness and correctness of the algorithm are proved. The results of our experiments with queens' problem, and a comparison of productivity for our hybrid and two other algorithms Dis-GLS and iGL are given.Представлено гібридний алгоритм improved Guided Local and Systematic Search розв’язання розподіленої задачі задоволення обмежень, який поєднує компоненти локального та конструктивного пошуку. Доведено повноту і коректність алгоритму. Описано результати його експериментальної оцінки на модельній задачі про ферзі. Проведено порівняння його продуктивності з продуктивністю алгоритмів класу Dis-GLS та iGL

A join-based hybrid parameter for constraint satisfaction

We propose joinwidth, a new complexity parameter for the Constraint Satisfaction Problem (CSP). The definition of joinwidth is based on the arrangement of basic operations on relations (joins, projections, and pruning), which inherently reflects the steps required to solve the instance. We use joinwidth to obtain polynomial-time algorithms (if a corresponding decomposition is provided in the input) as well as fixed-parameter algorithms (if no such decomposition is provided) for solving the CSP. Joinwidth is a hybrid parameter, as it takes both the graphical structure as well as the constraint relations that appear in the instance into account. It has, therefore, the potential to capture larger classes of tractable instances than purely structural parameters like hypertree width and the more general fractional hypertree width (fhtw). Indeed, we show that any class of instances of bounded fhtw also has bounded joinwidth, and that there exist classes of instances of bounded joinwidth and unbounded fhtw, so bounded joinwidth properly generalizes bounded fhtw. We further show that bounded joinwidth also properly generalizes several other known hybrid restrictions, such as fhtw with degree constraints and functional dependencies. In this sense, bounded joinwidth can be seen as a unifying principle that explains the tractability of several seemingly unrelated classes of CSP instances

Job-shop scheduling with an adaptive neural network and local search hybrid approach

This article is posted here with permission from IEEE - Copyright @ 2006 IEEEJob-shop scheduling is one of the most difficult production scheduling problems in industry. This paper proposes an adaptive neural network and local search hybrid approach for the job-shop scheduling problem. The adaptive neural network is constructed based on constraint satisfactions of job-shop scheduling and can adapt its structure and neuron connections during the solving process. The neural network is used to solve feasible schedules for the job-shop scheduling problem while the local search scheme aims to improve the performance by searching the neighbourhood of a given feasible schedule. The experimental study validates the proposed hybrid approach for job-shop scheduling regarding the quality of solutions and the computing speed

Hybrid tractability of soft constraint problems

The constraint satisfaction problem (CSP) is a central generic problem in computer science and artificial intelligence: it provides a common framework for many theoretical problems as well as for many real-life applications. Soft constraint problems are a generalisation of the CSP which allow the user to model optimisation problems. Considerable effort has been made in identifying properties which ensure tractability in such problems. In this work, we initiate the study of hybrid tractability of soft constraint problems; that is, properties which guarantee tractability of the given soft constraint problem, but which do not depend only on the underlying structure of the instance (such as being tree-structured) or only on the types of soft constraints in the instance (such as submodularity). We present several novel hybrid classes of soft constraint problems, which include a machine scheduling problem, constraint problems of arbitrary arities with no overlapping nogoods, and the SoftAllDiff constraint with arbitrary unary soft constraints. An important tool in our investigation will be the notion of forbidden substructures.Comment: A full version of a CP'10 paper, 26 page

On the Practical use of Variable Elimination in Constraint Optimization Problems: 'Still-life' as a Case Study

Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the applicability of variable elimination to the challenging problem of finding still-lifes. We illustrate several alternatives: variable elimination as a stand-alone algorithm, interleaved with search, and as a source of good quality lower bounds. We show that these techniques are the best known option both theoretically and empirically. In our experiments we have been able to solve the n=20 instance, which is far beyond reach with alternative approaches