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Distributed CSPs by graph partitioning
Abstract
Nowadays, many real problems in artificial intelligence can be modelled as constraint satisfaction problems (CSPs). A general CSP is known to be NP-complete. Nevertheless, distributed models may reduce the exponential complexity by partitioning the problem into a set of subproblems. In this paper, we present a preprocess technique to break a single large problem into a set of smaller loosely connected ones. These semi-independent CSPs can be efficiently solved and, furthermore, they can be solved concurrently.
... (Salido 2007). Only some works include a set of variables into an agent (Silaghi & Faltings 2005),(Ezzahir & Bouyakhf 2007),(Salido & Barber 2006). Nevertheless, few works have been focused on distributed techniques for solving large scale problems (Yokoo et al. 1998). ...
... Nevertheless , some subproblems are too large and they can be divided/decomposed again into smaller ones in order to be solved in a reasonable time. A reasonable way to divide the problem is by means of graph partitioning techniques (Salido & Barber 2006). However, in many real problems, the best way to partition the problem is by carrying out a domain dependent partition. ...
A distributed constraint satisfaction problem (DisCSP) is a CSP in which variables and constraints are distributed among multiple automated agents. Many researchers have developed techniques for solving DisCSPs. They assume for simplicity that each agent has exactly one variable. For real planning and scheduling problems, these techniques require a large number of messages passing among agents, so these problems are very difficult to solve. In this paper, we present a general distributed model for solving real-life scheduling problems. This distributed model is based on the idea of holonic systems. Furthermore, we propose some guidelines for distributing large-scale problems. Finally, we present two case studies in which two scheduling problems are distributed by using our model.
... DCSP techniques were used to parallelise the search to a centralized CSP (Salido and Barber 2006). A graph partitioning algorithm was used to divide the original CSP into an appropriate number of subproblems, in this case 10, aiming to minimise the number of variables shared between subproblems. ...
As multicore computing is now standard, it seems irresponsible for constraints researchers to ignore the implications of it. Researchers need to address a number of issues to exploit parallelism, such as: investigating which constraint algorithms are amenable to parallelisation; whether to use shared memory or distributed computation; whether to use static or dynamic decomposition; and how to best exploit portfolios and cooperating search. We review the literature, and see that we can sometimes do quite well, some of the time, on some instances, but we are far from a general solution. Yet there seems to be little overall guidance that can be given on how best to exploit multicore computers to speed up constraint solving. We hope at least that this survey will provide useful pointers to future researchers wishing to correct this situation. Under consideration in Theory and Practice of Logic Programming (TPLP).
... Similar approaches have been applied to improve the performance of SAT and constraint solvers (Salido and Barber, 2006), e.g. to allow analyzing each subproblem in parallel. These techniques can be more successful at the model level than at the solver level for several reasons: ...
... These considerations have not proven problematic in our experience. However, reactor design is still heuristically driven; techniques developed for partitioning constraint graphs such as (Salido & Barber 2006) for example, may be relevant in this context. ...
In this chapter Teleo-Reactive Executive (T-REX) is designed, developed, tested and deployed as an onboard adaptive control system that integrates artificial intelligence (AI)-based planning and probabilistic state estimation in a hybrid executive. Probabilistic state estimation integrates a number of science observations to produce a likelihood that the vehicle sensors perceive a feature of interest. Onboard planning and execution enable adaptation of navigation and instrument control based on the probability of having detected such a phenomenon. It further enables goal-directed commanding within the context of projected mission state and allows for replanning for off-nominal situations and opportunistic science events.
... This can be an advantage for large but not very densely coupled problems. However, as Salido and Barber (2006) CoCSP algorithms surveyed in the literature minimize the number of decision constraints rejected at any stage of the design process. This approach considers only the number of decision constraints, but it does not take into account the amount of the restriction and the satisfaction obtained by constraints. ...
In the product dimensioning phase of a distributed design, inconsistencies can emerge among design objectives as well as among working procedures of heterogeneous subsystems. In this phase, design actors which compose subsystems must collaborate concurrently, since their works are linked to each other through dimensioning couplings among their sub-problems. Inconsistencies through these couplings yield thus to design conflicts. The issue is how to obtain a collaborative convergence to satisfy the global and individual objectives of design actors when making design decisions under uncertainty. The objective of this dissertation is to propose a model for preventing and resolving design conflicts in order to obtain a collaborative convergence, while overcoming the design uncertainty through Set-based Design (SBD). Design attitudes are modeled with Belief-Desire-Intention paradigm to explore inconsistencies and manage conflicts in design processes. The conventional bottom-up approach is thus extended through agent-based attitude modeling techniques. In this approach, design agents can set requirements directly on their wellbeing values that represent how their design targets are likely to be met at a given moment of the design process. Monte Carlo simulations are performed to evaluate the performance of this approach, providing a variety of agent attitudes. Compared to conventional bottom-up and top-down design approaches, the results reveal a fewer number of design conflicts and a reduced aggregated conflict intensity. Constraint satisfaction problem (CSP) techniques and design attitudes are both applied to detect and justify design conflicts of heterogeneous design agents. A novel cooperative CSP (CoCSP) is developed in order to resolve design conflicts through compromising constraint restriction. The conflict resolution system can be adopted for different proposed strategies which take into account the solidarity architecture of design agents. The simulation results show that while promoting solidarity in distributed design by helping agents that suffer, the conflict intensity is reduced, and better design results are obtained.
... These considerations have not proven problematic in our experience. However, reactor design is still heuristically driven; techniques developed for partitioning constraint graphs such as (Salido & Barber 2006) for example, may be relevant in this context. ...
... They communicate with each other in order to reach a solution. This approach includes negotiation protocols, in which agents trade resources until they are all satisfied with the allocation [38], and also distributed constraint optimization problems [52,63]. ...
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... Many real life problems can be modeled as constraint satisfaction problems and are solved using constraint programming techniques. Much effort has been spent to increase the efficiency of the constraint satisfaction algorithms: filtering [18], learning and distributed techniques [20], the use of efficient representations and heuristics [4,15,16], etc. This effort resulted in the design of constraint reasoning tools which were used to solve numerous real problems. ...
Constraint programming is a successful technology for solving combinatorial problems modeled as constraint satisfaction problems (CSPs). Many real life problems are dynamic, which means that the initial description of the problem may change during its execution. These problems can be modeled as dynamic constraint satisfaction problems (DynCSPs), which are an important extension of the CSPs. In this paper, we focus our attention on the concept of robustness. Our aim is to find robust solutions which have a high probability of remaining valid faced with possible future changes in the constraints of the problem. We introduce the informed DynCSPs, proposing an approach to solve them by the weighted CSP (WCSP) modeling. Thus, the best solution for the modeled WCSP will be a robust solution for the original DynCSP. Furthermore, this technique has been evaluated in order to analyze the robustness of the solutions obtained.
... They communicate with each other in order to reach a solution. This approach includes negotiation protocols, in which agents trade resources until they are all satisfied with the allocation [40], and also distributed constraint optimization problems (DCOP) [50,64]. ...
ADVERTIMENT. La consulta d'aquesta tesi queda condicionada a l'acceptació de les següents condicions d'ús: La difusió d'aquesta tesi per mitjà del servei TDX ha estat autoritzada pels titulars dels drets de propietat intel·lectual únicament per a usos privats emmarcats en activitats d'investigació i docència. No s'autoritza la seva reproducció amb finalitats de lucre ni la seva difusió i posada a disposició des d'un lloc aliè al servei TDX. No s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant al resum de presentació de la tesi com als seus continguts. En la utilització o cita de parts de la tesi és obligat indicar el nom de la persona autora. ADVERTENCIA. La consulta de esta tesis queda condicionada a la aceptación de las siguientes condiciones de uso: La difusión de esta tesis por medio del servicio TDR sido autorizada por los titulares de los derechos de propiedad intelectual únicamente para usos privados enmarcados en actividades de investigación y docencia. No se autoriza su reproducción con finalidades de lucro ni su difusión y puesta a disposición desde un sitio ajeno al servicio TDR. No se autoriza la presentación de su contenido en una ventana o marco ajeno a TDR (framing). Esta reserva de derechos afecta tanto al resumen de presentación de la tesis como a sus contenidos. En la utilización o cita de partes de la tesis es obligado indicar el nombre de la persona autora. WARNING. On having consulted this thesis you're accepting the following use conditions: Spreading this thesis by the TDX service has been authorized by the titular of the intellectual property rights only for private uses placed in investigation and teaching activities. Reproduction with lucrative aims is not authorized neither its spreading and availability from a site foreign to the TDX service. Introducing its content in a window or frame foreign to the TDX service is not authorized (framing). This rights affect to the presentation summary of the thesis as well as to its contents. In the using or citation of parts of the thesis it's obliged to indicate the name of the author.
... This can be an advantage for large but not very densely coupled problems. However, as Salido and Barber [32] highlight, DisCSP is not suitable when the problem is Canbaz B., Yannou B., Yvars P.-A., (2013), Resolving design conflicts and promoting solidarity in distributed design. IEEE Transactions on Systems, Man and Cybernetics: Systems. ...
The resolution of complex design problems requires a distributed design system that considers the involvement of various designers. Inconsistencies of design objectives and working procedures of distributed subsystems can cause design conflicts due to couplings among their sub-problems. Another issue is the management of imprecision in design systems caused by the lack of knowledge about the final decision. In this paper, we define a conflict management model using the concept of set-based design (SBD) in order to overcome these issues. We utilize constraint satisfaction problem (CSP) techniques and model agent attitudes in order to detect and justify design conflicts of heterogeneous design agents. A novel cooperative CSP (CoCSP) is defined for resolving design conflicts through compromising constraint restriction. The conflict resolution system can be adopted with different strategies which take into account the solidarity architecture of design agents. The gains and costs of centralized, decentralized and controlled conflict resolution system strategies are simulated with Monte Carlo simulations where design agent characters and their interactions reflect a stochastic nature.
... Many problems can be cast as CSPs: diagnosis and temporal reasoning (Allen, 1984; Tsang, 1987), design, graph problems (Barber and Salido, 2006), timetabling (Abbas and Tsang, 2001), flight crews scheduling (Graves et al., 1993). Another field in which CSPs are used is scheduling, for which the literature offers extensive references: Cheng and Smith (1997) apply CSP to a deadline scheduling 'to provide a basis for highperformance approximate solution procedures in optimisation context', another example of CSP applied to scheduling is given by Cheng and Smith (1997). ...
Workers scheduling in not highly automated production lines is an important task, especially when in a production line the number of operators is less than the number of workstations. Finding an optimal distribution plan can increase the line throughput, managing the workforce and the workload in a better way. This work focuses on the operator-scheduling problem for an electromechanical assembly line. Workforce distribution on the workstations has been made with a centralised scheduling based on a mathematical model which, through constraint optimisation principles, is able to find the optimal distribution of workforce optimising fundamental parameters, such as man-hours, throughput, makespan and work in process.
... Absent this assumption, global synchronization requires iterative local synchronization to a fixed point which cannot guarantee polynomial time convergence necessary for real-world systems. Determining how to arrive at a suitable partition design is challenging; [Salido and Barber, 2006] offers a promising direction in using constraint cliques. Synchronizing the Agent Algorithm 2 shows how the agent is synchronized by synchronizing each reactor in the order defined by R[i]. ...
This paper uses Constraint-based Temporal Plan-ning (CTP) techniques to integrate deliberation and reaction in a uniform representation for au-tonomous robot control. We do so by formulating a control structure that partitions an agent into a collection of coordinated control loops, with a re-curring sense, plan, act cycle. Algorithms are pre-sented for sharing state between controllers to en-sure consistency during execution and enable com-positional control. The partitioned structure makes it practical to apply CTP for both deliberative and reactive behavior and promises a scalable and ro-bust approach for control of real-world autonomous robots operating in dynamic environments. The resulting framework is independant of the domain and provides a principled approach to building au-tonomous systems.
... The next step is to build the DFS-tree CSP structure with r DFS-nodes in order to be studied by agents. The number of agents (r) is obtained by using the formulae given in [10]. The DFS-tree CSP structure is used as a hierarchy to communicate messages between DFS-nodes. ...
Many real problems can be naturally modelled as constraint satisfaction problems (CSPs). However, some of these problems are
of a distributed nature, which requires problems of this kind to be modelled as distributed constraint satisfaction problems
(DCSPs). In this work, we present a distributed model for solving CSPs. Our technique carries out a partition over the constraint
network using a graph partitioning software; after partitioning, each sub-CSP is arranged into a DFS-tree CSP structure that is used as a hierarchy of communication by our distributed algorithm. We show that our distributed algorithm outperforms
well-known centralized algorithms solving partitionable CSPs.
... Also, hard problems can be solved more efficiently overall in problems where many (or all) solutions are required. Furthermore, this heuristic technique has also been modelled by a multi-agent system [23] in which agents are committed to solve their own subproblems. For future work, we are working on a combination of COH with a variable ordering heuristic in order to manage efficiently more complex problems.Figure 1 ...
Nowadays many real problems can be modelled as constraint satisfaction problems (CSPs). A search algorithm for constraint programming requires an order in which variables and values should to be considered. Choosing the right order of variables and values can noticeably improve the efficiency of constraint satisfaction.Furthermore, the order in which constraints are studied can improve efficiency, particularly in problems with non-binary constraints. In this paper, we present a preprocess heuristic called constraint ordering heuristic (COH) that studies the constrainedness of the scheduling problem and mainly classifies the constraints so that the tightest ones are studied first. Thus, constrainedness can be known in advance and overall inconsistencies can be found earlier and the number of constraint checks can significantly be reduced.
... In an asynchronous approach, each agent runs concurrently and asynchronously (see next section). In this section we deal with the synchronous approach following the distributed framework of Salido and Barber (2006) in which the problem is partitioned into k subproblems, which are as independent as possible. The subproblems are classified in the appropriate order and are solved concurrently. ...
Analyzing the state of the art in a given field in order to tackle a new problem is always a mandatory task. Literature provides surveys based on summaries of previous studies, which are often based on theoretical descriptions of the methods. An engineer, however, requires some evidence from experimental evaluations in order to make the appropriate decision when selecting a technique for a problem. This is what we have done in this paper: experimentally analyzed a set of representative state-of-the-art techniques in the problem we are dealing with, namely, the road passenger transportation problem. This is an optimization problem in which drivers should be assigned to transport services, fulfilling some constraints and minimizing some function cost. The experimental results have provided us with good knowledge of the properties of several methods, such as modeling expressiveness, anytime behavior, computational time, memory requirements, parameters, and free downloadable tools. Based on our experience, we are able to choose a technique to solve our problem. We hope that this analysis is also helpful for other engineers facing a similar problem.
... Thus, we can use graph partitioning when dealing with large-scale CSPs to distribute the problem into a set of sub-CSPs. For instance, we can divide a CSP into several subCSPs so that constraints among variables of each sub-CSP are minimized (Salido & Barber 2006). Otherwise, a domain-dependent partition can be used. ...
Many problems of theoretical and practical interest can be formulated as Constraint Satisfaction Problems (CSPs). Solving a general CSP is known to be NP-complete; however, distributed models may take advantage of dividing the problem into a set of simpler inter-connected sub-problems which can be more easily solved. The purpose of this paper is three-fold: first, we present a technique to distribute the constraint network by means of selection of tree structures. Thus, the CSP is represented as a meta-tree CSP structure that is used as a hierarchy of communication by our distributed algorithm. Then, a distributed and asynchronous search algorithm (DTS) is presented. DTS is committed to solving the meta-tree CSP structure in a depth-first search tree. Finally, an intra-agent search algorithm is presented. This algorithm takes into account the Nogood_message to prune the search space. We have focused our research on the railway scheduling problem which can be distributed by tree structures. We show that our distributed algorithm outperforms well-known centralized algorithms.
... These considerations have not proven problematic in our experience. However, reactor design is still heuristically driven; techniques developed for partitioning constraint graphs such as [21] for example, may be relevant in this context. ...
We present a formal framework of an autonomous agent as a collection of coordinated control loops, with a recurring sense, plan, act cycle. Our framework manages the informa- tion ow within the partitioned structure to ensure consis- tency in order to direct the ow of goals and observations in a timely manner. The resulting control structure improves scalability since many details of each controller can be encap- sulated within a single control loop. This partitioned agent design promises a domain-independent, scalable and robust approach for control of real-world autonomous robots oper- ating in dynamic environments. We validate our framework with experimental results from deployments in two dierent real-world domains.
... Only some works include a set of variables into an agent [4], [2]. Therefore, more research must be done to solve more realistic problems. ...
Nowadays, many real problems can be formalized as Distributed CSPs. A distributed constraint satisfaction problem (DisCSP)
is a CSP in which variables and constraints are distributed among multiple automated agents. Many researchers assume for simplicity
that each agent has exactly one variable. For real distributed problem these techniques require a large amount of messages
passed among agents, so these problems are very difficult to solve. In this research summary, we question why the lack of
works to manage large-scale problems.
... (Salido, 2007). Only some works include a set of variables into an agent (Salido & Barber, 2006),(Ezzahir et al., 2007). Therefore, more research must be done to solve more realistic problems. ...
During recent years, the development of new techniques for constraint satisfaction, planning, and scheduling has received increased attention, and substantial effort has been invested in trying to exploit such techniques to find solutions to real-life problems. In this paper, we present a survey on constraint satisfaction, planning, and scheduling from the Artificial Intelligence point of view. In particular, we present the main definitions and techniques, and discuss possible ways of integrating such techniques. We also analyze the role of constraint satisfaction in planning and scheduling, and hint at some open research issues related to planning, scheduling, and constraint satisfaction.
... They communicate with each other in order to reach a solution. This approach includes negotiation protocols, in which agents trade resources until they are all satisfied with the allocation [16], and also distributed constraint optimization problems [18,23]. ...
When selfish industries are competing for limited shared resources, they need to coordinate their activities to handle possible conflicting situations. Moreover, this coor- dination should not affect the activities already planned by the industries, since this could have negative effects on their performance. Although agents may have buffers that allow them to delay the use of resources, these are of a finite ca- pacity, and therefore cannot be used indiscriminately. Thus, we are faced with the problem of coordinating schedules that have already been generated by the agents. To address this task, we propose to use a recurrent auction mechanism to mediate between the agents. Through this auction mecha- nism, the agents can express their interest in using the re- sources, thus helping the scheduler to find the best distrib- ution. We also introduce a priority mechanism to add fair- ness to the coordination process. The proposed coordination mechanism has been applied to a waste water treatment sys- tem scenario, where different industries need to discharge their waste. We have simulated the behavior of the system, and the results show that using our coordination mechanism the waste water treatment plant can successfully treat most of the discharges, while the production activity of the indus- tries is almost not affected by it.
... A distributed constraint satisfaction problem (DisCSP) is a CSP in which variables and constraints are distributed among multiple automated agents. Many real-life problems are inherently distributed by nature but other large scale problems can be artificially partitioned in order to be managed as a distributed problem [7]. -Solving: Constraint models must be designed in such a way that constraint solvers will find a satisfying instantiation of variables. ...
The areas of planning and scheduling (from the Artificial Intelligence point of view) have seen important advances thanks to application of constraint satisfaction techniques. Currently, many important real-world problems require efficient constraint handling for planning, scheduling and resource allocation to competing goal activities over time in the presence of complex state-dependent constraints. Solutions to these problems require integration of resource allocation and plan synthesis capabilities. Hence to manage such complex problems planning, scheduling and constraint satisfaction must be interrelated. This special issue on Constraint Satisfaction for Planning and Scheduling Problems compiles a selection of papers dealing with various aspects of applying constraint satisfaction techniques in planning and scheduling. The core of submitted papers was formed by the extended versions of papers presented at COPLAS'2009: ICAPS 2009 Workshop on Constraint Satisfaction Techniques for Planning and Scheduling Problems. This issue presents novel advances on planning, scheduling, constraint programming/constraint satisfaction problems (CSPs) and many other common areas that exist among them. On the whole, this issue mainly focus on managing complex problems where planning, scheduling, constraint satisfaction and search must be combined and/or interrelated, which entails an enormous potential for practical applications and future research.
... For larger networks, a preprocessing step of graph partitioning may be used first to divide the graph into a set of smaller loosely connected ones, hence, enabling an efficient framework for obtaining the solution to underlying smaller Constraint Satisfaction Problems in a concurrent way. This approach is investigated in [20]. ...
Primary Component Carrier Selection and Physical Cell ID Assignment are two important self-configuration problems pertinent to LTE-Advanced. In this work, we investigate the possibility to solve these problems in a distributive manner using a graph coloring approach. Algorithms based on real-valued interference pricing of conflicts converge rapidly to a local optimum, whereas algorithms with binary interference pricing have a chance to find a global optimum. We apply both local search algorithms and complete algorithms such as Asynchronous Weak-Commitment Search. For system level performance evaluation, a picocellular scenario is considered, with indoor base stations in office houses placed in a Manhattan grid. We investigate a growing network, where neighbor cell lists are generated using practical measurement and reporting models. Distributed selection of conflict-free primary component carriers is shown to converge with 5 or more component carriers, while distributed assignment of confusion-free physical cell IDs is shown to converge with less than 15 IDs. The results reveal that the use of binary pricing of interference with an attempt to find a global optimum outperforms real-valued pricing.
In the distributed constraint satisfaction problems (DCSPs), the elements of the problem, such as variables, domains and constraints, are distributed among a group of agents and thus, communications and coordination are needed for finding a solution. In this work, we consider the situation when the underlying constraint graph of the given DCSP consists of several components which are loosely-coupled (i.e. disconnected or connected via less-restrict constraints), and propose an approach to pipeline the solving processes on each component under the multi-channel wireless communication model.
Nowadays, many real problems can be formalized as Distributed CSPs. A distributed constraint satisfaction problem (DisCSP) is a CSP in which variables and constraints are distributed among multiple automated agents. Many researchers assume for simplicity that each agent has exactly one variable. For real planning and scheduling problems, these distributed techniques require a large amount of messages passed among agents, so these problems are very difficult to solve. In this paper, we present a general distributed model for solving real-life scheduling problems and propose some guidelines for distributing large-scale problems. Furthermore, we present two case studies in which two scheduling problems are distributed by using our model. © 2007, Association for the Advancement of Artificial Intelligence.
In this paper, we propose a distributed heuristic solution for the replica placement problem in Wireless Mesh Networks (WMNs). This problem is known to be NP-complete. Our heuristic considers the local popularity of an object replica. The local popularity can be defined as the relative demand for an object within a partition of the network compared to the whole network. The heuristic collects popularity information periodically to compute the number of replicas for future period requests. We perform simulation experiments to investigate the performance of our heuristic.
Recently, Wireless Mesh Networks (WMNs) have attracted much of interest from both academia and industry, due to their potential to provide an aLTErnative broadband wireless Internet connectivity. However, due to different reasons such as multi-hop forwarding and the dynamic wireless link characteristics, the performance of current WMNs is rather low when clients are soliciting Web contents. Due to the evolution of advanced mobile computing devices; it is anticIPated that the demand for bandwidth-onerous popular content (especially multimedia content) in WMNs will dramatically increase in the coming future. Content replication is a popular approach for outsourcing content on behalf of the origin content provider. This area has been well explored in the context of the wired Internet, but has received comparatively less attention from the research community when it comes to WMNs. There are a number of replica placement algorithms that are specifically designed for the Internet. But they do not consider the special features of wireless networks such as insufficient bandwidth, low server capacity, contention to access the wireless medium, etc. In this paper, we propose a distributed heuristic solution for the replica placement problem in WMNs. This problem is known to be NP-complete. Our heuristic considers the local popularity of an object replica. The local popularity can be defined as the relative demand for an object within a partition of the network compared to the whole network. The heuristic collects popularity information periodically to compute the number of replicas for future period requests. Using extensive simulation tests, we demonstrate the performance gain of our heuristic compared to other relevant ones.
The areas of planning and scheduling (from the Artificial Intelligence point of view) have seen important advances thanks
to application of constraint satisfaction techniques. Currently, many important real-world problems require efficient constraint
handling for planning, scheduling and resource allocation to competing goal activities over time in the presence of complex
state-dependent constraints. Solutions to these problems require integration of resource allocation and plan synthesis capabilities.
Hence to manage such complex problems planning, scheduling and constraint satisfaction must be interrelated. This special
issue on Constraint Satisfaction for Planning and Scheduling Problems compiles a selection of papers dealing with various aspects of applying constraint satisfaction techniques in planning and
scheduling. The core of submitted papers was formed by the extended versions of papers presented at COPLAS’2009: ICAPS 2009
Workshop on Constraint Satisfaction Techniques for Planning and Scheduling Problems. This issue presents novel advances on
planning, scheduling, constraint programming/constraint satisfaction problems (CSPs) and many other common areas that exist
among them. On the whole, this issue mainly focus on managing complex problems where planning, scheduling, constraint satisfaction
and search must be combined and/or interrelated, which entails an enormous potential for practical applications and future
research.
KeywordsPlanning–Scheduling–Constraint programming–Search
This paper deals with the problem of spatially distributed causal model-based diagnosis on interacting behavioral petri nets (BPNs). The system to be diagnosed comprises different interacting subsystems (each modeled as a BPN) and the diagnostic system is defined as a multi-agent system where each agent is designed to diagnose a particular subsystem on the basis of its local model, the local received observation and the information exchanged with the neighboring agents. The interactions between subsystems are captured by tokens that may pass from one net model to another via bordered places. The diagnostic reasoning scheme is accomplished locally within each agent by exploiting classical analysis techniques of Petri nets like reachability graph and invariant analysis. Once local diagnoses are obtained, agents begin to communicate to ensure that such diagnoses are consistent and recover completely the results that would be obtained by a centralized agent having a global view about the whole system. The paper concludes with an empirical comparison, in terms of the running time, of two implementations of Petri net analysis techniques used as a distributed diagnostic reasoning schemes.
Nowadays, many real problem in Artificial Intelligence can be modeled as constraint satisfaction problems (CSPs). A general rule in constraint satisfaction is to tackle the hardest part of a search problem first. In this paper, we introduce a parameter (τ) that measures the constrainedness of a search problem. This parameter represents the probability of the problem being feasible. A value of τ=0 corresponds to an over-constrained problem and no states are expected to be solutions. A value of τ=1 corresponds to an under-constrained problem which every state is a solution. This parameter can also be used in a heuristic to guide search. To achieve this parameter, a sample in finite population is carried out to compute the tightnesses of each constraint. We take advantage of this tightnesses to classify the constraints from the tightest constraint to the loosest constraint. This heuristic may accelerate the search due to inconsistencies can be found earlier and the number of constraint checks can significantly be reduced.
Traditional graph partitioning algorithms compute a k-way partitioning of a graph such that the number of edges that are cut by the partitioning is minimized and each partition has an equal number of vertices. The task of minimizing the edge-cut can be considered as the objective and the requirement that the partitions will be of the same size can be considered as the constraint. In this paper we extend the partitioning problem by incorporating an arbitrary number of balancing constraints. In our formulation, a vector of weights is assigned to each vertex, and the goal is to produce a k-way partitioning such that the partitioning satisfies a balancing constraint associated with each weight, while attempting to minimize the edge-cut. Applications of this multi-constraint graph partitioning problem include parallel solution of multi-physics and multi-phase computations, that underlay many existing and emerging large-scale scientific simulations. We present new multi-constraint graph partitioning algorithms that are based on the multilevel graph partitioning paradigm. Our work focuses on developing new types of heuristics for coarsening, initial partitioning, and refinement that are capable of successfully handling multiple constraints. We experimentally evaluate the effectiveness of our multi-constraint partitioners on a variety of synthetically generated problems.
The graph partitioning problem is that of dividing the vertices of a graph into sets of specified sizes such that few edges cross between sets. This NP-complete problem arises in many important scientific and engineering problems. Prominent examples include the decomposition of data structures for parallel computation, the placement of circuit elements and the ordering of sparse matrix computations. We present a multilevel algorithm for graph partitioning in which the graph is approximated by a sequence of increasingly smaller graphs. The smallest graph is then partitioned using a spectral method, and this partition is propagated back through the hierarchy of graphs. A variant of the Kernighan-Lin algorithm is applied periodically to refine the partition. The entire algorithm can be implemented to execute in time proportional to the size of the original graph. Experiments indicate that, relative to other advanced methods, the multilevel algorithm produces high quality partitions at low cost.
Looking ahead during search is often useful when solving constraint satisfaction problems. Previous studies have shown that looking ahead helps by causing dead-ends to occur earlier in the search, and by providing information that is useful for dynamic variable ordering. In this paper, we show that another benefit of looking ahead is a useful domain value ordering heuristic, which we call look-ahead value ordering or LVO. LVO counts the number of times each value of the current variable conflicts with some value of a future variable, and the value with the lowest number of conflicts is chosen first. Our experiments show that look-ahead value ordering can be of substantial benefit, especially on hard constraint satisfaction problems. 1
Arc consistency algorithms are used in solving constraint satisfaction problems and are important in constraint logic programming languages.
In this paper, we develop a formalism called a distributedconstraint satisfaction problem (distributed CSP) and algorithms for solving distributed CSPs. A distributed CSP is a constraint satisfaction problem in which variables and constraints are distributed among multiple agents. Various application problems in Distributed Artificial Intelligence can be formalized as distributed CSPs. We present our newly developed technique called asynchronous backtracking that allows agents to act asynchronously and concurrently without any global control, while guaranteeing the completeness of the algorithm. Furthermore, we describe how the asynchronous backtracking algorithm can be modified into a more efficient algorithm called asynchronous weak-commitment search, which can revise a bad decision without exhaustive search by changing the priority order of agents dynamically. The experimental results on various example problems show that the asynchronous weak-commitment search algorithm is by far more efficient than the asynchronous backtracking algorithm and can solve fairly large-scale problems. Makoto Yokoo is with NTT Communication Science Laboratories, Kyoto, Japan. E-mail: yokoo@cslab.kecl.ntt.co.jp . Edmund H. Durfee is with Dept. of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, U.S.A. E-mail: durfee@umich.edu . Toru Ishida is with Dept. of Information Science, Kyoto University,Kyoto, Japan. E-mail: ishida@kuis.kyoto-u.ac.jp . Kazuhiro Kuwabara is with Nippon Telegraph and Telephone Corporation, Tokyo, Japan. E-mail: kuwabara@rdh.ecl.ntt.co.jp . This paper is the extended version of the authors' previous conference papers [21],[22]. 2 Keywords Backtracking Algorithms, Constraint Satisfaction Problem, Distributed Artificial In...
This paper discusses the performance analysis of two generic fundamental parallel search techniques on shared memory multi-processor systems in solving the constraint satisfaction problem (CSP). Probabilistic analysis on their expected computation steps needed and their inherent load-balancing capability is performed. Corresponding experimental results are also provided to verify the correctness of the proposed analysis. This fundamental analysis approach can be further applied to various advanced parallel search techniques or various problem solving techniques on parallel platforms.
In this paper we present a parallel formulation of the multilevel graph partitioning and sparse matrix ordering algorithm. A key feature of our parallel formulation (that distinguishes it from other proposed parallel formulations of multilevel algorithms) is that it partitions the vertices of the graph intoparts while distributing the overall adjacency matrix of the graph among allpprocessors. This mapping results in substantially smaller communication than one-dimensional distribution for graphs with relatively high degree, especially if the graph is randomly distributed among the processors. We also present a parallel algorithm for computing a minimal cover of a bipartite graph which is a key operation for obtaining a small vertex separator that is useful for computing the fill reducing ordering of sparse matrices. Our parallel algorithm achieves a speedup of up to 56 on 128 processors for moderate size problems, further reducing the already moderate serial run time of multilevel schemes. Furthermore, the quality of the produced partitions and orderings are comparable to those produced by the serial multilevel algorithm that has been shown to outperform both spectral partitioning and multiple minimum degree.
Many AI tasks can be formulated as constraint-satisfaction problems (CSP), i.e., the assignment of values to variables subject to a set of constraints. While some CSPs are hard, those that are easy can often be mapped into sparse networks of constraints which, in the extreme case, are trees. This paper identifies classes of problems that lend themselves to easy solutions, and develops algorithms that solve these problems optimally. The paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree-structured CSPs. The advice is generated by simplifying the pending subproblems into trees, counting the number of consistent solutions in each simplified subproblem, and comparing these counts to decide among the choices pending in the original problem.
A constraint satisfaction problem revolves finding values for a set of variables subject to a set of constraints (relations) on those variables Backtrack search is often used to solve such problems. A relationship involving the structure of the constraints is described which characterizes to some degree the extreme case of mimmum backtracking (none) The relationship involves a concept called "width," which may,provide some guidance in the representation of constraint satisfaction problems and the order m which they are searched The width concept is studied and applied, in particular, to constraints which form tree structures. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]' Nonnu-
We consider the problem of partitioning the nodes of a graph with costs on its edges into subsets of given sizes so as to minimize the sum of the costs on all edges cut. This problem arises in several physical situations—for example, in assigning the components of electronic circuits to circuit boards to minimize the number of connections between boards.
This paper presents a heuristic method for partitioning arbitrary graphs which is both effective in finding optimal partitions, and fast enough to be practical in solving large problems.
Nowadays, many real problem in Artificial Intelligence can be modeled as constraint satisfaction problems (CSPs). A general rule in constraint satisfaction is to tackle the hardest part of a search problem first. In this paper, we introduce a parameter (#) that measures the constrainedness of a search problem. This parameter represents the probability of the problem being feasible. A value of # = 0 corresponds to an over-constrained problem and no states are expected to be solutions. A value of # = 1 corresponds to an under-constrained problem which every state is a solution. This parameter can also be used in a heuristic to guide search. To achieve this parameter, a sample in finite population is carried out to compute the tightnesses of each constraint. We take advantage of this tightnesses to classify the constraints from the tightest constraint to the loosest constraint. This heuristic may accelerate the search due to inconsistencies can be found earlier and the number of constraint checks can significantly be reduced.
Using METIS and parMETIS
- G Karypis
- V Kumar
G. Karypis, V. Kumar, Using METIS and parMETIS, Technical report (1995).
Exploiting the constrainedness in constraint satisfaction problems, Artificial Intelligence: Methodology, Systems, and Applications LNAI 3192
- M A Salido
- F Barber
M.A. Salido, F. Barber, Exploiting the constrainedness in constraint satisfaction problems, Artificial Intelligence: Methodology, Systems, and Applications LNAI 3192 (2004) 126–136. 498 M.A. Salido, F. Barber / Applied Mathematics and Computation 183 (2006) 491–498
Parallel forward checking: First part
- B Burg
B. Burg, Parallel forward checking: First part, Technical Report TR-594, Institute for New Generation Computer Technology (1990).