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66
AND/OR branchandbound search for combinatorial optimization in graphical models
, 2008
"... We introduce a new generation of depthfirst BranchandBound algorithms that explore the AND/OR search tree using static and dynamic variable orderings for solving general constraint optimization problems. The virtue of the AND/OR representation of the search space is that its size may be far small ..."
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Cited by 39 (19 self)
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We introduce a new generation of depthfirst BranchandBound algorithms that explore the AND/OR search tree using static and dynamic variable orderings for solving general constraint optimization problems. The virtue of the AND/OR representation of the search space is that its size may be far smaller than that of a traditional OR representation, which can translate into significant time savings for search algorithms. The focus of this paper is on linear space search which explores the AND/OR search tree rather than the search graph and therefore make no attempt to cache information. We investigate the power of the minibucket heuristics within the AND/OR search space, in both static and dynamic setups. We focus on two most common optimization problems in graphical models: finding the Most Probable Explanation (MPE) in Bayesian networks and solving Weighted CSPs (WCSP). In extensive empirical evaluations we demonstrate that the new AND/OR BranchandBound approach improves considerably over the traditional OR search strategy and show how various variable ordering schemes impact the performance of the AND/OR search scheme.
Bounded approximate decentralised coordination using the maxsum algorithm
 IN DISTRIBUTED CONSTRAINT REASONING WORKSHOP
, 2009
"... In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution qualit ..."
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Cited by 30 (9 self)
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In this paper we propose a novel algorithm that provides bounded approximate solutions for decentralised coordination problems. Our approach removes cycles in any general constraint network by eliminating dependencies between functions and variables which have the least impact on the solution quality. It uses the maxsum algorithm to optimally solve the resulting tree structured constraint network, providing a bounded approximation specific to the particular problem instance. We formally prove that our algorithm provides a bounded approximation of the original problem and we present an empirical evaluation in a synthetic scenario. This shows that the approximate solutions that our algorithm provides are typically within 95 % of the optimum and the approximation ratio that our algorithm provides is typically 1.23.
Distributed problem solving
 AI Magazine
, 2012
"... Broadly, distributed problem solving is a subfield withinmultiagent systems, where the focus is to enable multipleagents to work together to solve a problem. These agents are often assumed to be cooperative, that is, they are part of a team or they are selfinterested but incentives or disincentives ..."
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Cited by 17 (13 self)
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Broadly, distributed problem solving is a subfield withinmultiagent systems, where the focus is to enable multipleagents to work together to solve a problem. These agents are often assumed to be cooperative, that is, they are part of a team or they are selfinterested but incentives or disincentives have been applied such that the individual agent rewards are aligned with the team reward. We illustrate the motivations for distributed problem solving with an example. Imagine a decentralized channelallocation problem in a wireless local area network (WLAN), where each access point (agent) in the WLAN needs to allocate itself a channel to broadcast such that no two access points with overlapping broadcast regions (neighboring agents) are allocated the same channel to avoid interference. Figure 1 shows example mobile WLAN access points, where each access point is a Create robot fitted with a wireless CenGen radio card. Figure 2a shows an illustration of such a problem with three access points in a WLAN, where each oval ring represents the broadcast region of an access point. This problem can, in principle, be solved with a centralized approach by having each and every agent transmit all the relevant information, that is, the set of possible channels that the agent can allocate itself and its set of neighboring agents, to a centralized server. However, this centralized approach may incur unnecessary communication cost compared to a distrib
Anytime AND/OR Depthfirst Search for Combinatorial Optimization
"... One popular and efficient scheme for solving exactly combinatorial optimization problems over graphical models is depthfirst Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This paper 1) analyzes and demonstr ..."
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Cited by 12 (5 self)
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One popular and efficient scheme for solving exactly combinatorial optimization problems over graphical models is depthfirst Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This paper 1) analyzes and demonstrates this inherent conflict between effective exploitation of problem decomposition (through AND/OR search spaces) and the anytime behavior of depthfirst search (DFS), 2) presents a first scheme to address this issue while maintaining desirable DFS memory properties, 3) analyzes and demonstrates its effectiveness. Our work is applicable to any problem that can be cast as search over an AND/OR search space.
Saving redundant messages in BnBADOPT
 In Proc. of AAAI
, 2010
"... We have found that some messages of BnBADOPT are redundant. Removing most of those redundant messages we obtain BnBADOPT+, which achieves the optimal solution and terminates. In practice, BnBADOPT+ causes substantial reductions on communication costs with respect to the original algorithm. BnB ..."
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Cited by 12 (3 self)
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We have found that some messages of BnBADOPT are redundant. Removing most of those redundant messages we obtain BnBADOPT+, which achieves the optimal solution and terminates. In practice, BnBADOPT+ causes substantial reductions on communication costs with respect to the original algorithm. BnBADOPT (Yeoh, Felner, and Koenig 2008) is a reference algorithm for distributed constraint optimization (DCOP), defined as follows. There is a finite number of agents, each holding one variable that can take values from a finite and discrete domain, related by binary cost functions. The cost of a variable assigning a value is the sum of cost functions evaluated on that assignment. The goal is to find a complete assignment of minimum cost by message passing
BnBADOPT+ with several soft arc consistency levels
 In ECAI
, 2010
"... Abstract. Distributed constraint optimization problems can be solved by BnBADOPT+, a distributed asynchronous search algorithm. In the centralized case, local consistency techniques applied to constraint optimization have been shown very beneficial to increase performance. In this paper, we combin ..."
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Cited by 9 (4 self)
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Abstract. Distributed constraint optimization problems can be solved by BnBADOPT+, a distributed asynchronous search algorithm. In the centralized case, local consistency techniques applied to constraint optimization have been shown very beneficial to increase performance. In this paper, we combine BnBADOPT+ with different levels of soft arc consistency, propagating unconditional deletions caused by either the enforced local consistency or by distributed search. The new algorithm maintains BnBADOPT+ optimality and termination. In practice, this approach decreases substantially BnBADOPT+ requirements in communication cost and computation effort when solving commonly used benchmarks. 1
Caching schemes for DCOP search algorithms
 In Proceedings of AAMAS
, 2009
"... Distributed Constraint Optimization (DCOP) is useful for solving agentcoordination problems. Anyspace DCOP search algorithms require only a small amount of memory but can be sped up by caching information. However, their current caching schemes do not exploit the cached information when deciding w ..."
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Cited by 9 (5 self)
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Distributed Constraint Optimization (DCOP) is useful for solving agentcoordination problems. Anyspace DCOP search algorithms require only a small amount of memory but can be sped up by caching information. However, their current caching schemes do not exploit the cached information when deciding which information to preempt from the cache when a new piece of information needs to be cached. Our contributions are threefold: (1) We frame the problem as an optimization problem. (2) We introduce three new caching schemes (MaxPriority, MaxEffort and MaxUtility) that exploit the cached information in a DCOPspecific way. (3) We evaluate how the resulting speed up depends on the search strategy of the DCOP search algorithm. Our experimental results show that, on all tested DCOP problem classes, our MaxEffort and MaxUtility schemes speed up ADOPT (which uses bestfirst search) more than the other tested caching schemes, while our MaxPriority scheme speeds up BnBADOPT (which uses depthfirst branchandbound search) at least as much as the other tested caching schemes.
Directed Soft Arc Consistency in Pseudo Trees
"... We propose an efficient method that applies directed soft arc consistency to a Distributed Constraint Optimization Problem (DCOP) which is a fundamental framework of multiagent systems. With DCOPs a multiagent system is represented as a set of variables and a set of constraints/cost functions. We ..."
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Cited by 8 (2 self)
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We propose an efficient method that applies directed soft arc consistency to a Distributed Constraint Optimization Problem (DCOP) which is a fundamental framework of multiagent systems. With DCOPs a multiagent system is represented as a set of variables and a set of constraints/cost functions. We focus on DCOP solvers that employ pseudotrees. A pseudotree is a graph structure for a constraint network that represents a partial ordering of variables. Most pseudotreebased search algorithms perform optimistic searches using explicit/implicit backtracking in parallel. However, for cost functions taking a wide range of cost values, such exact algorithms require many search iterations, even if the constraint density is relatively low. Therefore additional improvements are necessary to reduce the search process. A previous study used a dynamic programmingbased preprocessing technique that estimates the lower
Trading Off Solution Quality for Faster Computation in DCOP Search Algorithms ∗
"... Distributed Constraint Optimization (DCOP) is a key technique for solving agent coordination problems. Because finding costminimal DCOP solutions is NPhard, it is important to develop mechanisms for DCOP search algorithms that trade off their solution costs for smaller runtimes. However, existing ..."
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Cited by 8 (3 self)
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Distributed Constraint Optimization (DCOP) is a key technique for solving agent coordination problems. Because finding costminimal DCOP solutions is NPhard, it is important to develop mechanisms for DCOP search algorithms that trade off their solution costs for smaller runtimes. However, existing tradeoff mechanisms do not provide relative error bounds. In this paper, we introduce three tradeoff mechanisms that provide such bounds, namely the Relative Error Mechanism, the Uniformly Weighted Heuristics Mechanism and the NonUniformly Weighted Heuristics Mechanism, for two DCOP algorithms, namely ADOPT and BnBADOPT. Our experimental results show that the Relative Error Mechanism generally dominates the other two tradeoff mechanisms for ADOPT and the Uniformly Weighted Heuristics Mechanism generally dominates the other two tradeoff mechanisms for BnBADOPT. 1
Maintaining Soft Arc Consistencies in BnBADOPT + during Search
 In Proceedings of the International Conference on Principles and Practice of Constraint Programming (CP
"... Abstract. Gutierrez and Meseguer show how to enforce consistency in BnBADOPT+ for distributed constraint optimization, but they consider unconditional deletions only. However, during search, more values can be pruned conditionally according to variable instantiations that define subproblems. Enforc ..."
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Cited by 7 (2 self)
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Abstract. Gutierrez and Meseguer show how to enforce consistency in BnBADOPT+ for distributed constraint optimization, but they consider unconditional deletions only. However, during search, more values can be pruned conditionally according to variable instantiations that define subproblems. Enforcing consistency in these subproblems can cause further search space reduction. We introduce efficient methods to maintain soft arc consistencies in every subproblem during search, a non trivial task due to asynchronicity and induced overheads. Experimental results show substantial benefits on three different benchmarks. 1