Katsutoshi Hirayama

Algorithms for Distributed Constraint Satisfaction: A Review

When multiple agents are in a shared environment, there usually exist constraints among the possible actions of these agents. A distributed constraint satisfaction problem (distributed CSP) is a problem to find a consistent combination of actions that satisfies these inter-agent constraints. Various application problems in multi-agent systems can be formalized as distributed CSPs. This paper gives an overview of the existing research on distributed CSPs. First, we briefly describe the problem formalization and algorithms of normal, centralized CSPs. Then, we show the problem formalization and several MAS application problems of distributed CSPs. Furthermore, we describe a series of algorithms for solving distributed CSPs, i.e., the asynchronous backtracking, the asynchronous weak-commitment search, the distributed breakout, and distributed consistency algorithms. Finally, we show two extensions of the basic problem formalization of distributed CSPs, i.e., handling multiple local variables, and dealing with over-constrained problems.

Distributed partial constraint satisfaction problem

Many problems in multi-agent systems can be described as distributed Constraint Satisfaction Problems (distributed CSPs), where the goal is to find a set of assignments to variables that satisfies all constraints among agents. However, when real problems are formalized as distributed CSPs, they are often over-constrained and have no solution that satisfies all constraints. This paper provides the Distributed Partial Constraint Satisfaction Problem (DPCSP) as a new framework for dealing with over-constrained situations. We also present new algorithms for solving Distributed Maximal Constraint Satisfaction Problems (DMCSPs), which belong to an important class of DPCSP. The algorithms are called the Synchronous Branch and Bound (SBB) and the Iterative Distributed Breakout (IDB). Both algorithms were tested on hard classes of over-constrained random binary distributed CSPs. The results can be summarized as SBB is preferable when we are mainly concerned with the optimality of a solution, while IDB is preferable when we want to get a nearly optimal solution quickly.

Distributed constraint satisfaction algorithm for complex local problems

A distributed constraint satisfaction problem can formalize various application problems in MAS, and several algorithms for solving this problem have been developed. One limitation of these algorithms is that they assume each agent has only one local variable. Although simple modifications enable these algorithms to handle multiple local variables, obtained algorithms are neither efficient nor scalable to larger problems. We develop a new algorithm that can handle multiple local variables efficiently, which is based on the asynchronous weak-commitment search algorithm. In this algorithm, a bad local solution can be modified without forcing other agents to exhaustively search local problems. Also, the number of interactions among agents can be decreased since agents communicate only when they find local solutions that satisfy all of the local constraints. Experimental evaluations show that this algorithm is far more efficient than an algorithm that uses the prioritization among agents.

The distributed breakout algorithms

We present a new series of distributed constraint satisfaction algorithms, the distributed breakout algorithms, which is inspired by local search algorithms for solving the constraint satisfaction problem (CSP). The basic idea of these algorithms is for agents to repeatedly improve their tentative and flawed sets of assignments for variables simultaneously while communicating such tentative sets with each other until finding a solution to an instance of the distributed constraint satisfaction problem (DisCSP). We introduce four implementations of the distributed breakout algorithms: Single-DB, Multi-DB, Multi-DB^+, and Multi-DB^+^+. Single-DB is a distributed breakout algorithm for solving the DisCSP, where each agent has a single local variable and its related constraints. Multi-DB, on the other hand, is another distributed breakout algorithm for solving the distributed SAT (DisSAT) problem, where each agent has multiple local variables and their related clauses. Multi-DB^+ and Multi-DB^+^+ are stochastic variations of Multi-DB. In Multi-DB^+, we introduce a technique called random break into Multi-DB; in Multi-DB^+^+, we introduce a technique called random walk into Multi-DB^+. We conducted experiments to compare these algorithms with the asynchronous type of distributed constraint satisfaction algorithm. Through these experiments, we found that Single-DB, Multi-DB, and Multi-DB^+ scale up better than the asynchronous type of distributed constraint satisfaction algorithms, but they sometimes show very poor performance. On the other hand, we also found that Multi-DB^+^+, which uses random walk, provides a clear performance improvement.

Secure Distributed Constraint Satisfaction: Reaching Agreement without Revealing Private Information

This paper develops a secure distributed Constraint Satisfaction algorithm. A Distributed Constraint Satisfaction Problem (DisCSP) is a CSP in which variables and constraints are distributed among multiple agents. A major motivation for solving a DisCSP without gathering all information in one server is the concern about privacy/security. However, existing DisCSP algorithms leak some information during the search process and privacy/security issues are not dealt with formally. Our newly developed algorithm utilizes a public key encryption scheme. In this algorithm, multiple servers, which receive encrypted information from agents, cooperatively perform a search process that is equivalent to a standard chronological backtracking. This algorithm does not leak any private information, i.e., neither agents nor servers can obtain any additional information on the value assignment of variables that belong to other agents.

The effect of nogood learning in distributed constraint satisfaction

We present resolvent-based learning as a new nogood learning method for a distributed constraint satisfaction algorithm. This method is based on a look-back technique in constraint satisfaction algorithms and can efficiently make effective nogoods. We combine the method with the asynchronous weak-commitment search algorithm (AWC) and evaluate the performance of the resultant algorithm on distributed 3-coloring problems and distributed 3SAT problems. As a result, we found that the resolvent-based learning works well compared to previous learning methods for distributed constraint satisfaction algorithms. We also found that the AWC with the resolvent-based learning is able to find a solution with fewer cycles than the distributed breakout algorithm, which was known to be the most efficient algorithm (in terms of cycles) for solving distributed constraint satisfaction problems.

Secure distributed constraint satisfaction: reaching agreement without revealing private information

This paper develops a secure distributed constraint satisfaction algorithm. A Distributed Constraint Satisfaction Problem (DisCSP) is a constraint satisfaction problem in which variables and constraints are distributed among multiple agents. A major motivation for solving a DisCSP without gathering all information in one server is the concern about privacy/security. However, existing DisCSP algorithms leak some information during the search process, and privacy/security issues are not dealt with formally. Our newly developed algorithm utilizes a public key encryption scheme. In this algorithm, multiple servers, which receive encrypted information from agents, cooperatively perform a search process that is equivalent to a standard chronological backtracking algorithm. This algorithm does not leak any private information on the obtained solution, i.e., neither agents nor servers can obtain any additional information on the value assignment of variables that belong to other agents.

An approach to over-constrained distributed constraint satisfaction problems: distributed hierarchical constraint satisfaction

Many problems in multi-agent systems can be described as distributed CSPs. However some real-life problems can be over-constrained and without a set of consistent variable values when described as a distributed CSP. We have presented the distributed partial CSP for handling such an over-constrained situation and the distributed maximal CSP as a subclass of distributed partial CSP. We first show another subclass of distributed partial CSP, the distributed hierarchical CSP. Next, we present a series of new algorithms for solving a distributed hierarchical CSP, each of which is designed based on our previous distributed constraint satisfaction algorithms. Finally we evaluate the performance of our new algorithms on distributed 3-coloring problems in terms of optimality and anytime characteristics. The results show that our new algorithms perform much better than the previous algorithm for finding an optimal solution and produce good results for anytime characteristics.

Local search for distributed SAT with complex local problems

A distributed constraint satisfaction problem(DisCSP) is a general framework that can formalize various application problems in Multi-Agent Systems. The authors have developed a series of algorithms for solving DisCSPs, including an iterative improvement algorithm called the distributed breakout (DB) algorithm. This algorithm, however, deals only with DisCSPs where each agent has exactly one local variable and the relevant constraints to the variable. In this paper, we propose a new algorithm called Multi-DB for solving distributed SAT (DisSAT) where each agent has multiple local variables and the relevant clauses to the variables. We conduct an experiment to compare Multi-DB with the previous algorithm called Multi-AWC on well-known (Dis)3-SAT benchmarks. The results are very impressive since Multi-DB has much less average communication and computation costs for almost all cases (at least an order of magnitude less for larger problems). We also identify a trade-off between communication and computation costs of algorithms when we vary the degree of decentralization.

Distributed Search Method with Bounded Cost Vectors on Multiple Objective DCOPs

We generalize a pseudo-tree based solver to employ boundaries of multi-objective DCOPs. Multi-objective problems have been addressed in the research area of DCOPs recently. For the case of multiple objectives, the objective values are defined as the result of separate evaluation schemes. Applying multi-objectives to pseudo-tree based search is also important to generalize several traditional solvers. Here, we introduce boundaries for the vector of objective values in a solver based on pseudo-trees. Both the bottom-up computation of the partial dynamic-programming and the top-down computation of the tree-search employ the bounded vectors of the objective values. Several operations including aggregation, decomposition and comparison of objective values are extended for the bounded vectors.