Algorithms and Ordering Heuristics for Distributed Constraint Satisfaction Problems

Abstract

Distributed Constraint Satisfaction Problems (DisCSP) is a general framework for solving distributed problems. DisCSP have a wide range of applications in multi-agent coordination. In this thesis, we extend the state of the art in solving the DisCSPs by proposing several algorithms. Firstly, we propose the Nogood-Based Asynchronous Forward Checking (AFC-ng), an algorithm based on Asynchronous Forward Checking (AFC). However, instead of using the shortest inconsistent partial assignments, AFC-ng uses nogoods as justifications of value removals. Unlike AFC, AFC-ng allows concurrent backtracks to be performed at the same time coming from different agents having an empty domain to different destinations. Then, we propose the Asynchronous Forward-Checking Tree (AFCtree). In AFC-tree, agents are prioritized according to a pseudo-tree arrangement of the constraint graph. Using this priority ordering, AFC-tree performs multiple AFC-ng processes on the paths from the root to the leaves of the pseudo-tree. Next, we propose to maintain arc consistency asynchronously on the future agents instead of only maintaining forward checking. Two new synchronous search algorithms that maintain arc consistency asynchronously (MACA) are presented. After that, we developed the Agile Asynchronous Backtracking (Agile-ABT), an asynchronous dynamic ordering algorithm that does not follow the standard restrictions in asynchronous backtracking algorithms. The order of agents appearing before the agent receiving a backtrack message can be changed with a great freedom while ensuring polynomial space complexity. Next, we present a corrigendum of the protocol designed for establishing the priority between orders in the asynchronous backtracking algorithm with dynamic ordering using retroactive heuristics (ABT_DO-Retro). Finally, the new version of the DisChoco open-source platform for solving distributed constraint reasoning problems is described. The new version is a complete redesign of the DisChoco platform. DisChoco 2.0 is an open source Java library which aims at implementing distributed constraint reasoning algorithms.

A colored Petri net model for DisCSP algorithms

“…The DisCSP algorithms have been implied in manufacturing control architectures, mainly in the research field; even so, they were rarely applied in real‐life problems, the weak adoption of multiagent control systems being discussed in Leitão . About this, the use of a CPN model can facilitate the design and implementation of multiagent and holonic control schemes .…”

A General Framework for Reordering Agents Asynchronously in Distributed CSP

“…If no λ i stronger than λ i exists, the backtracking target x t is the variable that has the lowest priority among Σ i in the current order λ i . For more details we refer the reader to [1,25].…”

“…It has been proved that AgileABT is sound, complete and terminates [1,25]. The termination proofs of AgileABT are based on the fact that the termination value is a tuple of positive integers (representing the expected sizes of the domains of other agents) and, as search progresses, these tuples can only decrease lexicographically.…”

Computer modeling based on CSPs for managing personnel lack in courts

“…For example, on the previous CSP, A = {(b,0),(c,1)} is the assignment that instantiates b to 0 and c to 1. [8] An assignment is said to be total if it instantiates all the variables of the problem; it is said to be partial if it instantiates only one part. In our example, A1 = {(a,1),(b,0),(c,0),(d,0)} is a total assignment ; A2 = {(a,0),(b,0)} is a partial assignment.…”