Max/min-sum distributed constraint optimization through value propagation on an alternating DAG

Abstract

Distributed Constraint Optimization Problems (DCOPs) are NP-hard and therefore the number of studies that consider incomplete algorithms for solving them is growing. Specifically, the Max-sum algorithm has drawn attention in recent years and has been applied to a number of realistic applications. Unfortunately, in many cases Max-sum does not produce high quality solutions. More specifically, when problems include cycles of various sizes in the factor graph upon which Max-sum performs, the algorithm does not converge and the states that it visits are of low quality.In this paper we advance the research on incomplete algorithms for DCOPs by: (1) Proposing a version of the Max-sum algorithm that operates on an alternating directed acyclic graph (Max-sum_AD), which guarantees convergence in linear time. (2) Identifying major weaknesses of Max-sum and Max-sum_AD that cause inconsistent costs/utilities to be propagated and affect the assignment selection. (3) Solving the identified problems by introducing value propagation to Max-sum_AD. Our empirical study reveals a large improvement in the quality of the solutions produced by Max-sum_AD with value propagation (VP), when solving problems which include cycles, compared with the solutions produced by the standard Max-sum algorithm, Bounded Max-sum and Max-sum_AD with no value propagation.