Parallel Hybrid Best-First Search for Cost Function Networks

Cost Function Networks (CFNs), also known as Weighted Constraint Satisfaction Problems (Meseguer, Rossi, and Schiex 2006) is a mathematical model which has been derived from Constraint Satisfaction Problems by replacing constraints with cost functions. In a CFN, we are given a set of variables with an associated finite domain and a set of local cost functions. Each cost function involves some variables and associates a non-negative integer cost to each of the possible combinations of values they may take. The usual problem considered is to assign all variables in a way that minimizes the sum of all costs. This problem is NP-hard, and exact methods usually rely on Branch and Bound (B&B) algorithms exploring a binary search tree with propagation at each node in order to improve the problem lower bound and prune domain values with a forbidden cost (Cooper et al. 2010). Several B&B search methods have been developed in the CFN solver toulbar21. In this work we describe a first parallel version of Hybrid Best-First Search (HBFS) (Allouche et al. 2015) and give a preliminary empirical evaluation on combinatorial optimization problems from uncapacitated warehouse location, computational protein design, and genetics. This last section includes solving time and speed-up comparisons between our approach within toulbar2 and other parallel approaches available in IBM Ilog cplex and daoopt (Otten and Dechter 2017) (i.e., respectively a Mixed Integer Programming and an AND/OR search Graphical Model solver).