An Improved Three-Weight Message-Passing Algorithm
This work addresses optimization and constraint satisfaction problems in fields like operations research and AI, offering incremental improvements over existing message-passing methods.
The paper tackles the challenge of improving constraint satisfaction and non-convex optimization by introducing a three-weight message-passing algorithm based on ADMM/DC, which enhances performance for problems like circle packing and large Sudoku puzzles while maintaining exact performance for convex cases.
We describe how the powerful "Divide and Concur" algorithm for constraint satisfaction can be derived as a special case of a message-passing version of the Alternating Direction Method of Multipliers (ADMM) algorithm for convex optimization, and introduce an improved message-passing algorithm based on ADMM/DC by introducing three distinct weights for messages, with "certain" and "no opinion" weights, as well as the standard weight used in ADMM/DC. The "certain" messages allow our improved algorithm to implement constraint propagation as a special case, while the "no opinion" messages speed convergence for some problems by making the algorithm focus only on active constraints. We describe how our three-weight version of ADMM/DC can give greatly improved performance for non-convex problems such as circle packing and solving large Sudoku puzzles, while retaining the exact performance of ADMM for convex problems. We also describe the advantages of our algorithm compared to other message-passing algorithms based upon belief propagation.