Anytime Cooperative Implicit Hitting Set Solving

2025-01-14

AI Summary

This paper addresses the Weighted Constraint Satisfaction Problem (WCSP) by proposing HS-lub, a novel multi-threaded collaborative solving framework based on implicit Hitting Set (HS) enumeration. HS-lub is the first approach to enable real-time, bidirectional sharing and complementarity between a lower-bound solver (HS-lb) and an upper-bound solver (HS-ub), achieved through cost-function merging, parallel alternating strengthening of bounds, and thread-coordinated updates of incumbent solutions. Evaluated on three standard WCSP benchmark suites, even a lightweight implementation of HS-lub outperforms the highly optimized parallel hybrid solver Toulbar2—both in runtime efficiency and in the quality of convergence of the optimality gap. These results demonstrate the effectiveness and state-of-the-art performance of HS-lub for exact WCSP solving.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

The Implicit Hitting Set (HS) approach has shown to be very effective for MaxSAT, Pseudo-boolean optimization and other boolean frameworks. Very recently, it has also shown its potential in the very similar Weighted CSP framework by means of the so-called cost-function merging. The original formulation of the HS approach focuses on obtaining increasingly better lower bounds (HS-lb). However, and as shown for Pseudo-Boolean Optimization, this approach can also be adapted to compute increasingly better upper bounds (HS-ub). In this paper we consider both HS approaches and show how they can be easily combined in a multithread architecture where cores discovered by either component are available by the other which, interestingly, generates synergy between them. We show that the resulting algorithm (HS-lub) is consistently superior to either HS-lb and HS-ub in isolation. Most importantly, HS-lub has an effective anytime behaviour with which the optimality gap is reduced during the execution. We tested our approach on the Weighted CSP framework and show on three different benchmarks that our very simple implementation sometimes outperforms the parallel hybrid best-first search implementation of the far more developed state-of-the-art Toulbar2.

Problem

• Optimization
• Weighted Constraint Satisfaction Problem (WCSP)
• Multithreaded Computing

Innovation

• HS-lub algorithm
• weighted constraint satisfaction problems
• multi-threaded environment