Solving Weighted CSPs by Successive Relaxations

Delisle, Erin; Bacchus, Fahiem

doi:10.1007/978-3-642-40627-0_23

Cited by 3 publications

(6 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The core-extraction solver (CES, line 3 in Algorithm 1) uses the assumption-based SAT solver CaDiCal (Biere et al 2020), and the minimum hitting vector solver (MHV, line 8 in Algorithm 1) is implemented as a 0-1 integer program solved to optimality with CPLEX. Our encodings are similar to (Delisle and Bacchus 2013)). The merged cost-functions for both symbolic and numeric merging are encoded into SAT using the totalizer encoding (Joshi, Martins, and Manquinho 2015).…”

Section: Resultsmentioning

confidence: 99%

“…Next we review (and largely rephrase in an arguably simplified way) the HS approach for WCSP introduced in (Delisle and Bacchus 2013). The following definitions assume an arbitrary WCSP P = (X, D, C, F ) with m cost functions F = {f 1 , f 2 , .…”

Section: Hs For Weighted Cspsmentioning

confidence: 99%

“…In (Delisle and Bacchus 2013) the MHV problem is modeled as an Integer Program and CES is modeled as a SAT formula with assumptions, so both problems are solved with off-the-shelf solvers. They also propose some practical improvements of HS-WCSP.…”

Section: Core Extracting Solver (Ces)mentioning

confidence: 99%

“…For this experiment, we used a more realistic HS-WCSP implementation that does not guarantee that the CES function returns a maximal core. Instead, the algorithm includes two of the improvements proposed in (Delisle and Bacchus 2013): (i) the CES function computes several disjoin cores at each iteration and, (ii) it improves each of them by greedely increasing the lowest k i value until the induced CSP becomes satisfiable. When it happens it undoes the last increment and returns it as a core.…”

Section: Benchmark Instancesmentioning

confidence: 99%

“…A surprisingly very effective technique for MaxSAT solving is the so called Implicit Hitting Set (HS) approach (Davies and Bacchus 2013;Berg, Bacchus, and Poole 2020;Bacchus et al 2018). The HS approach was adapted from MaxSAT to WCSP in (Delisle and Bacchus 2013) and a simple algorithm, HS-WCSP, showed some promising preliminary results. Given the similarity between MaxSAT and WCSP, we believe that it is worth advancing further towards efficient HS-based WCSP solvers.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Theoretical and Empirical Analysis of Cost-Function Merging for Implicit Hitting Set WCSP Solving

Larrosa,

Martínez,

Rollon

2024

AAAI

View full text Add to dashboard Cite

The Implicit Hitting Set (HS) approach has shown very effective for MaxSAT solving. However, only preliminary promising results have been obtained for the very similar Weighted CSP framework. In this paper we contribute towards both a better theoretical understanding of the HS approach and a more effective HS-based solvers for WCSP. First, we bound the minimum number of iterations of HS thanks to what we call distinguished cores. Then, we show a source of inefficiency by introducing two simple problems where HS is unfeasible. Next, we propose two reformulation methods that merge cost-functions to overcome the problem. We provide a theoretical analysis that quantifies the magnitude of the improvement of each method with respect to the number of iterations of the algorithm. In particular, we show that the reformulations can bring an exponential number of iterations down to a constant number in our working examples. Finally, we complement our theoretical analysis with two sets of experiments. First, we show that our results are aligned with real executions. Second, and most importantly, we conduct experiments on typical benchmark problems and show that cost-function merging may be heuristically applied and it may accelerate HS algorithms by several orders of magnitude. In some cases, it even outperforms state-of-the-art solvers.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Hs For Weighted Cspsmentioning

confidence: 99%

Section: Core Extracting Solver (Ces)mentioning

confidence: 99%

Section: Benchmark Instancesmentioning

confidence: 99%