Automatic Detection of At-Most-One and Exactly-One Relations for Improved SAT Encodings of Pseudo-Boolean Constraints

Ansótegui, Carlos; Bofill, Miquel; Coll, Jordi; Dang, Nguyen; Esteban, Juan Luis; Miguel, Ian; Nightingale, Peter; Salamon, András Z.; Suy, Josep; Villaret, Mateu

doi:10.1007/978-3-030-30048-7_2

Cited by 8 publications

(21 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, the following is a matrix literal containing four integer literals. [ 1,3,2,4 ] Matrix literals may contain any valid expression in ESSENCE PRIME. For example a matrix literal is allowed to contain other matrix literals to build up a matrix with two or more dimensions.…”

Section: -5 True Falsementioning

confidence: 99%

“…Finally a multi-dimensional matrix value can be expressed by nesting matrix literals. Suppose we have the following domain: matrix indexed by [int(-2..0),int (1,2,4)] of int (1..5) One value contained in this domain is the following:…”

Section: -5 True Falsementioning

confidence: 99%

“…However the allDiff will perform better in most situations. 2 Table 1 summarises the global constraints available in ESSENCE PRIME. Now we have the allDiff global constraint, the Sudoku example can be improved and simplified as shown in Figure 3.…”

Section: Global Constraintsmentioning

confidence: 99%

“…If the direct literals are not needed, then using the language of the ladder encoding of Gent et al [11], we have only the ladder variables and the clauses in Gent et al formula (2). If both order and direct literals are required, then we use the full ladder encoding with the clauses in formulas (1), ( 2…”

Section: Solver Control -Smt Solversmentioning

confidence: 99%

See 3 more Smart Citations

Savile Row Manual

Nightingale

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Section: -5 True Falsementioning

confidence: 99%

Section: -5 True Falsementioning

confidence: 99%

Section: Global Constraintsmentioning

confidence: 99%

Section: Solver Control -Smt Solversmentioning

confidence: 99%

See 2 more Smart Citations

Savile Row Manual

Nightingale

2022

Preprint

Self Cite

View full text Add to dashboard Cite

“…The pseudo-Boolean constraint (2) (often called at-most-one constraint) can be translated to clauses in multiple different ways (Ansótegui, Bofill, Coll, Dang, Esteban, Miguel, Nightingale, Salamon, Suy, & Villaret, 2019). One simple and efficient translation at the same time is to forbid all possible pairs variables to be simultaneously TRUE as follows.…”

Section: Detailed Description Of the Sat Encodingmentioning

confidence: 99%

Migrating Techniques from Search-based Multi-Agent Path Finding Solvers to SAT-based Approach

Surynek¹,

Stern²,

Boyarski³

et al. 2022

jair

View full text Add to dashboard Cite

In the multi-agent path finding problem (MAPF) we are given a set of agents each with respective start and goal positions. The task is to find paths for all agents while avoiding collisions, aiming to minimize a given objective function. Many MAPF solvers were introduced in the past decade for optimizing two specific objective functions: sum-of-costs and makespan. Two prominent categories of solvers can be distinguished: search-based solvers and compilation-based solvers. Search-based solvers were developed and tested for the sum-of-costs objective, while the most prominent compilation-based solvers that are built around Boolean satisfiability (SAT) were designed for the makespan objective. Very little is known on the performance and relevance of solvers from the compilation-based approach on the sum-of-costs objective. In this paper, we start to close the gap between these cost functions in the compilation-based approach. Our main contribution is a new SAT-based MAPF solver called MDD-SAT, that is directly aimed to optimally solve the MAPF problem under the sum-of-costs objective function. Using both a lower bound on the sum-of-costs and an upper bound on the makespan, MDD-SAT is able to generate a reasonable number of Boolean variables in our SAT encoding. We then further improve the encoding by borrowing ideas from ICTS, a search-based solver. In addition, we show that concepts applicable in search-based solvers like ICTS and ICBS are applicable in the SAT-based approach as well. Specifically, we integrate independence detection, a generic technique for decomposing an MAPF instance into independent subproblems, into our SAT-based approach, and we design a relaxation of our optimal SAT-based solver that results in a bounded suboptimal SAT-based solver. Experimental evaluation on several domains shows that there are many scenarios where our SAT-based methods outperform state-of-the-art sum-of-costs search-based solvers, such as variants of the ICTS and ICBS algorithms.

show abstract

Multiple-choice Knapsack Constraint in Graphical Models

Montalbano¹,

Givry²,

Katsirelos

2022

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

View full text Add to dashboard Cite

Graphical models, such as cost function networks (CFNs), can compactly express large decomposable functions, which leads to efficient inference algorithms. Most methods for computing lower bounds in Branch-and-Bound minimization compute feasible dual solutions of a specific linear relaxation. These methods are more effective than solving the linear relaxation exactly, with better worst-case time complexity and better performance in practice. However, these algorithms are specialized to the structure of the linear relaxation of a CFN and cannot, for example, deal with constraints that cannot be expressed in extension, such as linear constraints of large arity. In this work, we show how to extend soft local consistencies, a set of approximate inference techniques for CFNs, so that they handle linear constraints, as well as combinations of linear constraints with at-mostone constraints. We embedded the resulting algorithm in toulbar2, an exact Branch-and-Bound solver for CFNs which has demonstrated superior results in several graphical model competitions and is state-of-theart for solving large computational protein design (CPD) problems. We significantly improved performance of the solver in CPD with diversity guarantees. It also compared favorably with integer linear programming solvers on knapsack problems with conflict graphs.

show abstract

Automatic Detection of At-Most-One and Exactly-One Relations for Improved SAT Encodings of Pseudo-Boolean Constraints

Cited by 8 publications

References 23 publications

Savile Row Manual

Savile Row Manual

Migrating Techniques from Search-based Multi-Agent Path Finding Solvers to SAT-based Approach

Multiple-choice Knapsack Constraint in Graphical Models

Contact Info

Product

Resources

About