An MDD-based SAT encoding for pseudo-Boolean constraints with at-most-one relations

Bofill, Miquel; Coll, Jordi; Suy, Josep; Villaret, Mateu

doi:10.1007/s10462-020-09817-6

Cited by 5 publications

(23 citation statements)

References 27 publications

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“…We deduce the following dual optimal solution : y cc = 2, y 1 = 55 − 2 × 14 = 27, y 2 = 47 − 2 × 16 = 15. The following reduced costs are obtained : rc(x 12 ) = rc(x 21 ) = rc(x 22 ) = 0 and rc(x 11 ) = 5, rc(x 13 ) = 10, we deduce that replacing the previous objective function by the following one does not change the cost of the optimal solution: min 35x 11 + 55x 12 + 75x 13 + 47x 21 + 95x 22 We observe that the solution x * = {0, 1, 0, 7 12 , 5 12 } is still optimal.…”

Section: Solving the Knapsack Lpmentioning

confidence: 82%

“…Also, PB solvers are usually restricted to a linear objective, whereas our approach can combine PB constraints with non-linear quadratic (or more) cost functions. PB solvers can also exploit the presence of AMO or EO constraints to strengthen propagation of PB constraints [5,7].…”

Section: Related Workmentioning

confidence: 99%

“…Pisinger's algorithm gives the optimal primal solution x * = {0, 1, 0, 7 12 , 5 12 } with cost o = 55 + 7 12 × 47 + 5 12 × 95 = 122. We deduce the following dual optimal solution : y cc = 2, y 1 = 55 − 2 × 14 = 27, y 2 = 47 − 2 × 16 = 15.…”

Section: Solving the Knapsack Lpmentioning

confidence: 99%

“…The Computational Protein Design (CPD) [4] problem consists of identifying the sequence of amino acids that should fold into a given 3D shape. This problem can be modeled as a CFN 7 with unary and binary cost functions representing the energy of the protein but the criteria only approximate the reality, thus producing a sequence of diverse solutions increases the chance of finding the correct real sequence of amino acids. Each time a solution is found, a Hamming distance constraint is added to the model to enforce the next solution to be different from the previous ones.…”

Section: Sequence Of Diverse Solutions For Cpdmentioning

confidence: 99%

“…8 Selected instances have from 23 to 97 residues/variables with 6 https://github.com/toulbar2/toulbar2 version 1.2. 7 Other paradigms such as ILP or Max-SAT have been tested but the experimental results using their corresponding state-of-the-art solvers were inferior to the CFN approach using toulbar2 -divm=(0 for dual, 1 for hidden, 2 for ternary, and 3 for the PB encoding)). Figure 1 reports the solving time of each encoding.…”

Section: Sequence Of Diverse Solutions For Cpdmentioning

confidence: 99%

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Multiple-choice Knapsack Constraint in Graphical Models

Montalbano¹,

Givry²,

Katsirelos

2022

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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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.

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Section: Solving the Knapsack Lpmentioning

confidence: 82%

Section: Related Workmentioning

confidence: 99%

Section: Solving the Knapsack Lpmentioning

confidence: 99%

Section: Sequence Of Diverse Solutions For Cpdmentioning

confidence: 99%

Section: Sequence Of Diverse Solutions For Cpdmentioning

confidence: 99%

See 3 more Smart Citations

Multiple-choice Knapsack Constraint in Graphical Models

Montalbano¹,

Givry²,

Katsirelos

2022

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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Learning to select SAT encodings for pseudo-Boolean and linear integer constraints

Ulrich-Oltean,

Nightingale,

Walker

2023

Constraints

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Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.

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