Relaxation-Aware Heuristics for Exact Optimization in Graphical Models

Trösser, Fulya; Givry, Simon de; Katsirelos, George

doi:10.1007/978-3-030-58942-4_31

Cited by 4 publications

(5 citation statements)

References 15 publications

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“…We evaluate three solvers: daoopt (version from UAI 2012 competition with 1-hour settings as given in [23]), cplex (version 20.1.0.0, forcing completeness with zero absolute and relative gaps, translating CFN to 0-1 LP by the tuple encoding [15]), and toulbar2 (version 1.2.0) using two state-of-the-art methods, Variable Neighborhood Search (VNS) [24] winner of UAI 2014 competition, 7 and Hybrid Best-First Search with VAC in preprocessing (VACpre-HBFS), including VAC integrality heuristics [31]. 8 We implemented VPWC in the latest version of toulbar2.…”

Section: Experimental Results On Uai 2022 Competitionmentioning

confidence: 99%

“…Additional preprocessing is performed beforehand for all the HBFS methods in order to find better bounds. An initial upper bound is found by local search [21,3] and VAC-based heuristics [31]. To reduce the problem size and improve lower bounds, we apply bounded variable elimination with a min-fill ordering [10,18,14] 11 and add ternary zero-cost functions on the most-preferred triangles (total memory space of extra ternary functions limited to 1MB).…”

Section: Experimental Results On Uai 2022 Competitionmentioning

confidence: 99%

“…We report in Fig. 2 the average normalized lower and upper bounds as time passes (computed as in [31]). Here VNS provides the best upper bounds in limited time whereas HBFS-VPWC is slightly slower than VPWCpre-HBFS, VACpre-HBFS, and VNS, but still faster than daoopt and cplex.…”

Section: Experimental Results On Uai 2022 Competitionmentioning

confidence: 99%

See 2 more Smart Citations

Virtual Pairwise Consistency in Cost Function Networks

Montalbano¹,

Allouche²,

Givry³

et al. 2023

Lecture Notes in Computer Science

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In constraint satisfaction, pairwise consistency (PWC) is a well-known local consistency improving generalized arc consistency in theory but not often in practice. A popular approach to enforcing PWC enforces arc consistency on the dual encoding of the problem, allowing to reuse existing AC algorithms. In this paper, we explore the benefit of this simple approach in the optimization context of cost function networks and soft local consistencies. Using a dual encoding, we obtain an equivalent binary cost function network where enforcing virtual arc consistency achieves virtual PWC on the original problem. We experimentally observed that adding extra non-binary cost functions before the dual encoding results in even stronger bounds. Such supplementary cost functions may be produced by bounded variable elimination or by adding ternary zero-cost functions. Experiments on (probabilistic) graphical models, from the UAI 2022 competition benchmark, show a clear improvement when using our approach inside a branch-and-bound solver compared to the state-of-the-art.

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Section: Experimental Results On Uai 2022 Competitionmentioning

confidence: 99%

Section: Experimental Results On Uai 2022 Competitionmentioning

confidence: 99%

See 1 more Smart Citation

Virtual Pairwise Consistency in Cost Function Networks

Montalbano¹,

Allouche²,

Givry³

et al. 2023

Lecture Notes in Computer Science

Self Cite

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show abstract

“…On the right, we again wrote Farkas' alternative system, so that any ȳ satisfying this system is a dual-improving direction from the current point y. The left-hand system (29) is the LP relaxation of the CSP with allowed tuples J (Cooper et al, 2010;Nguyen, Bessiere, de Givry, & Schiex, 2017;Trösser, de Givry, & Katsirelos, 2020;Werner, 2007), which we denote by (V, D, E, J). 17…”

Section: Lp Relaxation Of Weighted Cspmentioning

confidence: 99%

Using Constraint Propagation to Bound Linear Programs

Dlask,

Werner

2024

jair

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We present an approach to compute bounds on the optimal value of linear programs based on constraint propagation. Given a feasible dual solution, we apply constraint propagation to the complementary slackness conditions and, if propagation succeeds to prove these conditions infeasible, the infeasibility certificate (in the sense of Farkas’ lemma) is reconstructed from the propagation history. This certificate is a dual-improving direction, which allows us to improve the bound. As constraint propagation need not always detect infeasibility of a linear inequality system, the method is not guaranteed to converge to a global solution of the linear program but only to an upper bound, whose tightness depends on the structure of the program and the used propagation method. The approach is suited for large sparse linear programs (such as LP relaxations of combinatorial optimization problems), for which the classical LP algorithms may be infeasible, if only for their super-linear space complexity. The approach can be seen as a generalization of the Virtual Arc Consistency (VAC) algorithm to bound the LP relaxation of the Weighted CSP (WCSP). We newly apply it to the LP relaxation of the Weighted Max-SAT problem, experimentally showing that the obtained bounds are often not far from optima of the relaxation and proving that they are exact for known tractable subclasses of Weighted Max-SAT.

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“…Dlask and Werner [16,17] have shown how to handle arbitrary LPs using BCA algorithms, based on a generalization of VAC. However, despite recent advances [50], BCA algorithms remain too costly for use at every node of a B&B. Many (soft) global constraints can be described by a set of (soft) linear constraints, but require an LP solver [35].…”

Section: Related Workmentioning

confidence: 99%

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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Relaxation-Aware Heuristics for Exact Optimization in Graphical Models

Cited by 4 publications

References 15 publications

Virtual Pairwise Consistency in Cost Function Networks

Virtual Pairwise Consistency in Cost Function Networks

Using Constraint Propagation to Bound Linear Programs

Multiple-choice Knapsack Constraint in Graphical Models

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