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Many combinatorial problems can be solved in time $O^*(c^{tw})$ on graphs of treewidth $tw$, for a problem-specific constant $c$. In several cases, matching upper and lower bounds on $c$ are known based on the Strong Exponential Time…
We study propagation algorithms for the conjunction of two AllDifferent constraints. Solutions of an AllDifferent constraint can be seen as perfect matchings on the variable/value bipartite graph. Therefore, we investigate the problem of…
There have been recent efforts for incorporating Graph Neural Network models for learning full-stack solvers for constraint satisfaction problems (CSP) and particularly Boolean satisfiability (SAT). Despite the unique representational power…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
A limited-memory influence diagram (LIMID) generalizes a traditional influence diagram by relaxing the assumptions of regularity and no-forgetting, allowing a wider range of decision problems to be modeled. Algorithms for solving…
There are numerous NP-hard combinatorial problems which involve searching for an undirected graph satisfying a certain property. One way to solve such problems is to translate a problem into an instance of the boolean satisfiability (SAT)…
In pseudo-boolean solving the currently most successful unit propagation strategy is a hybrid mode combining the watched literal scheme with the counting method. This short paper introduces new heuristics for this hybrid decision, which are…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…
Parallel solving via cube-and-conquer is a key method for scaling SAT solvers to hard instances. While cube-and-conquer has proven successful for pure SAT problems, notably the Pythagorean triples conjecture, its application to SAT solvers…
For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semidefinite programming (SDP) relaxation…
Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional…
Generating diverse solutions to the Boolean Satisfiability Problem (SAT) is a hard computational problem with practical applications for testing and functional verification of software and hardware designs. We explore the way to generate…
In this paper, we design low correlation binary sequences favorable in wireless communication and radar applications. First, we formulate the designing problem as a nonconvex combination optimization problem with flexible correlation…
Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics…
This paper presents a novel pairwise constraint propagation approach by decomposing the challenging constraint propagation problem into a set of independent semi-supervised learning subproblems which can be solved in quadratic time using…
Diffusion models have shown promise in learning to solve constraint optimization problems. However, they are mostly restricted to problems with binary variables and rely on graph neural networks, hindering their application to a broader…
We introduce the dual-path fixing strategy to exploit dual algorithms for solving relaxations of mixed-integer nonlinear-optimization problems. Such dual algorithms are naturally applied in the context of branch-and-bound, and eventual…
We describe decomposition during search (DDS), an integration of And/Or tree search into propagation-based constraint solvers. The presented search algorithm dynamically decomposes sub-problems of a constraint satisfaction problem into…
Modeling decision-dependent scenario probabilities in stochastic programs is difficult and typically leads to large and highly non-linear MINLPs that are very difficult to solve. In this paper, we develop a new approach to obtain a compact…
Path planning is an active area of research essential for many applications in robotics. Popular techniques include graph-based searches and sampling-based planners. These approaches are powerful but have limitations. This paper continues…