PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite

Maher, Stephen J.; Miltenberger, Matthias; Pedroso, João Pedro; Rehfeldt, Daniel; Schwarz, R.; Serrano, Felipe

doi:10.1007/978-3-319-42432-3_37

Cited by 43 publications

(23 citation statements)

References 3 publications

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“…We compute H (X ) by finding a maximum cardinality clique in the hiding graph by solving an integer program. We have implemented the aforementioned methods in Python 3.7.8, using SageMath 9.1 [34] for polyhedral computations; all mixed-integer programs were solved using SCIP 7.0.0 [17], which has been called via its Python interface [28]. Note that SCIP is not an exact solver and thus the results reported below are only correct up to numerical tolerances.…”

Section: Mixed-integer Programming Formulations For Computing the Relaxation Complexitymentioning

confidence: 99%

Computational aspects of relaxation complexity: possibilities and limitations

2021

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The relaxation complexity $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) of the set of integer points X contained in a polyhedron is the smallest number of facets of any polyhedron P such that the integer points in P coincide with X. It is a useful tool to investigate the existence of compact linear descriptions of X. In this article, we derive tight and computable upper bounds on $${{\,\mathrm{rc}\,}}_\mathbb {Q}(X)$$ rc Q ( X ) , a variant of $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) in which the polyhedra P are required to be rational, and we show that $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) can be computed in polynomial time if X is 2-dimensional. Further, we investigate computable lower bounds on $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) with the particular focus on the existence of a finite set $$Y \subseteq \mathbb {Z}^d$$ Y ⊆ Z d such that separating X and $$Y \setminus X$$ Y \ X allows us to deduce $${{\,\mathrm{rc}\,}}(X) \ge k$$ rc ( X ) ≥ k . In particular, we show for some choices of X that no such finite set Y exists to certify the value of $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) , providing a negative answer to a question by Weltge (2015). We also obtain an explicit formula for $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) for specific classes of sets X and present the first practically applicable approach to compute $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) for sets X that admit a finite certificate.

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Section: Mixed-integer Programming Formulations For Computing the Relaxation Complexitymentioning

confidence: 99%

Computational aspects of relaxation complexity: possibilities and limitations

2021

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“…The experiments were run on a Dell Precision 5820 Tower workstation with a Intel Xeon(R) W-2175 CPU @ 2.50GHz 28, 128 RAM and operating system Ubuntu Linux 18.04.5 LTS. We implemented our code in python and used the python interface package pyscipopt [14] to connect to the solver SCIP with version 6.0.1 [8]. As this interface does not support parallel mode, we could just use one core.…”

Section: Specificationsmentioning

confidence: 99%

Embedding of complete graphs in broken Chimera graphs

Lobe

Schürmann

Stollenwerk

2021

Quantum Inf Process

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In order to solve real-world combinatorial optimization problems with a D-Wave quantum annealer, it is necessary to embed the problem at hand into the D-Wave hardware graph, namely Chimera or Pegasus. Most hard real-world problems exhibit a strong connectivity. For the worst-case scenario of a complete graph, there exists an efficient solution for the embedding into the ideal Chimera graph. However, since real machines almost always have broken qubits, it is necessary to find an embedding into the broken hardware graph. We present a new approach to the problem of embedding complete graphs into broken Chimera graphs. This problem can be formulated as an optimization problem, more precisely as a matching problem with additional linear constraints. Although being NP-hard in general, it is fixed-parameter tractable in the number of inaccessible vertices in the Chimera graph. We tested our exact approach on various instances of broken hardware graphs, both related to real hardware and randomly generated. For fixed runtime, we were able to embed larger complete graphs compared to previous, heuristic approaches. As an extension, we developed a fast heuristic algorithm which enables us to solve even larger instances. We compared the performance of our heuristic and exact approaches.

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“…Our code is written in Python 3.7 and we use Pytorch 1.60 (Paszke et al 2019), Pytorch Geometric 1.7.0 (Fey and Lenssen 2019), PySCIPOpt 3.1.1 (Maher et al 2016), SCIP 7.01 (Gamrath et al 2020) for developing our models and sovling MILPs.…”

Section: A Appendixmentioning

confidence: 99%

Learning to Search in Local Branching

Liu¹,

Fischetti²,

Lodi³

2021

Preprint

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Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce improving solutions and has been highly influential for the development of local search methods in MILP. The algorithm iteratively explores a sequence of solution neighborhoods defined by the so-called local branching constraint, namely, a linear inequality limiting the distance from a reference solution. For a LB algorithm, the choice of the neighborhood size is critical to performance. Although it was initialized by a conservative value in the original LB scheme, our new observation is that the "best" size is strongly dependent on the particular MILP instance. In this work, we investigate the relation between the size of the search neighborhood and the behavior of the underlying LB algorithm, and we devise a leaning based framework for guiding the neighborhood search of the LB heuristic. The framework consists of a two-phase strategy. For the first phase, a scaled regression model is trained to predict the size of the LB neighborhood at the first iteration through a regression task. In the second phase, we leverage reinforcement learning and devise a reinforced neighborhood search strategy to dynamically adapt the size at the subsequent iterations. We computationally show that the neighborhood size can indeed be learned, leading to improved performances and that the overall algorithm generalizes well both with respect to the instance size and, remarkably, across instances.

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PySCIPOpt: Mathematical Programming in Python with the SCIP Optimization Suite

Cited by 43 publications

References 3 publications

Computational aspects of relaxation complexity: possibilities and limitations

Computational aspects of relaxation complexity: possibilities and limitations

Embedding of complete graphs in broken Chimera graphs

Learning to Search in Local Branching

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