arXiv subjects

Mark Turner

Publications and source records attributed to Mark Turner.

18 recordsLinked to original sources

arXiv2025

Clique Probing for Mixed-Integer Programs

Probing is an important presolving technique in mixed-integer programming solvers. It selects binary variables, tentatively fixes them to 0 and 1, and performs propagation to deduce additional variable fixings, bound tightenings, substitutions, and implications. In this work, we propose clique probing instead of probing on individual variables, we select cliques, a set of binary variables of which at most one can be set to one, and systematically probe on all variables of a clique. Experiments with our implementation in the open-source presolve library PaPILO demonstrate that exploiting clique information in this form significantly increases the number of reductions. When integrated into the MIP solver SCIP, we observe a 3% performance improvement on MIPLIB instances containing cliques.

math.OC↗

arXiv2025

The SCIP Optimization Suite 10.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in SCIP Optimization Suite 10.0. The updates in SCIP 10.0 include a new solving mode for exactly solving rational mixed-integer linear programs, a new presolver for detecting implied integral variables, a novel cut-based conflict analysis and separator for flower inequalities, two new heuristics, a novel tool for explaining infeasibility, a new interface for nonlinear solvers as well as improvements in symmetry handling, branching strategies, and SCIP's Benders' decomposition framework. SCIP Optimization Suite 10.0 also includes new and improved features in the the presolving library PaPILO, the parallel framework UG, and the decomposition framework GCG. Moreover, the SCIP Optimization Suite 10.0 contains MIP-DD, the first open-source delta debugger for mixed-integer programming solvers. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver.

math.OC↗

arXiv2025

FutureVision: A methodology for the investigation of future cognition

This paper presents a methodology combining multimodal semantic analysis with an eye-tracking experimental protocol to investigate the cognitive effort involved in understanding the communication of future scenarios. To demonstrate the methodology, we conduct a pilot study examining how visual fixation patterns vary during the evaluation of valence and counterfactuality in fictional ad pieces describing futuristic scenarios, using a portable eye tracker. Participants eye movements are recorded while evaluating the stimuli and describing them to a conversation partner. Gaze patterns are analyzed alongside semantic representations of the stimuli and participants descriptions, constructed from a frame semantic annotation of both linguistic and visual modalities. Preliminary results show that far-future and pessimistic scenarios are associated with longer fixations and more erratic saccades, supporting the hypothesis that fractures in the base spaces underlying the interpretation of future scenarios increase cognitive load for comprehenders.

cs.CL↗

arXiv2024

A Multi-Reference Relaxation Enforced Neighborhood Search Heuristic in SCIP

This paper proposes and evaluates a Multi-Reference Relaxation Enforced Neighborhood Search (MRENS) heuristic within the SCIP solver. This study marks the first integration and evaluation of MRENS in a full-fledged MILP solver, specifically coupled with the recently-introduced Lagromory separator for generating multiple reference solutions. Computational experiments on the MIPLIB 2017 benchmark set show that MRENS, with multiple reference solutions, improves the solver's ability to find higher-quality feasible solutions compared to single-reference approaches. This study highlights the potential of multi-reference heuristics in enhancing primal heuristics in MILP solvers.

math.OC↗

arXiv2024

Leakage Mobility in Superconducting Qubits as a Leakage Reduction Unit

Leakage from the computational subspace is a damaging source of noise that degrades the performance of most qubit types. Unlike other types of noise, leakage cannot be overcome by standard quantum error correction techniques and requires dedicated leakage reduction units. In this work, we study the effects of leakage mobility between superconducting qubits on the performance of a quantum stability experiment, which is a benchmark for fault-tolerant logical computation. Using the Fujitsu Quantum Simulator, we perform full density-matrix simulations of stability experiments implemented on the surface code. We observe improved performance with increased mobility, suggesting leakage mobility can itself act as a leakage reduction unit by naturally moving leakage from data to auxiliary qubits, where it is removed upon reset. We compare the performance of standard error-correction circuits with "patch wiggling", a specific leakage reduction technique where data and auxiliary qubits alternate their roles in each round of error correction. We observe that patch wiggling becomes inefficient with increased leakage mobility, in contrast to the improved performance of standard circuits. These observations suggest that the damage of leakage can be overcome by stimulating leakage mobility between qubits without the need for a dedicated leakage reduction unit.

quant-ph↗

arXiv2024

The SCIP Optimization Suite 9.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a new cut generator and two new cut selection schemes, a new branching rule, a new LP interface, and several bug fixes. The SCIP Optimization Suite 9.0 also features new Rust and C++ interfaces for SCIP, new Python interface for SoPlex, along with enhancements to existing interfaces. The SCIP Optimization Suite 9.0 also includes new and improved features in the LP solver SoPlex, the presolving library PaPILO, the parallel framework UG, the decomposition framework GCG, and the SCIP extension SCIP-SDP. These additions and enhancements have resulted in an overall performance improvement of SCIP in terms of solving time, number of nodes in the branch-and-bound tree, as well as the reliability of the solver.

math.OC↗

arXiv2023

PySCIPOpt-ML: Embedding Trained Machine Learning Models into Mixed-Integer Programs

A standard tool for modelling real-world optimisation problems is mixed-integer programming (MIP). However, for many of these problems, information about the relationships between variables is either incomplete or highly complex, making it difficult or even impossible to model the problem directly. To overcome these hurdles, machine learning (ML) predictors are often used to represent these relationships and are then embedded in the MIP as surrogate models. Due to the large amount of available ML frameworks and the complexity of many ML predictors, formulating such predictors into MIPs is a highly non-trivial task. In this paper, we introduce PySCIPOpt-ML, an open-source tool for the automatic formulation and embedding of trained ML predictors into MIPs. By directly interfacing with a broad range of commonly used ML frameworks and an open-source MIP solver, PySCIPOpt-ML provides a way to easily integrate ML constraints into optimisation problems. Alongside PySCIPOpt-ML, we introduce, SurrogateLIB, a library of MIP instances with embedded ML constraints, and present computational results over SurrogateLIB, providing intuition on the scale of ML predictors that can be practically embedded. The project is available at https://github.com/Opt-Mucca/PySCIPOpt-ML.

math.OC↗

arXiv2023

A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming

The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set.

math.OC↗

arXiv2023

Branching via Cutting Plane Selection: Improving Hybrid Branching

Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017.

math.OC↗

arXiv2023

How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem

It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.

math.OC↗

arXiv2023

Enabling Research through the SCIP Optimization Suite 8.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this paper is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Further, the paper gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.

math.OC↗

arXiv2023

Standardizing Paediatric Clinical Data: The Development of the conect4children (c4c) Cross Cutting Paediatric Data Dictionary

Standardization of data items collected in paediatric clinical trials is an important but challenging issue. The Clinical Data Interchange Standards Consortium (CDISC) data standards are well understood by the pharmaceutical industry but lack the implementation of some paediatric specific concepts. When a paediatric concept is absent within CDISC standards, companies and research institutions take multiple approaches in the collection of paediatric data, leading to different implementations of standards and potentially limited utility for reuse. To overcome these challenges, the conect4children consortium has developed a cross-cutting paediatric data dictionary (CCPDD). The dictionary was built over three phases - scoping (including a survey sent out to ten industrial and 34 academic partners to gauge interest), creation of a longlist and consensus building for the final set of terms. The dictionary was finalized during a workshop with attendees from academia, hospitals, industry and CDISC. The attendees held detailed discussions on each data item and participated in the final vote on the inclusion of the item in the CCPDD. Nine industrial and 34 academic partners responded to the survey, which showed overall interest in the development of the CCPDD. Following the final vote on 27 data items, three were rejected, six were deferred to the next version and a final opinion was sought from CDISC. The first version of the CCPDD with 25 data items was released in August 2019. The continued use of the dictionary has the potential to ensure the collection of standardized data that is interoperable and can later be pooled and reused for other applications. The dictionary is already being used for case report form creation in three clinical trials. The CCPDD will also serve as one of the inputs to the Paediatric User Guide, which is being developed by CDISC.

q-bio.OT↗

arXiv2022

Cutting Plane Selection with Analytic Centers and Multiregression

Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.

math.OC↗

arXiv2022

Controlling transient gas flow in real-world pipeline intersection areas

Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest Transmission System Operators to develop a decision support system for their dispatching center, we investigated how to automatize control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time, while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real world data we demonstrate the performance of our approach.

math.OC↗

arXiv2022

Adaptive Cut Selection in Mixed-Integer Linear Programming

Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.

math.OC↗

arXiv2021

The SCIP Optimization Suite 8.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack.

math.OC↗

arXiv2021

Generative deep learning for decision making in gas networks

A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5%.

math.OC↗

arXiv2019

Petascale Cloud Supercomputing for Terapixel Visualization of a Digital Twin

Background: Photo-realistic terapixel visualization is computationally intensive and to date there have been no such visualizations of urban digital twins, the few terapixel visualizations that exist have looked towards space rather than earth. Objective: our aims are: creating a scalable cloud supercomputer software architecture for visualization; a photo-realistic terapixel 3D visualization of urban IoT data supporting daily updates; a rigorous evaluation of cloud supercomputing for our application. Method: we migrated the Blender Cycles path tracer to the public cloud within a new software framework designed to scale to petaFLOP performance. Results: we demonstrate we can compute a terapixel visualization in under one hour, the system scaling at 98% efficiency to use 1024 public cloud GPU nodes delivering 14 petaFLOPS. The resulting terapixel image supports interactive browsing of the city and its data at a wide range of sensing scales. Conclusion: The GPU compute resource available in the cloud is greater than anything available on our national supercomputers providing access to globally competitive resources. The direct financial cost of access, compared to procuring and running these systems, was low. The indirect cost, in overcoming teething issues with cloud software development, should reduce significantly over time.

cs.DC↗