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Thorsten Koch

Publications and source records attributed to Thorsten Koch.

At least 37 records · Page 2Linked to original sources

Clustering scientific publications: lessons learned through experiments with a real citation network

Clustering scientific publications can reveal underlying research structures within bibliographic databases. Graph-based clustering methods, such as spectral, Louvain, and Leiden algorithms, are frequently utilized due to their capacity to effectively model citation networks. However, their performance may degrade when applied to real-world data. This study evaluates the performance of these clustering algorithms on a citation graph comprising approx. 700,000 papers and 4.6 million citations extracted from Web of Science. The results show that while scalable methods like Louvain and Leiden perform efficiently, their default settings often yield poor partitioning. Meaningful outcomes require careful parameter tuning, especially for large networks with uneven structures, including a dense core and loosely connected papers. These findings highlight practical lessons about the challenges of large-scale data, method selection and tuning based on specific structures of bibliometric clustering tasks.

cs.DL↗

Quantum Approximate Multi-Objective Optimization

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. In this work, we use low-depth Quantum Approximate Optimization Algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with Matrix Product State numerical simulation, and show its potential to outperform classical approaches.

quant-ph↗

40 Years of Interdisciplinary Research: Phases, Origins, and Key Turning Points (1981-2020)

This study examines the historical evolution of interdisciplinary research (IDR) over a 40-year period, focusing on its dynamic trends, phases, and key turning points. We apply time series analysis to identify critical years for interdisciplinary citations (CYICs) and categorizes IDR into three distinct phases based on these trends: Period I (1981-2002), marked by sporadic and limited interdisciplinary activity; Period II (2003-2016), characterized by the emergence of large-scale IDR led primarily by Medicine, with significant breakthroughs in cloning and medical technology; and Period III (2017-present), where IDR became a widely adopted research paradigm. Our findings indicate that IDR has been predominantly concentrated within the Natural Sciences, with Medicine consistently at the forefront, and highlights increasing contributions from Engineering and Environmental disciplines as a new trend. These insights enhance the understanding of the evolution of IDR, its driving factors, and the shifts in the focus of interdisciplinary collaborations.

stat.AP↗

From Coverage to Prestige: A Comprehensive Assessment of Large-Scale Scientometric Data

As research in the Scientometric deepens, the impact of data quality on research outcomes has garnered increasing attention. This study, based on Web of Science (WoS) and Crossref datasets, systematically evaluates the differences between data sources and the effects of data merging through matching, comparison, and integration. Two core metrics were employed: Reference Coverage Rate (RCR) and Article Scientific Prestige (ASP), which respectively measure citation completeness (quantity) and academic influence (quality). The results indicate that the WoS dataset outperforms Crossref in its coverage of high-impact literature and ASP scores, while the Crossref dataset provides complementary value through its broader coverage of literature. Data merging significantly improves the completeness of the citation network, with particularly pronounced benefits in smaller disciplinary clusters such as Education and Arts. However, data merging also introduces some low-quality citations, resulting in a polarization of overall data quality. Moreover, the impact of data merging varies across disciplines; high-impact clusters such as Science, Biology, and Medicine benefit the most, whereas clusters like Social Sciences and Arts are more vulnerable to negative effects. This study highlights the critical role of data sources in Scientometric research and provides a framework for assessing and improving data quality.

cs.DL↗

Developing heuristic solution techniques for large-scale unit commitment models

Shifting towards renewable energy sources and reducing carbon emissions necessitate sophisticated energy system planning, optimization, and extension. Energy systems optimization models (ESOMs) often form the basis for political and operational decision-making. ESOMs are frequently formulated as linear (LPs) and mixed-integer linear (MIP) problems. MIPs allow continuous and discrete decision variables. Consequently, they are substantially more expressive than LPs but also more challenging to solve. The ever-growing size and complexity of ESOMs take a toll on the computational time of state-of-the-art commercial solvers. Indeed, for large-scale ESOMs, solving the LP relaxation -- the basis of modern MIP solution algorithms -- can be very costly. These time requirements can render ESOM MIPs impractical for real-world applications. This article considers a set of large-scale decarbonization-focused unit commitment models with expansion decisions based on the REMix framework (up to 83 million variables and 900,000 discrete decision variables). For these particular instances, the solution to the LP relaxation and the MIP optimum lie close. Based on this observation, we investigate the application of relaxation-enforced neighborhood search (RENS), machine learning guided rounding, and a fix-and-propagate (FP) heuristic as a standalone solution method. Our approach generated feasible solutions 20 to 100 times faster than GUROBI, achieving comparable solution quality with primal-dual gaps as low as 1% and up to 35%. This enabled us to solve numerous scenarios without lowering the quality of our models. For some instances that GUROBI could not solve within two days, our \FP method provided feasible solutions in under one hour.

math.OC↗

Benchmarking of Quantum and Classical Computing in Large-Scale Dynamic Portfolio Optimization Under Market Frictions

Quantum computing is poised to transform the financial industry, yet its advantages over traditional methods have not been evidenced. As this technology rapidly evolves, benchmarking is essential to fairly evaluate and compare different computational strategies. This study presents a challenging yet solvable problem of large-scale dynamic portfolio optimization under realistic market conditions with frictions. We frame this issue as a Quadratic Unconstrained Binary Optimization (QUBO) problem, compatible with digital computing and ready for quantum computing, to establish a reliable benchmark. By applying the latest solvers to real data, we release benchmarks that help verify true advancements in dynamic trading strategies, either quantum or digital computing, ensuring that reported improvements in portfolio optimization are based on robust, transparent, and comparable metrics.

math.OC↗

State-of-the-art Methods for Pseudo-Boolean Solving with SCIP

The Pseudo-Boolean problem deals with linear or polynomial constraints with integer coefficients over Boolean variables. The objective lies in optimizing a linear objective function, or finding a feasible solution, or finding a solution that satisfies as many constraints as possible. In the 2024 Pseudo-Boolean competition, solvers incorporating the SCIP framework won five out of six categories it was competing in. From a total of 1,207 instances, SCIP successfully solved 759, while its parallel version FiberSCIP solved 776. Based on the results from the competition, we further enhanced SCIP's Pseudo-Boolean capabilities. This article discusses the results and presents the winning algorithmic ideas.

math.OC↗

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↗

Challenges and Opportunities in Quantum Optimization

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of different approaches for major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions. This work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory - highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains - finance and sustainability - as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

quant-ph↗

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↗

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↗

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↗

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↗

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↗

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↗

Optimal discrete pipe sizing for tree-shaped CO2 networks

Many energy-intensive industries, like the steel industry, plan to switch to renewable energy sources. Other industries, such as the cement industry, have to rely on carbon capture utilization and storage (CCUS) technologies to reduce their production processes' inevitable carbon dioxide (CO2) emissions. However, a new transport infrastructure needs to be established to connect the point of capture and the point of storage or utilization. Given a tree-shaped network transporting captured CO2 from multiple sources to a single sink, we investigate how to select optimal pipeline diameters from a discrete set of diameters. The general problem of optimizing arc capacities in potential-based fluid networks is already a challenging mixed-integer nonlinear optimization problem. The problem becomes even more complex when adding the highly sensitive nonlinear behavior of CO2 regarding temperature and pressure changes. We propose an iterative algorithm that splits the problem into two parts: a) the pipe-sizing problem under a fixed supply scenario and temperature distribution and b) the thermophysical modeling, including mixing effects, the Joule-Thomson effect, and the heat exchange with the surrounding environment. We show the effectiveness of our approach by applying our algorithm to a real-world network planning problem for a CO2 network in Germany.

math.OC↗

How far are German companies in improving security through static program analysis tools?

As security becomes more relevant for many companies, the popularity of static program analysis (SPA) tools is increasing. In this paper, we target the use of SPA tools among companies in Germany with a focus on security. We give insights on the current issues and the developers' willingness to configure the tools to overcome these issues. Compared to previous studies, our study considers the companies' culture and processes for using SPA tools. We conducted an online survey with 256 responses and semi-structured interviews with 17 product owners and executives from multiple companies. Our results show a diversity in the usage of tools. Only half of our survey participants use SPA tools. The free tools tend to be more popular among software developers. In most companies, software developers are encouraged to use free tools, whereas commercial tools can be requested. However, the product owners and executives in our interviews reported that their developers do not request new tools. We also find out that automatic security checks with tools are rarely performed on each release.

cs.CR↗

Progress in Mathematical Programming Solvers from 2001 to 2020

This study investigates the progress made in LP and MILP solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving LP/MILP, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for LP and around 50 for MILP, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time.

math.OC↗