arXiv subjects

Thorsten Koch

Publications and source records attributed to Thorsten Koch.

At least 19 recordsLinked to original sources

arXiv2026

Beyond Hardware: Adaptive Algorithmic Control by State-Proxy Equalization

Recent advances in quantum computing have been driven primarily by improvements in hardware. Here we show that substantial gains can instead arise from how finite computational resources are allocated throughout a quantum computation. We introduce Adaptive Algorithmic Control (A2C), a software paradigm founded on a State-Proxy Equalization theorem, which proves that the optimal allocation for a state-derived proxy-error functional equalizes cumulative computational hardness rather than physical time. The required computational hardness is inferred directly from the evolving quantum state, avoiding explicit reconstruction of the exponentially large many-body spectrum. Across quantum optimization problems containing up to 156 qubits, combining exact simulations, large-scale supercomputer computations and IBM quantum hardware experiments, A2C improves the low-energy sampling probabilities by $22\%$ to over $100,000\%$ under matched circuit depths and measurement budgets. These results demonstrate that quantum computational performance depends not only on hardware capabilities, but also on how finite computational resources are organized, establishing adaptive algorithmic control as a complementary software pathway for advancing quantum computation.

quant-ph↗

arXiv2026

Robust Unit Commitment in District Heating Networks: Chance-Constrained and CVaR Optimization Under Demand Uncertainty

While district heating networks are a key component of the energy transition, their operational planning is challenging due to substantial uncertainty in heat demand. We address this volatility without compromising system reliability. By adapting chance-constrained programming (CC) and conditional value-at-risk (CVaR) optimization to the mixed-integer unit-commitment problem for district-heating networks, we can compute optimal unit-commitment schedules under demand uncertainty. We generate heat demand time series using a Bayesian model, which explicitly quantifies forecasting uncertainty and yields predictive distributions as input to the network optimization. To handle the inherent uncertainty in heat demand, we apply both robust optimization approaches: chance-constrained programming limits the probability of unmet demand, while CVaR optimization penalizes severe shortfalls in the tail of the distribution. We evaluate the approaches both on real-world data from the Berlin district heating network and on a benchmark set of synthetic, realistically parameterized instances of varying sizes. The results compare the two uncertainty-handling methods with respect to solution quality, risk exposure, and computational effort.

math.OC↗

arXiv2026

Computational acceleration strategies for large-scale energy system optimization: a comparative study of GPU-accelerated and distributed-memory solvers

Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM), which combine robustness and accuracy but face scalability limits as model instance size grows. Recently, two promising directions for specialized solver architectures have emerged: (i) GPU-accelerated first-order methods (FOM); and (ii) distributed-memory IPM, which can exploit block structure that arises in many energy system models. This paper presents a computational study comparing these solver classes on a diverse test set of large-scale linear programs arising from energy system analysis, including scenario-based formulations derived from stochastic programming. The results illustrate that distributed-memory IPM can leverage problem structure to deliver substantial speed-ups on specific problems with block-angular structures. GPU-accelerated FOMs demonstrate strong scalability but may yield solutions with higher relative infeasibilities, which, depending on the use case and model uncertainty, can still be acceptable. Overall, our findings indicate that recent algorithmic and hardware advances substantially broaden the computational toolbox available to the energy system optimization community. Each solver class exhibits distinct advantages: shared-memory IPMs remain a powerful tool for reliably obtaining high-accuracy solutions; distributed-memory IPMs can extend scalability to hundreds of cores for certain structured models, enabling faster time-to-solution; and GPU-based FOM can deliver fast solutions when such lower accuracy levels are appropriate. Together, they help make high-resolution, multi-scenario energy system optimization models tractable across a broader range of problem sizes and computing environments.

math.OC↗

arXiv2026

Reconnecting Fragmented Citation Networks with Semantic Augmentation

Citation graphs are fundamental tools for modeling scientific structure, but are often fragmented due to missing citations of scientifically connected articles. To address this issue, we propose a computationally efficient hybrid framework integrating citation topology with large language model (LLM)-based text similarity. Using 662,369 Web of Science publications in Mathematics and Operations Research & Management Science, we augment the original graph by adding semantic edges from small, disconnected components and weighting existing citations according to textual similarity. Semantic augmentation substantially reduces fragmentation while preserving disciplinary homogeneity. Compared to embedding-only clustering, cluster detection on augmented graphs using the Leiden algorithm retains structural interpretability while offering multi-scale organization. The method scales efficiently to large datasets and offers a practical strategy for strengthening citation-based indicators without collapsing disciplinary boundaries.

cs.DL↗

arXiv2026

CHAP: A Hybrid GPU-CPU Heuristic for MIP

We present CHAP (Coordinating Heuristics Across Platforms) a GPU-CPU-hybrid primal heuristic framework for mixed-integer programming. CHAP adopts a portfolio approach where it coordinates a set of primal heuristics, including Local Search, Fix-and-Propagate, and Feasibility Pump, via a shared solution pool. The solution pool is used to exchange feasible incumbent solutions, LP solutions, along with promising infeasible solution candidates, enabling a more comprehensive exploration of the solution space. On the GPU side, we implement a native tabu search featuring a novel best-shift algorithm built on sort, scan, and reduce primitives, along with specialized kernel designs. We additionally leverage cuPDLPx as an approximate LP solver. On the CPU side, we employ various Fix-and-Propagate strategies, guided by information from the solution pool, complemented by a CPU-based tabu search and a Feasibility Pump. All components operate collaboratively, iteratively repairing and improving candidate solutions maintained in the pool. We evaluate our framework on the 50-instances benchmark from the 2026 Land-Doig MIP Competition under competition constraints, including a five-minute time limit. In these settings, CHAP finds solutions to 47 instances outperforming both Gurobi (44) in default mode and NVIDIA cuOpt (43) in heuristics-only mode. The results demonstrate that coordinated cross-platform portfolios offer a promising direction for the integration of GPU heuristics into modern high-performance MIP solvers. The code will be made available on GitHub.

math.OC↗

arXiv2026

A Massively Parallel Interior-Point Method for Arrowhead Linear Programs with Local Linking Structure

In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required, especially for large-scale linear programs. This article describes a new decomposition technique for systems of linear equations implemented in the parallel interior-point solver PIPS-IPM++. The algorithm exploits a matrix structure commonly found in optimization problems: a doubly-bordered block-diagonal or arrowhead structure. This structure is preserved in the linear KKT systems solved during each iteration of the interior-point method. We present a hierarchical Schur complement decomposition that distributes and solves the linear optimization problem; it is designed for high-performance architectures and scales well with the availability of additional computing resources. The decomposition approach uses the border constraints' locality to decouple the factorization process. Our approach is motivated by large-scale unit commitment problems. We demonstrate the performance of our method on a set of mid-to large-scale instances, some of which have more than 10^9 nonzeros in their constraint matrix.

math.OC↗

arXiv2026

GPU accelerated variant of Schroeppel-Shamir's algorithm for solving the market split problem

The market split problem (MSP), introduced by Cornuejols and Dawande (1998), is a challenging binary optimization problem that performs poorly on state-of-the-art linear programming-based branch-and-cut solvers. We present a novel algorithm for solving the feasibility version of this problem, derived from Schroeppel-Shamir's algorithm for the one-dimensional subset sum problem. Our approach is based on exhaustively enumerating one-dimensional solutions of MSP and utilizing GPUs to evaluate candidate solutions across the entire problem. The resulting hybrid CPU-GPU implementation efficiently solves instances with up to 10 constraints and 90 variables. We demonstrate the algorithm's performance on benchmark problems, solving instances of size (9, 80) in less than fifteen minutes and (10, 90) in up to one day.

math.OC↗

arXiv2026

The Quest for Quantum Advantage in Combinatorial Optimization: End-to-end Benchmarking of Quantum Solvers vs. Multi-core Classical Solvers

We perform an end-to-end benchmark of a hybrid sequential quantum computing (HSQC) solver for higher-order unconstrained binary optimization (HUBO), executed on IBM Heron r3 quantum processors to evaluate the potential of current quantum hardware for combinatorial optimization with sub-second end-to-end runtimes. All reported runtimes include the complete pipeline--from preprocessing to QPU execution and postprocessing--under strict wall-clock accounting. Across 20 benchmark instances, a single hybrid attempt produces high-quality solutions in less than one second, matching the ground-state energy in 14 cases. At the same runtime, CPU-based solvers, including simulated annealing, memetic tabu search, and EasySolve, do not reach the value obtained by HSQC, whereas an enhanced parallel tempering method and the GPU-accelerated solver ABS3 reach or surpass it. These results show that HSQC, executed on a single QPU, can achieve performance competitive with strong classical solvers running on 128 vCPUs or 8 NVIDIA A100 GPUs, while also providing a reproducible system-level benchmark for tracking progress as quantum hardware and hybrid sequential workflows improve.

quant-ph↗

arXiv2026

Fix-and-Propagate Heuristics Using Low-Precision First-Order LP Solutions for Large-Scale Mixed-Integer Linear Optimization

We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). We employ GPU-accelerated PDLP, a variant of the Primal-Dual Hybrid Gradient (PDHG) method specialized to LP problems, to solve the \LP-relaxation of our MIPs to low accuracy. This solution is used to motivate fixings within our FP framework. We evaluate the performance of our heuristic on MIPLIB 2017, demonstrating that low-accuracy LP solutions do not lead to a loss in the quality of the FP heuristic solutions. Further, we use our FP framework to produce high-accuracy solutions for large-scale (up to 243 million nonzeros and 8 million decision variables) unit commitment-based dispatch and expansion planning problems created with the modeling framework REMix. For the largest problems, we can generate solutions with a primal-dual gap of under 2% in less than 4 hours, whereas state-of-the-art commercial solvers cannot produce feasible solutions within 2 days of runtime.

math.OC↗

arXiv2026

Distributed Parallel Structure-Aware Presolving for Arrowhead Linear Programs

We present a structure-aware parallel presolve framework specialized to arrowhead linear programs (AHLPs) and designed for high-performance computing (HPC) environments, integrated into the parallel interior point solver PIPS-IPM++. Large-scale LPs arising from automated model generation frequently contain redundancies and numerical pathologies that necessitate effective presolve, yet existing presolve techniques are primarily serial or structure-agnostic and can become time-consuming in parallel solution workflows. Within PIPS-IPM++, AHLPs are stored in distributed memory, and our presolve builds on this to apply a highly parallel, distributed presolve across compute nodes while keeping communication overhead low and preserving the underlying arrowhead structure. We demonstrate the scalability and effectiveness of our approach on a diverse set of AHLPs and compare it against state-of-the-art presolve implementations, including PaPILO and the presolve implemented within Gurobi. Even on a single machine, our presolve significantly outperforms PaPILO by a factor of 18 and Gurobi's presolve by a factor of 6 in terms of shifted geometric mean runtime, while reducing the problems by a similar amount to PaPILO. Using a distributed compute environment, we outperform Gurobi's presolve by a factor of 13.

math.OC↗

arXiv2026

Mapping the Web of Science, a large-scale graph and text-based dataset with LLM embeddings

Large text data sets, such as publications, websites, and other text-based media, inherit two distinct types of features: (1) the text itself, its information conveyed through semantics, and (2) its relationship to other texts through links, references, or shared attributes. While the latter can be described as a graph structure and can be handled by a range of established algorithms for classification and prediction, the former has recently gained new potential through the use of LLM embedding models. Demonstrating these possibilities and their practicability, we investigate the Web of Science dataset, containing ~56 million scientific publications through the lens of our proposed embedding method, revealing a self-structured landscape of texts.

cs.CL↗

arXiv2025

Integrated Wind Farm Design: Optimizing Turbine Placement and Cable Routing with Wake Effects

An accelerated deployment of renewable energy sources is crucial for a successful transformation of the current energy system, with wind energy playing a key role in this transition. This study addresses the integrated wind farm layout and cable routing problem, a challenging nonlinear optimization problem. We model this problem as an extended version of the quota Steiner tree problem (QSTP), optimizing turbine placement and network connectivity simultaneously to meet specified expansion targets. Our proposed approach accounts for the wake effect $-$ a region of reduced wind speed induced by each installed turbine $-$ and enforces minimum spacing between turbines. We introduce an exact solution framework in terms of the novel quota Steiner tree problem with interference (QSTPI). By leveraging an interference-based splitting strategy, we develop an advanced solver capable of tackling large-scale problem instances. The presented approach outperforms generic state-of-the-art mixed integer programming solvers on our dataset by up to two orders of magnitude. Further, we present a hop-constrained variant of the QSTPI to handle cable capacities in the context of radial topologies. Moreover, we demonstrate that our integrated method significantly reduces the costs in contrast to a sequential approach. Thus, we provide a planning tool that enhances existing planning methodologies for supporting a faster and cost-efficient expansion of wind energy.

math.OC↗

arXiv2025

Multi-Agent Reinforcement Learning for Intraday Operating Rooms Scheduling under Uncertainty

Intraday surgical scheduling is a multi-objective decision problem under uncertainty-balancing elective throughput, urgent and emergency demand, delays, sequence-dependent setups, and overtime. We formulate the problem as a cooperative Markov game and propose a multi-agent reinforcement learning (MARL) framework in which each operating room (OR) is an agent trained with centralized training and decentralized execution. All agents share a policy trained via Proximal Policy Optimization (PPO), which maps rich system states to actions, while a within-epoch sequential assignment protocol constructs conflict-free joint schedules across ORs. A mixed-integer pre-schedule provides reference starting times for electives; we impose type-specific quadratic delay penalties relative to these references and a terminal overtime penalty, yielding a single reward that captures throughput, timeliness, and staff workload. In simulations reflecting a realistic hospital mix (six ORs, eight surgery types, random urgent and emergency arrivals), the learned policy outperforms six rule-based heuristics across seven metrics and three evaluation subsets, and, relative to an ex post MIP oracle, quantifies optimality gaps. Policy analytics reveal interpretable behavior-prioritizing emergencies, batching similar cases to reduce setups, and deferring lower-value electives. We also derive a suboptimality bound for the sequential decomposition under simplifying assumptions. We discuss limitations-including OR homogeneity and the omission of explicit staffing constraints-and outline extensions. Overall, the approach offers a practical, interpretable, and tunable data-driven complement to optimization for real-time OR scheduling.

cs.LG↗

arXiv2025

Exact Objective Space Contraction for the Preprocessing of Multi-objective Integer Programs

Solving integer optimization problems with large or widely ranged objective coefficients can lead to numerical instability and increased runtimes. When the problem also involves multiple objectives, the impact of the objective coefficients on runtimes and numerical issues multiplies. We address this issue by transforming the coefficients of linear objective functions into smaller integer coefficients. To the best of our knowledge, this problem has not been defined before. Next to a straightforward scaling heuristic, we introduce a novel exact transformation approach for the preprocessing of multi-objective binary problems. In this exact approach, the large or widely ranged integer objective coefficients are transformed into the minimal integer objective coefficients that preserve the dominance relation of the points in the objective space. The transformation problem is solved with an integer programming formulation with an exponential number of constraints. We present a cutting-plane algorithm that can efficiently handle the problem size. In a first computational study, we analyze how often and in which settings the transformation actually leads to smaller coefficients. In a second study, we evaluate how the exact transformation and a typical scaling heuristic, when used as preprocessing, affect the runtime and numerical stability of the Defining Point Algorithm.

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

Quantum Optimization Benchmarking Library - The Intractable Decathlon

Through recent progress in hardware development, quantum computers have advanced to the point where benchmarking of (heuristic) quantum algorithms at scale is within reach. Particularly in combinatorial optimization - where most algorithms are heuristics - it is key to empirically analyze their performance on hardware and track progress towards quantum advantage. To this extent, we present ten optimization problem classes that are difficult for existing classical algorithms and can (mostly) be linked to practically relevant applications, with the goal to enable systematic, fair, and comparable benchmarks for quantum optimization methods. Further, we introduce the Quantum Optimization Benchmarking Library (QOBLIB) where the problem instances and solution track records can be found. The individual properties of the problem classes vary in terms of objective and variable type, coefficient ranges, and density. Crucially, they all become challenging for established classical methods already at system sizes ranging from less than 100 to, at most, an order of 100,000 decision variables, allowing to approach them with today's quantum computers. We reference the results from state-of-the-art solvers for instances from all problem classes and demonstrate exemplary baseline results obtained with quantum solvers for selected problems. The baseline results illustrate a standardized form to present benchmarking solutions, which has been designed to ensure comparability of the used methods, reproducibility of the respective results, and trackability of algorithmic and hardware improvements over time. We encourage the optimization community to explore the performance of available classical or quantum algorithms and hardware platforms with the benchmarking problem instances presented in this work toward demonstrating quantum advantage in optimization.

quant-ph↗

arXiv2025

Warm-starting Strategies in Scalarization Methods for Multi-Objective Optimization

We explore how warm-starting strategies can be integrated into scalarization-based approaches for multi-objective optimization in (mixed) integer linear programming. Scalarization methods remain widely used classical techniques to compute Pareto-optimal solutions in applied settings. They are favored due to their algorithmic simplicity and broad applicability across continuous and integer programs with an arbitrary number of objectives. While warm-starting has been applied in this context before, a systematic methodology and analysis remain lacking. We address this gap by providing a theoretical characterization of warm-starting within scalarization methods, focusing on the sequencing of subproblems. However, optimizing the order of subproblems to maximize warm-start efficiency may conflict with alternative criteria, such as early identification of infeasible regions. We quantify these trade-offs through an extensive computational study.

math.OC↗

arXiv2025

Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives

Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science - containing about 70 million articles and a billion citations - poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the structure of the problem. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data.

math.OC↗