arXiv subjects

Steffen Rebennack

Publications and source records attributed to Steffen Rebennack.

4 recordsLinked to original sources

arXiv2025

From Cables to Qubits: A Decomposed Variational Quantum Optimization Pipeline

The Cable Routing Optimization Problem (CROP) is a Multi-Commodity Flow Problem (MCFP) central to industrial layouts and smart manufacturing. Historically, quantum optimization has modeled MCFPs as Quadratic Unconstrained Binary Optimization problems (QUBOs). Recent studies suggest that mapping routing problems to Polynomial Unconstrained Binary Optimization problems (PUBOs) can improve efficiency. However, solving full-scale MCFPs with quantum optimization remains computationally challenging. To bridge this gap, we introduce a Decomposed Variational Quantum Pipeline that exploits the block-diagonal structure of CROP, breaking the multi-cable routing task into modular, single-commodity subproblems. We explicitly derive both the QUBO and PUBO representations for CROP and demonstrate that our pipeline can evaluate both formulations within the same pipeline. Our empirical study highlights a trade-off: PUBO eliminates auxiliary qubits at the cost of circuit depth. In our experiments, the decomposed pipeline accelerates time-to-solution, reliably generating feasible cable layouts while trading strict optimality for computational scalability. PUBO formulations achieved full routing feasibility across all tested seeds, while global QUBO formulations showed substantially lower robustness.

quant-ph↗

arXiv2025

LinearizeLLM: An Agent-Based Framework for LLM-Driven Exact Linear Reformulation of Nonlinear Optimization Problems

Reformulating nonlinear optimization problems into solver-ready linear optimization problems is often necessary for practical applications, but the process is often manual and requires domain expertise. We propose LinearizeLLM, an agent-based LLM framework that produces solver-ready linear reformulations of nonlinear optimization problems. Agents first detect the nonlinearity pattern (e.g., bilinear products) and apply nonlinearity pattern-aware reformulation techniques, selecting the most suitable linearization technique. We benchmark on 40 instances: 27 derived from ComplexOR by injecting exactly-linearizable operators, and 13 automatically generated instances with deeply nested nonlinearities. LinearizeLLM achieves 73\% mean end-to-end overall success (OSR) across nonlinearity depths (8.3x higher than a one-shot LLM baseline; 4.3x higher than Pyomo). The results suggest that a set of pattern-specialized agents can automate linearization, supporting natural-language-based modeling of nonlinear optimization.

cs.LG↗

arXiv2025

SPHERE: Spherical partitioning for large-scale routing optimization

We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the problem by identifying \emph{source-target} ($s$--$t$) overlaps of hop-distance spheres. Selecting an anchor node $a$ within this overlap partitions the task into independent induced subgraphs for $s\to a$ and $a\to t$, each restricted to its own induced subgraph. If resulting subgraphs remain large, the procedure recurses on that specific subgraph. We provide a formal guarantee that by using the partition cut within the shared overlap, the resulting subpaths preserve feasibility, thereby avoiding the need for boundary repair. Furthermore, \emph{SPHERE} acts as a solver-agnostic framework that naturally exposes parallelism across subproblems. On million-scale road networks, \emph{SPHERE} achieves faster runtimes and smaller optimality gaps than contemporary state-of-the-art partitioning and community-based routing pipelines. Crucially, it also substantially mitigates heavy-tail runtime outliers suffered by standard exact methods, yielding highly stable and predictable execution times across varying queries.

cs.DC↗

arXiv2025

Automated Market Makers: A Stochastic Optimization Approach for Profitable Liquidity Concentration

Concentrated liquidity automated market makers (AMMs), such as Uniswap v3, enable liquidity providers (LPs) to earn liquidity rewards by depositing tokens into liquidity pools. However, LPs often face significant financial losses driven by poorly selected liquidity provision intervals and high costs associated with frequent liquidity reallocation. To support LPs in achieving more profitable liquidity concentration, we developed a tractable stochastic optimization problem that can be used to compute optimal liquidity provision intervals for profitable liquidity provision. The developed problem accounts for the relationships between liquidity rewards, divergence loss, and reallocation costs. By formalizing optimal liquidity provision as a tractable stochastic optimization problem, we support a better understanding of the relationship between liquidity rewards, divergence loss, and reallocation costs. Moreover, the stochastic optimization problem offers a foundation for more profitable liquidity concentration.

q-fin.TR↗