arXiv subjects

Tobias Seidel

Publications and source records attributed to Tobias Seidel.

11 recordsLinked to original sources

arXiv2026

An adaptive discretization algorithm for locally optimal experimental design with constraints

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the constrained-design problem is solved and then the discretization is adaptively refined by adding an approximate violator of a suitable sufficient $\eps$-optimality condition for the current design. We prove that with $\eps = 0$, our algorithm converges to an optimal design and that with $\eps > 0$, our algorithm finitely terminates at an $\eps$-optimal design. Compared to the existing algorithms on constrained experimental design, our algorithm comes with considerably less computational effort because the nonlinear subproblems in our algorithm have a smaller dimension and have to be solved only approximately and only in selected iterations (typically the last few). Additionally, our algorithm covers a considerably larger class of constraints. We demonstrate the good convergence properties of the algorithm on experimental design problems from chemical engineering that feature time and yield constraints.

math.OC↗

arXiv2025

A Machine Learning-Fueled Modelfluid for Flowsheet Optimization

Process optimization in chemical engineering may be hindered by the limited availability of reliable thermodynamic data for fluid mixtures. Remarkable progress is being made in predicting thermodynamic mixture properties by machine learning techniques. The vast information provided by these prediction methods enables new possibilities in process optimization. This work introduces a novel modelfluid representation that is designed to seamlessly integrate these ML-predicted data directly into flowsheet optimization. Tailored for distillation, our approach is built on physically interpretable and continuous features derived from core vapor liquid equilibrium phenomena. This ensures compatibility with existing simulation tools and gradient-based optimization. We demonstrate the power and accuracy of this ML-fueled modelfluid by applying it to the problem of entrainer selection for an azeotropic separation. The results show that our framework successfully identifies optimal, thermodynamically consistent entrainers with high fidelity compared to conventional models. Ultimately, this work provides a practical pathway to incorporate large-scale property prediction into efficient process design and optimization, overcoming the limitations of both traditional thermodynamic models and complex molecular-based equations of state.

cs.CE↗

arXiv2025

Reusable Surrogate Models for Distillation Columns

Surrogate modeling is a powerful methodology in chemical process engineering, frequently employed to accelerate optimization tasks where traditional flowsheet simulators are computationally prohibitive. However, the state-of-the-art is dominated by surrogate models trained for a narrow range of fixed chemical systems and operating conditions, limiting their reusability. This work introduces a paradigm shift towards reusable surrogates by developing a single model for distillation columns that generalizes across a vast design space. The key enabler is a novel ML-fueled modelfluid representation which allows for the generation of datasets of more than $1,000,000$ samples. This allows the surrogate to generalize not only over column specifications but also over the entire chemical space of homogeneous ternary vapor-liquid mixtures. We validate the model's accuracy and demonstrate its practical utility in a case study on entrainer distillation, where it successfully screens and ranks candidate entrainers, significantly reducing the computational effort compared to rigorous optimization.

cs.CE↗

arXiv2025

An Exact Branch and Bound Algorithm for the generalized Qubit Mapping Problem

Quantum circuits are typically represented by a (ordered) sequence of gates over a set of virtual qubits. During compilation, the virtual qubits of the gates are assigned to the physical qubits of the underlying quantum hardware, a step often referred to as the qubit assignment problem. To ensure that the resulting circuit respects hardware connectivity constraints, additional SWAP gates are inserted as needed, which is known as the qubit routing problem. Together, they are called the Qubit Mapping Problem (QMP), which is known to be NP-hard. A very common way to deal with the complexity of the QMP is to partition the sequence of gates into a sequence of gate groups (or layers). However, this imposes a couple of important restrictions: (1) SWAP gates can only be added between pairs of consecutive groups, and (2) all the gates belonging to a certain group have to be executed (in parallel) in the same time slot. The first one prevents gates to be re-arranged optimally, while the second one imposes a time discretization that practically ignores gate execution time. While this clearly reduces the size of the feasible space, little is still known about how much is actually lost by imposing a fixed layering when looking at the minimization of either the number of SWAPs or the makespan of the compiled circuit. In this paper, we present a flexible branch and bound algorithm for a generalized version of the QMP that either considers or ignores the gate layering and the gate execution time. The algorithm can find find proven optimal solutions for all variations of the QMP, but also offers a great platform for different heuristic algorithms. We present results on several benchmark sets of small quantum circuits, and we show how ignoring the layering can significantly improve some key performance indicators of the compiled circuit.

quant-ph↗

arXiv2025

Influences of Uncertainties in Thermodynamic Models on Pareto-optimized Dividing Wall Columns for Ideal Mixtures

This article examines the effect of individual and combined uncertainties in thermodynamic models on the performance of simulated, steady-state Pareto-optimized Dividing Wall Columns. It is a follow-up of the previous work analogously treating deviations in process variables. Such deviations and uncertainties that may even be unknown during the design process can significantly influence the separation result. However, other than process variables, uncertainties in thermodynamics are usually not systematically considered during design. For the first time, the effects of uncertain thermodynamic properties on Pareto-optimized DWCs with different numbers of stages and for different mixtures are presented and compared qualitatively and quantitatively. Depending on the number of stages and mixture characteristics, particularly critical properties are identified. On the one hand, this provides information on aspects requiring special attention prior to design, and on the other hand, it also indicates in which section of the DWC a stage supplement might be most beneficial.

physics.chem-ph↗

arXiv2024

Multicriteria Adjustable Regret Robust Optimization for Building Energy Supply Design

Optimizing a building's energy supply design is a task with multiple competing criteria, where not only monetary but also, for example, an environmental objective shall be taken into account. Moreover, when deciding which storages and heating and cooling units to purchase (here-and-now-decisions), there is uncertainty about future developments of prices for energy, e.g. electricity and gas. This can be accounted for later by operating the units accordingly (wait-and-see-decisions), once the uncertainty revealed itself. Therefore, the problem can be modeled as an adjustable robust optimization problem. We combine adjustable robustness and multicriteria optimization for the case of building energy supply design and solve the resulting problem using a column and constraint generation algorithm in combination with an $\varepsilon$-constraint approach. In the multicriteria adjustable robust problem, we simultaneously minimize worst-case cost regret and carbon emissions. We take into account future price uncertainties and consider the results in the light of information gap decision theory to find a trade-off between security against price fluctuations and over-conservatism. We present the model, a solution strategy and discuss different application scenarios for a case study building.

math.OC↗

arXiv2023

A Decomposition Method for the Hybrid Quantum-Classical Solution of the Number Partitioning Problem

Current quantum computers can only solve optimization problems of a very limited size. For larger problems, decomposition methods are required in which the original problem is broken down into several smaller sub-problems. These are then solved on the quantum computer and their solutions are merged into a final solution for the original problem. Often, these decomposition methods do not take the specific problem structure into account. In this paper, we present a tailored method using a divide-and-conquer strategy to solve the number partitioning problem (NPP) with a large number of variables. The idea is to perform a specialized decomposition into smaller NPPs, which can be solved on a quantum computer, and then recombine the results into another small auxiliary NPP. Solving this auxiliary problem yields an approximate solution of the original larger problem. We experimentally verify that our method allows to solve NPPs with over a thousand variables using a D-Wave quantum annealer.

math.OC↗

arXiv2023

An Optimization Case Study for solving a Transport Robot Scheduling Problem on Quantum-Hybrid and Quantum-Inspired Hardware

We present a comprehensive case study comparing the performance of D-Waves' quantum-classical hybrid framework, Fujitsu's quantum-inspired digital annealer, and Gurobi's state-of-the-art classical solver in solving a transport robot scheduling problem. This problem originates from an industrially relevant real-world scenario. We provide three different models for our problem following different design philosophies. In our benchmark, we focus on the solution quality and end-to-end runtime of different model and solver combinations. We find promising results for the digital annealer and some opportunities for the hybrid quantum annealer in direct comparison with Gurobi. Our study provides insights into the workflow for solving an application-oriented optimization problem with different strategies, and can be useful for evaluating the strengths and weaknesses of different approaches.

quant-ph↗

arXiv2023

A unified approach to inverse robust optimization problems

A variety of approaches has been developed to deal with uncertain optimization problems. Often, they start with a given set of uncertainties and then try to minimize the influence of these uncertainties. Depending on the approach used, the corresponding price of robustness is different. The reverse view is to first set a budget for the price one is willing to pay and then find the most robust solution. In this article, we aim to unify these inverse approaches to robustness. We provide a general problem definition and a proof of the existence of its solution. We study properties of this solution such as closedness, convexity, and boundedness. We also provide a comparison with existing robustness concepts such as the stability radius, the resilience radius, and the robust feasibility radius. We show that the general definition unifies these approaches. We conclude with examples that demonstrate the flexibility of the introduced concept.

math.OC↗

arXiv2019

An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence

Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In this paper we combine a classical adaptive discretization method developed by Blankenship and Falk and techniques regarding a semi-infinite optimization problem as a bi-level optimization problem. We develop a new adaptive discretization method which combines the advantages of both techniques and exhibits a quadratic rate of convergence. We further show that a limit of the iterates is a stationary point, if the iterates are stationary points of the approximate problems.

math.OC↗

arXiv2019

Optimized data exploration applied to the simulation of a chemical process

In complex simulation environments, certain parameter space regions may result in non-convergent or unphysical outcomes. All parameters can therefore be labeled with a binary class describing whether or not they lead to valid results. In general, it can be very difficult to determine feasible parameter regions, especially without previous knowledge. We propose a novel algorithm to explore such an unknown parameter space and improve its feasibility classification in an iterative way. Moreover, we include an additional optimization target in the algorithm to guide the exploration towards regions of interest and to improve the classification therein. In our method we make use of well-established concepts from the field of machine learning like kernel support vector machines and kernel ridge regression. From a comparison with a Kriging-based exploration approach based on recently published results we can show the advantages of our algorithm in a binary feasibility classification scenario with a discrete feasibility constraint violation. In this context, we also propose an improvement of the Kriging-based exploration approach. We apply our novel method to a fully realistic, industrially relevant chemical process simulation to demonstrate its practical usability and find a comparably good approximation of the data space topology from relatively few data points.

stat.AP↗