GAMM2025

Session

S16: Optimization

S16

8 Apr 2025, 16:30

Lecture and Conference Centre

Conveners

S16: Optimization: S16.01

• Michael Stingl

S16: Optimization: S16.02

• Michał Nowak

S16: Optimization: S16.03

• Michael Stingl

S16: Optimization: S16.04

• Benedikt Wirth

S16: Optimization: S16.05

• Michael Stingl

S16: Optimization: S16.06

• Tomasz Lewiński

Description

Optimization is the next natural step after simulation with increasing importance in the future. The aim of this session is to provide the basis of a holistic overview of all areas of optimization. Thus abstracts from both a theoretical as well as an applied perspective are welcome.

615. Gradient type numerical methods of shape and topological optimization

Jan Sokolowski

08/04/2025, 16:30

Shape optimization problems are ill-posed in general because of the lack of convexity. Therefore, the appropriate regularization is required for the existence of an optimal shape in applications to solid mechanics, as well as fluid and gas mechanics. In the lecture the mathematical model of shape optimization problem is considered. The convergence of the associated gradient flow dynamical...

616. Numerical solutions of gradient flow dynamical system for shape optimization in elasticity

Yixin Tan

08/04/2025, 17:10

The shape and topology optimization is considered for linear elasticity. There are two methods to compute admissible solutions. The first is the gradient flow dynamical system which leads to the gradient type algorithm. The second is a level set method which is based on numerical solution of the Hamilton-Jacobi equations. The first method is actually superior from mathematical point of view,...

617. IGA Topology optimization based on topological derivatives

Guilherme Henrique Teixeira

08/04/2025, 17:30

Topology optimization is a valuable tool in engineering, facilitating the design of optimized structures. However, topological changes often require a remeshing step, which can become challenging. In this work, we propose an isogeometric approach to topology optimization driven by topological derivatives. The combination of a level-set method together with an immersed isogeometric framework...

618. Biomimetic Regularization of the Structural Optimization Method - Numerical Aspects

Michał Nowak

08/04/2025, 17:50

The standard approach to mechanical design is based on strength hypotheses. However, the structural optimization methods do not take into account this important condition determining the correctness of the engineering solution. The situation is different in the case of biological systems, where reference to material strength is a basic condition for the formation of functional mechanically...

619. Optimizing Printing Nozzle Design for Fused Deposition Modeling

Steffen Tillmann

08/04/2025, 18:10

Fused deposition modeling (FDM) is a widely used extrusion-based additive manufacturing process, primarily for 3D printing. It facilitates the cost-effective production of customized products. The polymer is melted and then extruded through a nozzle on the product, where the polymer solidifies. The quality of parts produced with FDM depends on multiple factors, including the extrusion nozzle...

620. Topology optimisation of non-periodic metamaterials via beam-based modelling

Philippa Weißinger

09/04/2025, 16:30

Additive manufacturing techniques such as 3D printing, selective laser sintering and others have enabled the fabrication of complex geometries such as meta-materials. Generally, the resulting geometry may be separated into scales, assuming sufficient characteristic length differences. For lattice cell meta-materials, a 'macro-scale' detailing the overall structure and its partitioning into...

621. Process modeling-based optimization of grayscale masked stereolithography 3D printed parts

Felix Rutsch

09/04/2025, 16:50

3D printing techniques based on the photopolymerization process stand out from other printing processes due to their high resolution. Applications include, for example, the fabrication of microfluidic devices and dental models. However, the dimensional conformity of the 3D printed objects is still a challenge. The properties and geometry are highly dependent on the process parameters.

In...

622. Minimization of the structural compliance over the elastic moduli with a convex unit cost leads to a nonlinear elasticity problem

Tomasz Lewiński

09/04/2025, 17:10

The paper concerns the problem of minimization of the compliance of linear elastic structures made of an isotropic material. The bulk and shear moduli are the design variables, both viewed as non-negative fields on the design domain. The design variables are subject to the isoperimetric condition which is the upper bound of two kinds of Lp-norms of the elastic moduli. The case of p=1...

623. Topology optimization in civil engineering – on the consideration of concrete failure characteristic and self-weight

Daniela Masarczyk

09/04/2025, 17:30

The mechanical efficiency of civil engineering structures is a key factor in the sustainable transformation of the building sector. Topology optimization is a powerful tool for the preliminary draft of mechanically improved structures. The interpretation as a material distribution problem in a predefined design space that is discretized by finite elements is a proven approach to the method;...

624. Topology Optimization Methods for Buckling Structures with Size Constraints

Manyu Xiao

09/04/2025, 17:50

This study focuses on the development and application of topology optimization methods for buckling structures under size constraints. Buckling, as a common failure mode in mechanical structures, can significantly affect the structural performance and reliability. Therefore, it is of great significance to optimize the topology of buckling structures to improve their stability and...

625. Lasserre hierarchy for topology optimization of frame structures under dynamic excitations

Marek Tyburec

09/04/2025, 18:10

Design optimization of frame structures is crucial for numerous civil engineering applications requiring lightweight yet dynamically robust designs. The minimum weight design of such structures under dynamic loading presents significant computational challenges due to the non-convexity of the feasible domain, polynomial dependence of stiffness on design variables, and disconnected feasible set...

626. Convexification can help optimization, at least sometimes

Benedikt Wirth

10/04/2025, 08:30

A number of interesting optimization problems is nonconvex and thus hard to optimize, particularly if the optimization variable is additionally high- or infinite-dimensional (e.g. a function on some domain). Often the nonconvexity is associated with some kind of discreteness or sparsity: For instance, the function to be optimized may only assume particular values or has sparse support. A...

627. Abs-Smooth Frank-Wolfe Method: Convergence Analysis and Implementation

Sri Harshitha Tadinada

10/04/2025, 09:10

Motivated by the conditional gradient descent methods, a.k.a the Frank-Wolfe algorithms in the smooth case, we present here an adaptation of these Frank-Wolfe methods for non-smooth problems. Needless to say the smooth Frank-Wolfe algorithms have seen many applications in various fields of optimization and data science. We analysed the non-smooth adaptation of the Frank-Wolfe algorithms called...

628. Addressing Risk Aversion in Energy Market Models: A Non-Smooth Optimization Approach

Adrian Schmidt

10/04/2025, 09:30

In a recent paper, the authors introduced a model for analyzing the strategic interactions of retail companies in the energy sector, where customers choose retail contracts over a longer period of time based on price and non-price characteristics. This framework is applicable to various energy markets, such as electricity, hydrogen, and natural gas [1]. In this talk, we extend this model by...

629. How Stringent is the Linear Independence Kink Qualification in Abs-Smooth Optimization?

Franz Bethke

10/04/2025, 09:50

Abs-smooth optimization problems consist of objective functions, and possibly constraints, that are build as finite compositions of smooth elementals and the absolute value function. These optimization problems can be written in the so-called abs-normal form by replacing all arguments of the absolute value by new variables and adding these relations as an additional constraint called switching...

630. A robust optimization method for functions with discontinuities along lower-dimensional manifolds

Lennart Igel

10/04/2025, 10:10

We propose a method for the optimization of discontinuous functions, for which all discontinuities are contained along lower dimensional manifolds. Traditional methods construct a robust optimization problem by either sampling or smoothing indifferently over the entire parameter space. However, these methods suffer from exponentially increasing cost for an increasing size of the parameter set....

631. Minimum compliance design of grillages via optimal transportation methods

Karol Bołbotowski

10/04/2025, 14:00

It is well known that the compliance minimization of trusses is an ill-posed problem. Even for the simplest loads one is forced to keep adding joints and bars of decreasing cross sections to assure that the objective function decreases. In the limit, we find ourselves in the realm of Michell structures, which combine continuum medium with bars, usually curved. In the bending regime, the...

632. Optimization of fold-patterns on elastic thin plates

Christoph Smoch

10/04/2025, 14:40

Isometric deformations of elastic thin plates are very rigid. Folds enable increased flexibility of elastic deformations. We ask for optimal fold-patterns on an elastic thin plate that minimize some cost of the resulting deformation subject to suitable boundary conditions. To approximate the elastic deformation for given fold-pattern and the optimization problem, we will take into account a...

633. Coordinated optimization of actuation and component structures in lightweight dynamic arm-like systems

Felix Janzik, Eike Uttich

10/04/2025, 15:00

The interaction between actuation and mechanical structures causes complexity in lightweight design optimizations of arm-like manipulators, e.g., industrial robots. While changes in the actuation concept cause changes in load cases which lead to different optimized structures, changes in structural components influence their inertial properties which influence the required actuation forces or...

634. Optimal simulation parameters for modeling phase transformations in steels

Paweł Potorski

10/04/2025, 15:20

The presentation will explore part of the stochastic model of phase transformations in eutectoid that had been developed (see [1,2,3]). In this model, the nucleation process is modeled using a sequence of random variables following the Bernoulli distribution with a given probability of success, which we interpret as the initiation of the nucleation. The initiation time plays a crucial role, as...

635. Minimization of non-linear least squares inverse problems via global linearization

Dominik Itner

10/04/2025, 15:40

Many overdetermined inverse problems for parameter estimation can be formulated as the minimization of the sum of squares of residuals between some reference and a corresponding parametrized simulation. The least squares objective is geometrically closely related to the Euclidean metric of points in an high-dimensional ambient space. The output of a differentiable simulation model with respect...

636. Topology optimization under chance constraints

Andrian Uihlein

10/04/2025, 16:30

In reliability-based topology optimization or topology optimization under uncertainty, an accurate evaluation of the probabilistic model requires the system to be simulated for a large number of varying parameters. Traditional gradient-based optimization schemes thus face the difficulty that reasonable accuracy and numerical efficiency often seem mutually exclusive. We propose a stochastic...

637. DC-Reformulation for Gradient-L⁰-Constrained Problems in Function Spaces

Evelyn Herberg

10/04/2025, 16:50

Cardinality constraints in optimization are commonly represented via L⁰-type constraints. One way of dealing with these constraints is reformulating the L⁰-constraint using the standard L¹-norm and the largest-K-norm, replacing the resulting constraint with a penalized version and solving the corresponding sequence of DC-type subproblems. We extend the DC-reformulation approach to problems...

638. A numerical method for solving the generalized tangent vector

Yizhou Zhou

10/04/2025, 17:10

This work is concerned with the computation of the first-order variation for one-dimensional hyperbolic partial differential equations. In the case of shock waves the main challenge is addressed by developing a numerical method to compute the evolution of the generalized tangent vector introduced by Bressan and Marson (1995). Our basic strategy is to combine the conservative numerical schemes...

639. A least-squares space-time approach for parabolic equations

Christian Kahle

10/04/2025, 17:30

We consider a least squares formulation of a linear parabolic equation in spaces with natural regularity. As a consequence the formulation contains the Riesz isomorphism. The discrete approach uses space-time finite elements and a suitable approximation of the Riesz isomorphism. Using finite elements that are separable with respect to space and time,the final fully discrete representation has...

640. Phase-Field Structural Optimization of Elasto-Plastic Contact Structures

Andrzej Myśliński

10/04/2025, 17:50

Contact problems with friction or heat generation appear in many different fields of mechanical engineering. Optimal control or optimization of elasto-plastic problems governed by nonlinear PDEs is subject of intensive research. The paper is concerned with the analysis as well as the numerical solution of the topology optimization problems for elasto–plastic rather than elastic structures in...

641. Neural network function approximation for solving parametric optimization problem via optimality condition penalties

Matthias Hoffmann, Kathrin Flaßkamp

10/04/2025, 18:10

Numerical optimization has long been a cornerstone in engineering disciplines, underpinning areas such as optimal control and design optimization. The multi-objective nature of design optimization problems raises the interest in computing entire Pareto fronts of optimal compromises. By suitable scalarization techniques, this can be formulated as solving a family of parametric optimization...

642. Solving Security-Constrained Optimal Power Flow with Benders Decomposition

Martin Hess

11/04/2025, 08:30

The optimal power flow problem lies at the intersection of power system engineering and operations research. Its application areas compromise expansion planning, operation, market clearing, network resiliency and unit commitment. Optimal power flow calculates optimal generator power and voltage setpoints to minimize the cost of system losses and costs of power generation. Security-constrained...

643. Recent advances in real-time optimal power flow of electric distribution networks

Shuo Chen

11/04/2025, 08:50

Due to the massive integration of decentralised energy resources (DER) such as photovoltaic systems, battery storage and e-charging stations, the optimal power flow (OPF) in electric distribution networks has gained significant research interest. Assuming that an active distribution network possesses a fixed topology, the equality constraints are described by the power flow equations, which...

644. Stochastic Optimal Control of Heating Networks under Demand Uncertainty

Johanna Heidrich

11/04/2025, 09:10

Operators of district heating networks are facing numerous technical challenges in course of the energy system transformation, which require innovations in network control. A realistic mapping of the energy transport through the distribution network is key to optimizing the use of operating resources. The underlying thermo-hydraulic PDE system and optimization problems constrained by this PDE...

645. Predictive Building Energy Management by Means of Mixed-Integer Optimal Control with Automated Setup

Artyom Burda

11/04/2025, 09:30

Today, a significant portion of total final energy consumption can be attributed to heating systems in buildings. Reducing energy consumption and carbon dioxide emissions in this sector is, therefore, crucial to achieving the goals of climate action initiatives worldwide. A promising approach to addressing this objective involves the use of advanced predictive control systems, which have the...

646. Minimizing the maximum cutting temperature of a milling process

Abraham Kalu-Uka

11/04/2025, 09:50

In the course of a milling process, heat is generated because of work done during the interaction(s) between the endmill (cutting tool) and the workpiece. This includes work done in: inducing plastic deformation within the workpiece, initiating fracture for chip production, and work due to friction between the cutting edges of the endmill and workpiece. The heat leads to a temperature...

647. Efficient Local Optimization of Optical Design Tasks

Tobias Seger

11/04/2025, 10:10

The task in optical design is to find a set of parameters such that an optical system meets certain performance criteria and boundary conditions. Mathematically, this can be described as a least-squares optimization problem, i.e., the objective function is the norm of an objective vector. For many years, the Levenberg-Marquardt algorithm has been the optimization method of choice in the...