A modified Levenberg–Marquardt method for estimating the elastic material parameters of polymer waveguides using residuals between autocorrelated frequency responses - Itner, Dominik; Dreiling, Dmitrij; Gravenkamp, Hauke; Henning, Bernd; Birk, Carolin (Mechanical Systems and Signal Processing)
In this contribution, we address the estimation of the frequency-dependent elastic parameters of polymers in the ultrasound range, which is formulated as an inverse problem. This inverse problem is implemented as a nonlinear regression-type optimization problem, in which the simulation signals are fitted to the measurement signals. These signals consist of displacement responses in waveguides, focusing on hollow cylindrical geometries to enhance the simulation efficiency. To accelerate the optimization and reduce the number of model evaluations and wait times, we propose two novel methods. First, we introduce an adaptation of the Levenberg–Marquardt method derived from a geometrical interpretation of the least-squares optimization problem. Second, we introduce an improved objective function based on the autocorrelated envelopes of the measurement and simulation signals. Given that this study primarily relies on simulation data to quantify optimization convergence, we aggregate the expected ranges of realistic material parameters and derive their distributions to ensure the reproducibility of optimizations with proper measurements. We demonstrate the effectiveness of our objective function modification and step adaptation for various materials with isotropic material symmetry by comparing them with the Broyden–Fletcher–Goldfarb–Shanno method. In all cases, our method reduces the total number of model evaluations, thereby shortening the time to identify the material parameters.
Keywords: Material parameter estimation; Waveguide; Nonlinear optimization; Inverse problem; Least squares

Inertial dynamics with vanishing Tikhonov regularization for multobjective optimization - Bot, Radu Ioan; Sonntag, Konstantin (Journal of Mathematical Analysis and Applications)
In this paper we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and differentiable components of the objective function. Trajectory solutions are shown to exist in finite dimensions. We prove fast convergence of the function values, quantified in terms of a merit function. Based on the regime considered, we establish both weak and, in some cases, strong convergence of trajectory solutions toward a weak Pareto optimal solution. To achieve this, we apply Tikhonov regularization individually to each component of the objective function. This work extends results from single objective convex optimization into the multiobjective setting.
Keywords: Pareto optimization; Lyapunov analysis; gradient-like dynamical systems; inertial dynamics; asymptotic vanishing damping; Tikhonov regularization; strong convergence

An Evolutionary Approach for the Computation of ∈-Locally Optimal Solutions for Multi-Objective Multimodal Optimization - Hernández, Carlos; Rodriguez-Fernandez, Angel E.; Schäpermeier, Lennart; Cuate, Oliver; Trautmann, Heike; Schütze, Oliver (IEEE Transactions on Evolutionary Computation)
Keywords: Optimization; Evolutionary computation; Hands; Proposals; Convergence; Computational efficiency; Artificial intelligence; Accuracy; Approximation algorithms; Aerospace electronics; Multi-objective optimization; evolutionary algorithms; nearly optimal solutions; multimodal optimization; archiving; continuation

A note on the convergence of deterministic gradient sampling in nonsmooth optimization - Gebken, Bennet (Computational Optimization and Applications)
Abstract Approximation of subdifferentials is one of the main tasks when computing descent directions for nonsmooth optimization problems. In this article, we propose a bisection method for weakly lower semismooth functions which is able to compute new subgradients that improve a given approximation in case a direction with insufficient descent was computed. Combined with a recently proposed deterministic gradient sampling approach, this yields a deterministic and provably convergent way to approximate subdifferentials for computing descent directions.
Keywords: Applied Mathematics; Computational Mathematics; Control and Optimization

Supporting Error Chains in Static Analysis for Precise Evaluation Results and Enhanced Usability - Wickert, Anna-Katharina; Schlichtig, Michael; Vogel, Marvin; Winter, Lukas; Mezini, Mira; Bodden, Eric
Context Static analyses are well-established to aid in understanding bugs or vulnerabilities during the development process or in large-scale studies. A low false-positive rate is essential for the adaption in practice and for precise results of empirical studies. Unfortunately, static analyses tend to report where a vulnerability manifests rather than the fix location. This can cause presumed false positives or imprecise results. Method To address this problem, we designed an adaption of an existing static analysis algorithm that can distinguish between a manifestation and fix location, and reports error chains. An error chain represents at least two interconnected errors that occur successively, thus building the connection between the fix and manifestation location. We used our tool CogniCryptSUBS for a case study on 471 GitHub repositories, a performance benchmark to compare different analysis configurations, and conducted an expert interview. Result We found that 50 % of the projects with a report had at least one error chain. Our runtime benchmark demonstrated that our improvement caused only a minimal runtime overhead of less than 4 %. The results of our expert interview indicate that with our adapted version participants require fewer executions of the analysis. Conclusion Our results indicate that error chains occur frequently in real-world projects, and ignoring them can lead to imprecise evaluation results. The runtime benchmark indicates that our tool is a feasible and efficient solution for detecting error chains in real-world projects. Further, our results gave a hint that the usability of static analyses may benefit from supporting error chains.
Keywords: Static analysis; error chains; false positive re- duction; empirical studies

Heteroclinic dynamics in network dynamical systems with higher-order interactions - Bick, Christian; von der Gracht, Sören (Journal of Complex Networks)
Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.
Keywords: Applied Mathematics; Computational Mathematics; Control and Optimization; Management Science and Operations Research; Computer Networks and Communications

Exploratory Landscape Analysis for Mixed-Variable Problems - Prager, Raphael Patrick; Trautmann, Heike (IEEE Transactions on Evolutionary Computation)
Keywords: Optimization; Evolutionary computation; Benchmark testing; Hyperparameter optimization; Portfolios; Extraterrestrial measurements; Dispersion; Exploratory landscape analysis; mixed-variable problem; mixed search spaces; automated algorithm selection

Fast Convergence of Inertial Multiobjective Gradient-Like Systems with Asymptotic Vanishing Damping - Sonntag, Konstantin; Peitz, Sebastian (SIAM Journal on Optimization)
We present a new gradient-like dynamical system related to unconstrained convex smooth multiobjective optimization which involves inertial effects and asymptotic vanishing damping. To the best of our knowledge, this system is the first inertial gradient-like system for multiobjective optimization problems including asymptotic vanishing damping, expanding the ideas previously laid out in [H. Attouch and G. Garrigos, Multiobjective Optimization: An Inertial Dynamical Approach to Pareto Optima, preprint, arXiv:1506.02823, 2015]. We prove existence of solutions to this system in finite dimensions and further prove that its bounded solutions converge weakly to weakly Pareto optimal points. In addition, we obtain a convergence rate of order \(\mathcal{O}(t^{-2})\) for the function values measured with a merit function. This approach presents a good basis for the development of fast gradient methods for multiobjective optimization.
Keywords: multiobjective optimization; Pareto optimization; Lyapunov analysis; gradient-likedynamical systems; inertial dynamics; asymptotic vanishing damping; fast convergence

Finding ϵ-Locally Optimal Solutions for Multi-Objective Multimodal Optimization - Rodriguez-Fernandez, Angel E.; Schäpermeier, Lennart; Hernández, Carlos; Kerschke, Pascal; Trautmann, Heike; Schütze, Oliver (IEEE Transactions on Evolutionary Computation)
Keywords: Optimization; Evolutionary computation; Approximation algorithms; Benchmark testing; Vectors; Surveys; Pareto optimization; multi-objective optimization; evolutionary computation; multimodal optimization; local solutions

Dual-Active Bridge Sequential Pareto Optimization for Fast Pre-Design and Final Component Selection - Förster, Nikolas; Wallscheid, Oliver; Schafmeister, Frank (2024 IEEE Design Methodologies Conference (DMC))
Keywords: MOSFET; Thermal resistance; Surface resistance; Bridge circuits; Zero voltage switching; Pareto optimization; Capacitance; Numerical simulation; Optimization; Resistance heating; Pareto Optimization; Dual-Active Bridge; ZVS; Inductor Optimization; Transformer Optimization; Heat Sink Optimization

Advancements in Hybrid Additive Manufacturing: Integrating SLM and LMD for High-Performance Applications - Chalicheemalapalli Jayasankar, Deviprasad; Gnaase, Stefan; Kaiser, Maximilian Alexander; Lehnert, Dennis; Tröster, Thomas (Metals)
Additive manufacturing (AM) technologies enable near-net-shape designs and demand-oriented material usage, which significantly minimizes waste. This points to a substantial opportunity for further optimization in material savings and process design. The current study delves into the advancement of sustainable manufacturing practices in the automotive industry, emphasizing the crucial role of lightweight construction concepts and AM technologies in enhancing resource efficiency and reducing greenhouse gas emissions. By exploring the integration of novel AM techniques such as selective laser melting (SLM) and laser metal deposition (LMD), the study aims to overcome existing limitations like slow build-up rates and limited component resolution. The study’s core objective revolves around the development and validation of a continuous process chain that synergizes different AM routes. In the current study, the continuous process chain for DMG MORI Lasertec 65 3D’s LMD system and the DMG MORI Lasertec 30 3D’s was demonstrated using 316L and 1.2709 steel materials. This integrated approach is designed to significantly curtail process times and minimize component costs, thus suggesting an industry-oriented process chain for future manufacturing paradigms. Additionally, the research investigates the production and material behavior of components under varying manufacturing processes, material combinations, and boundary layer materials. The culmination of this study is the validation of the proposed process route through a technology demonstrator, assessing its scalability and setting a benchmark for resource-efficient manufacturing in the automotive sector.
Keywords: additive manufacturing (AM); selective laser melting (SLM); laser metal deposition (LMD); hybrid manufacturing; process optimization; 316L; 1.2709

Neural Networks as Black-Box Benchmark Functions Optimized for Exploratory Landscape Features - Prager, Raphael Patrick; Dietrich, Konstantin; Schneider, Lennart; Schäpermeier, Lennart; Bischl, Bernd; Kerschke, Pascal; Trautmann, Heike; Mersmann, Olaf (Proceedings of the 17th ACM/SIGEVO Conference on Foundations of Genetic Algorithms)
Artificial benchmark functions are commonly used in optimization research because of their ability to rapidly evaluate potential solutions, making them a preferred substitute for real-world problems. However, these benchmark functions have faced criticism for their limited resemblance to real-world problems. In response, recent research has focused on automatically generating new benchmark functions for areas where established test suites are inadequate. These approaches have limitations, such as the difficulty of generating new benchmark functions that exhibit exploratory landscape analysis (ELA) features beyond those of existing benchmarks.The objective of this work is to develop a method for generating benchmark functions for single-objective continuous optimization with user-specified structural properties. Specifically, we aim to demonstrate a proof of concept for a method that uses an ELA feature vector to specify these properties in advance. To achieve this, we begin by generating a random sample of decision space variables and objective values. We then adjust the objective values using CMA-ES until the corresponding features of our new problem match the predefined ELA features within a specified threshold. By iteratively transforming the landscape in this way, we ensure that the resulting function exhibits the desired properties. To create the final function, we use the resulting point cloud as training data for a simple neural network that produces a function exhibiting the target ELA features. We demonstrate the effectiveness of this approach by replicating the existing functions of the well-known BBOB suite and creating new functions with ELA feature values that are not present in BBOB.
Keywords: Benchmarking; Instance Generator; Black-Box Continuous Optimization; Exploratory Landscape Analysis; Neural Networks

On the Impact of Basic Mutation Operators and Populations within Evolutionary Algorithms for the Dynamic Weighted Traveling Salesperson Problem - Bossek, Jakob; Neumann, Aneta; Neumann, Frank (Proceedings of the Genetic and Evolutionary Computation Conference)
Evolutionary algorithms have been shown to obtain good solutions for complex optimization problems in static and dynamic environments. It is important to understand the behaviour of evolutionary algorithms for complex optimization problems that also involve dynamic and/or stochastic components in a systematic way in order to further increase their applicability to real-world problems. We investigate the node weighted traveling salesperson problem (W-TSP), which provides an abstraction of a wide range of weighted TSP problems, in dynamic settings. In the dynamic setting of the problem, items that have to be collected as part of a TSP tour change over time. We first present a dynamic setup for the dynamic W-TSP parameterized by different types of changes that are applied to the set of items to be collected when traversing the tour. Our first experimental investigations study the impact of such changes on resulting optimized tours in order to provide structural insights of optimization solutions. Afterwards, we investigate simple mutation-based evolutionary algorithms and study the impact of the mutation operators and the use of populations with dealing with the dynamic changes to the node weights of the problem.
Keywords: dynamic optimization; evolutionary algorithms; re-optimization; weighted traveling salesperson problem

Global smooth solutions in a three-dimensional cross-diffusive SIS epidemic model with saturated taxis at large densities - Tao, Youshan; Winkler, Michael (Evolution Equations and Control Theory)
Keywords: Applied Mathematics; Control and Optimization; Modeling and Simulation

Turnpike Property in Optimal Microbial Metabolite Production - Caillau, Jean-Baptiste; Djema, Walid; Gouzé, Jean-Luc; Maslovskaya, Sofya; Pomet, Jean-Baptiste (Journal of Optimization Theory and Applications)
Abstract We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP). According to Pontryagin’s maximum principle, optimal solutions are concatenations of singular and bang arcs and exhibit the chattering or Fuller phenomenon, which is problematic for applications. To avoid chattering, we introduce a reduced model which is still biologically relevant and retains the important structural features of the original problem. Using a combination of analytical and numerical methods, we show that the singular arc is dominant in the studied DOCPs and exhibits the turnpike property. This property is further used in order to design simple and realistic suboptimal control strategies.
Keywords: Applied Mathematics; Management Science and Operations Research; Control and Optimization

BBE: Basin-Based Evaluation of Multimodal Multi-objective Optimization Problems - Heins, Jonathan; Rook, Jeroen; Schäpermeier, Lennart; Kerschke, Pascal; Bossek, Jakob; Trautmann, Heike (Parallel Problem Solving from Nature (PPSN XVII))
In multimodal multi-objective optimization (MMMOO), the focus is not solely on convergence in objective space, but rather also on explicitly ensuring diversity in decision space. We illustrate why commonly used diversity measures are not entirely appropriate for this task and propose a sophisticated basin-based evaluation (BBE) method. Also, BBE variants are developed, capturing the anytime behavior of algorithms. The set of BBE measures is tested by means of an algorithm configuration study. We show that these new measures also transfer properties of the well-established hypervolume (HV) indicator to the domain of MMMOO, thus also accounting for objective space convergence. Moreover, we advance MMMOO research by providing insights into the multimodal performance of the considered algorithms. Specifically, algorithms exploiting local structures are shown to outperform classical evolutionary multi-objective optimizers regarding the BBE variants and respective trade-off with HV.
Keywords: Anytime behavior; Benchmarking; Continuous optimization; Multi-objective optimization; Multimodality; Performance metric

On the Potential of Automated Algorithm Configuration on Multi-Modal Multi-Objective Optimization Problems - Rook, Jeroen; Trautmann, Heike; Bossek, Jakob; Grimme, Christian (Proceedings of the Genetic and Evolutionary Computation Conference Companion)
Hardness of Multi-Objective (MO) continuous optimization problems results from an interplay of various problem characteristics, e. g. the degree of multi-modality. We present a benchmark study of classical and diversity focused optimizers on multi-modal MO problems based on automated algorithm configuration. We show the large effect of the latter and investigate the trade-off between convergence in objective space and diversity in decision space.
Keywords: configuration; multi-modality; multi-objective optimization

Accessibility properties of abnormal geodesics in optimal control illustrated by two case studies - Bonnard, Bernard; Rouot, Jérémy; Wembe Moafo, Boris Edgar (Mathematical Control and Related Fields)
Keywords: Applied Mathematics; Control and Optimization; General Medicine

Neural Network-Based Demand-Side Management in a Stand-Alone Solar PV-Battery Microgrid Using Load-Shifting and Peak-Clipping - Philipo, Godiana Hagile; Kakande, Josephine Nakato; Krauter, Stefan (Energies)
Due to failures or even the absence of an electricity grid, microgrid systems are becoming popular solutions for electrifying African rural communities. However, they are heavily stressed and complex to control due to their intermittency and demand growth. Demand side management (DSM) serves as an option to increase the level of flexibility on the demand side by scheduling users’ consumption patterns profiles in response to supply. This paper proposes a demand-side management strategy based on load shifting and peak clipping. The proposed approach was modelled in a MATLAB/Simulink R2021a environment and was optimized using the artificial neural network (ANN) algorithm. Simulations were carried out to test the model’s efficacy in a stand-alone PV-battery microgrid in East Africa. The proposed algorithm reduces the peak demand, smoothing the load profile to the desired level, and improves the system’s peak to average ratio (PAR). The presence of deferrable loads has been considered to bring more flexible demand-side management. Results promise decreases in peak demand and peak to average ratio of about 31.2% and 7.5% through peak clipping. In addition, load shifting promises more flexibility to customers.
Keywords: Energy (miscellaneous); Energy Engineering and Power Technology; Renewable Energy; Sustainability and the Environment; Electrical and Electronic Engineering; Control and Optimization; Engineering (miscellaneous); Building and Construction

Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems - Schön, Oliver; Götte, Ricarda-Samantha; Timmermann, Julia (14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022))
While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose a physics-guided hybrid approach for modeling non-autonomous systems under control. Starting from a traditional physics-based model, this is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy yielding physically plausible models. While purely data-driven methods fail to produce satisfying results, experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model.
Keywords: neural networks; physics-guided; data-driven; multi-objective optimization; system identification; machine learning; dynamical systems