Applying Hybrid PSO to Optimize Directional Overcurrent Relay Coordination in Variable Network Topologies

In power systems, determining the values of time dial setting (TDS) and the plug setting (PS) for directional overcurrent relays (DOCRs) is an extremely constrained optimization problem that has been previously described and solved as a nonlinear programming problem. Optimization coordination problems of near-end faults and far-end faults occurring simultaneously in circuits with various topologies, including fixed and variable network topologies, are considered in this study. The aim of this study was to apply the Nelder-Mead (NM) simplex search method and particle swarm optimization (PSO) to solve this optimization problem. The proposed NM-PSO method has the advantage of NM algorithm, with a quicker movement toward optimal solution, as well as the advantage of PSO algorithm in the ability to obtain globally optimal solution. Neither a conventional PSO nor the proposed NM-PSO method is capable of dealing with constrained optimization problems. Therefore, we use the gradient-based repair method embedded in a conventional PSO and the proposed NM-PSO. This study used an IEEE 8-bus test system as a case study to compare the convergence performance of the proposed NM-PSO method and a conventional PSO approach. The results demonstrate that a robust and optimal solution can be obtained efficiently by implementing the proposal

Benchopt: Reproducible, efficient and collaborative optimization benchmarks

Numerical validation is at the core of machine learning research as it allows to assess the actual impact of new methods, and to confirm the agreement between theory and practice. Yet, the rapid development of the field poses several challenges: researchers are confronted with a profusion of methods to compare, limited transparency and consensus on best practices, as well as tedious re-implementation work. As a result, validation is often very partial, which can lead to wrong conclusions that slow down the progress of research. We propose Benchopt, a collaborative framework to automate, reproduce and publish optimization benchmarks in machine learning across programming languages and hardware architectures. Benchopt simplifies benchmarking for the community by providing an off-the-shelf tool for running, sharing and extending experiments. To demonstrate its broad usability, we showcase benchmarks on three standard learning tasks: $\ell_2$-regularized logistic regression, Lasso, and ResNet18 training for image classification. These benchmarks highlight key practical findings that give a more nuanced view of the state-of-the-art for these problems, showing that for practical evaluation, the devil is in the details. We hope that Benchopt will foster collaborative work in the community hence improving the reproducibility of research findings.Comment: Accepted in proceedings of NeurIPS 22; Benchopt library documentation is available at https://benchopt.github.io

Multidelity methods for multidisciplinary system design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 211-220).Optimization of multidisciplinary systems is critical as slight performance improvements can provide significant benefits over the system's life. However, optimization of multidisciplinary systems is often plagued by computationally expensive simulations and the need to iteratively solve a complex coupling-relationship between subsystems. These challenges are typically severe enough as to prohibit formal system optimization. A solution is to use multi- fidelity optimization, where other lower-fidelity simulations may be used to approximate the behavior of the higher-fidelity simulation. Low-fidelity simulations are common in practice, for instance, simplifying the numerical simulations with additional physical assumptions or coarser discretizations, or creating direct metamodels such as response surfaces or reduced order models. This thesis offers solutions to two challenges in multidisciplinary system design optimization: developing optimization methods that use the high-fidelity analysis as little as possible but ensure convergence to a high-fidelity optimal design, and developing methods that exploit multifidelity information in order to parallelize the optimization of the system and reduce the time needed to find an optimal design. To find high-fidelity optimal designs, Bayesian model calibration is used to improve low- fidelity models and systematically reduce the use of high-fidelity simulation. The calibrated low-fidelity models are optimized and using appropriate calibration schemes convergence to a high-fidelity optimal design is established. These calibration schemes can exploit high- fidelity gradient information if available, but when not, convergence is still demonstrated for a gradient-free calibration scheme. The gradient-free calibration is novel in that it enables rigorous optimization of high-fidelity simulations that are black-boxes, may fail to provide a solution, contain some noise in the output, or are experimental. In addition, the Bayesian approach enables us to combine multiple low-fidelity simulations to best estimate the high- fidelity function without nesting. Example results show that for both aerodynamic and structural design problems this approach leads to about an 80% reduction in the number of high-fidelity evaluations compared with single-fidelity optimization methods. To enable parallelized multidisciplinary system optimization, two approaches are developed. The first approach treats the system design problem as a bilevel programming problem and enables each subsystem to be designed concurrently. The second approach optimizes surrogate models of each discipline that are all constructed in parallel. Both multidisciplinary approaches use multifidelity optimization and the gradient-free Bayesian model calibration technique, but will exploit gradients when they are available. The approaches are demonstrated on an aircraft wing design problem, and enable optimization of the system in reasonable time despite lack of sensitivity information and 19% of evaluations failing. For cases when comparable algorithms are available, these approaches reduce the time needed to find an optimal design by approximately 50%.by Andrew I. March.Ph.D

Bilevel programming and applications

A great amount of new applied problems in the area of energy networks has recently arisen that can be efficiently solved only as mixed-integer bilevel programs. Among them are the natural gas cash-out problem, the deregulated electricity market equilibrium problem, biofuel problems, a problem of designing coupled energy carrier networks, and so forth, if we mention only part of such applications. Bilevel models to describe migration processes are also in the list of the most popular new themes of bilevel programming, as well as allocation, information protection, and cybersecurity problems. This survey provides a comprehensive review of some of the above-mentioned new areas including both theoretical and applied results

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Seeking multiple solutions:an updated survey on niching methods and their applications

Multi-Modal Optimization (MMO) aiming to locate multiple optimal (or near-optimal) solutions in a single simulation run has practical relevance to problem solving across many fields. Population-based meta-heuristics have been shown particularly effective in solving MMO problems, if equipped with specificallydesigned diversity-preserving mechanisms, commonly known as niching methods. This paper provides an updated survey on niching methods. The paper first revisits the fundamental concepts about niching and its most representative schemes, then reviews the most recent development of niching methods, including novel and hybrid methods, performance measures, and benchmarks for their assessment. Furthermore, the paper surveys previous attempts at leveraging the capabilities of niching to facilitate various optimization tasks (e.g., multi-objective and dynamic optimization) and machine learning tasks (e.g., clustering, feature selection, and learning ensembles). A list of successful applications of niching methods to real-world problems is presented to demonstrate the capabilities of niching methods in providing solutions that are difficult for other optimization methods to offer. The significant practical value of niching methods is clearly exemplified through these applications. Finally, the paper poses challenges and research questions on niching that are yet to be appropriately addressed. Providing answers to these questions is crucial before we can bring more fruitful benefits of niching to real-world problem solving

Geometric numerical integration for optimisation

In this thesis, we study geometric numerical integration for the optimisation of various classes of functionals. Numerical integration and the study of systems of differential equations have received increased attention within the optimisation community in the last decade, as a means for devising new optimisation schemes as well as to improve our understanding of the dynamics of existing schemes. Discrete gradient methods from geometric numerical integration preserve structures of first-order gradient systems, including the dissipative structure of schemes such as gradient flows, and thus yield iterative methods that are unconditionally dissipative, i.e. decrease the objective function value for all time steps. We look at discrete gradient methods for optimisation in several settings. First, we provide a comprehensive study of discrete gradient methods for optimisation of continuously differentiable functions. In particular, we prove properties such as well-posedness of the discrete gradient update equation, convergence rates, convergence of the iterates, and propose methods for solving the discrete gradient update equation with superior stability and convergence rates. Furthermore, we present results from numerical experiments which support the theory. Second, motivated by the existence of derivative-free discrete gradients, and seeking to solve nonsmooth optimisation problems and more generally black-box problems, including for parameter optimisation problems, we propose methods based on the Itoh--Abe discrete gradient method for solving nonconvex, nonsmooth optimisation problems with derivative-free methods. In this setting, we prove well-posedness of the method, and convergence guarantees within the nonsmooth, nonconvex Clarke subdifferential framework for locally Lipschitz continuous functions. The analysis is shown to hold in various settings, namely in the unconstrained and constrained setting, including epi-Lipschitzian constraints, and for stochastic and deterministic optimisation methods. Building on the work of derivative-free discrete gradient methods and the concept of structure preservation in geometric numerical integration, we consider discrete gradient methods applied to other differential systems with dissipative structures. In particular, we study the inverse scale space flow, linked to the well-known Bregman methods, which are central to variational optimisation problems and regularisation methods for inverse problems. In this setting, we propose and implement derivative-free schemes that exploit structures such as sparsity to achieve superior convergence rates in numerical experiments, and prove convergence guarantees for these methods in the nonsmooth, nonconvex setting. Furthermore, these schemes can be seen as generalisations of the Gauss-Seidel method and successive-over-relaxation. Finally, we return to parameter optimisation problems, namely nonsmooth bilevel optimisation problems, and propose a framework to employ first-order methods for these problems, when the underlying variational optimisation problem admits a nonsmooth structure in the partial smoothness framework. In this setting, we prove piecewise differentiability of the parameter-dependent solution mapping, and study algorithmic differentiation approaches to evaluating the derivatives. Furthermore, we prove that the algorithmic derivatives converge to the implicit derivatives. Thus we demonstrate that, although some parameter tuning problems must inevitably be treated as black-box optimisation problems, for a large number of variational problems one can exploit the structure of nonsmoothness to perform gradient-based bilevel optimisation

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference