Related papers: Quantifying Non-linearity in Topology Optimization…
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
Time-Optimal Path Parameterization (TOPP) is a well-studied problem in robotics and has a wide range of applications. There are two main families of methods to address TOPP: Numerical Integration (NI) and Convex Optimization (CO). NI-based…
This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…
In topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads…
An appropriate visualization of multiobjective non-dominated solutions is a valuable asset for decision making. Although there are methods for visualizing the solutions in the design space, they do not provide any information about their…
Stochastic optimization is an important task in many optimization problems where the tasks are not expressible as convex optimization problems. In the case of non-convex optimization problems, various different stochastic algorithms like…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Topology optimization facilitates the automated design of high-performance structures across various engineering fields but, if unconstrained, often produces designs that are complex and difficult to manufacture. A key attribute of the…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
This paper presents a density-based topology optimization approach to design structures under self-weight load. Such loads change their magnitude and/or location as the topology optimization advances and pose several unique challenges,…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry…
In topology optimization, the state of structures is typically obtained by numerically evaluating a discretized PDE-based model. The degrees of freedom of such a model can be partitioned in free and prescribed sets to define the boundary…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…
Recovering nonlinearly degraded signal in the presence of noise is a challenging problem. In this work, this problem is tackled by minimizing the sum of a non convex least-squares fit criterion and a penalty term. We assume that the…
The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…
With the rapid adoption of machine learning techniques for large-scale applications in science and engineering comes the convergence of two grand challenges in visualization. First, the utilization of black box models (e.g., deep neural…