Applications – Science and Engineering

Solving nonlinear systems of equations via spectral residual methods: stepsize selection and applications

Categories Mechanical Engineering, Nonlinear Systems and Least-Squares

Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a … Read more

Reliable Frequency Regulation through Vehicle-to-Grid: Encoding Legislation with Robust Constraints

Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Robust Optimization Tags , , , , ,

Problem definition: Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to electricity grids. We formulate a robust optimization problem that maximizes a vehicle owner’s expected profit from selling primary frequency regulation to the grid and guarantees that market commitments are met at all times for all frequency … Read more

A tactical maintenance optimization model for multiple interconnected energy production systems

Categories (Mixed) Integer Linear Programming, Facility Planning and Design Tags , , , ,

Multiple interconnected energy production systems are a common solution to satisfy the energy demand of industrial processes. Such energy demand is usually the combination of various energy types such as heat and electricity. This implies the installation of different technologies able to produce one or multiple energy types, to satisfy all energy needs. However, multiple … Read more

Solving Large-Scale Sparse PCA to Certifiable (Near) Optimality

Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming, Statistics Tags , , ,

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply certifiably optimal principal components with more than $p=100s$ of variables. By reformulating sparse PCA as a convex mixed-integer semidefinite optimization problem, we design a … Read more

Optimising the assignment of swabs and reagents for PCR testing during a viral epidemic

Categories Applications - OR and Management Sciences, Applications - Science and Engineering Tags , ,

Early large-scale swab testing is a fundamental tool for health authorities to assess the prevalence of a virus and enact appropriate mitigation measures during an epidemic. The COVID-19 pandemic has shown that the availability of chemical reagents required to carry out the tests is often a bottleneck in increasing a country’s testing capacity. Further, demand … Read more

Data Approximation by L1 Spline Fits with Free Knots

Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Nonlinear Optimization

L1 spline fits are a class of spline models that have shown advantages in approximating irregular and multiscale data. This paper investigates the knot placement problem of L1 spline fits under two scenarios. If the number of knots is given, we propose an augmented Lagrangian method to solve the bilevel L1 spline fit problem and … Read more

Enhancements to the DIDO© Optimal Control Toolbox

Categories Applications - Science and Engineering, Optimization Software and Modeling Systems, Optimization Software Design Principles Tags , , , ,

In 2020, DIDO© turned 20! The software package emerged in 2001 as a basic, user-friendly MATLAB teaching tool to illustrate the various nuances of Pontryagin’s Principle but quickly rose to prominence in 2007 after NASA announced it had executed a globally optimal maneuver using DIDO. Since then, the toolbox has grown in applications well beyond … Read more

Mixed-Integer Nonlinear Optimization for District Heating Network Expansion

Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , ,

We present a mixed-integer nonlinear optimization model for computing the optimal expansion of an existing tree-shaped district heating network given a number of potential new consumers. To this end, we state a stationary and nonlinear model of all hydraulic and thermal effects in the pipeline network as well as nonlinear models for consumers and the … Read more

High Dimensional Three-Periods Locally Ideal MIP Formulations for the UC Problem

Categories (Mixed) Integer Nonlinear Programming, Energy, Scheduling Tags , , , ,

The thermal unit commitment (UC) problem often can be formulated as a mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. The tighter characteristic re-duces the search space, therefore, as a natural conse-quence, significantly reduces the computational burden. In the literature, many tightened formulations for single units with parts … Read more

Modular-topology optimization with Wang tilings: An application to truss structures

Categories Civil and Environmental Engineering, Convex Optimization, Meta Heuristics Tags , , , ,

Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic Unit Cell (PUC) and the efficacy of non-uniform designs in multi-scale material optimization. Here, we introduce a novel strategy for concurrent minimum-compliance design of … Read more