Penalty-based heuristic direct method for constrained global optimization

This paper is concerned with an extension of the heuristic DIRECT method, presented in[8], to solve nonlinear constrained global optimization (CGO) problems. Using a penalty strategy based on a penalty auxiliary function, the CGO problem is transformed into a bound constrained problem. We have analyzed the performance of the proposed algorithm using fixed values of the penalty parameter, and we may conclude that the algorithm competes favourably with other DIRECT-type algorithms in the literature.The authors wish to thank two anonymous referees for their comments and suggestions to improve the paper. This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the R&D Units Project Scope: UIDB/00319/2020, UIDB/00013/2020 and UIDP/00013/2020 of CMAT-UM

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity

On grid aware refinement of the unit hypercube and simplex: Focus on the complete tree size

Branch and bound (BnB) Global Optimization algorithms can be used to find the global optimum (minimum) of a multiextremal function over the unit hypercube and unit simplex with a guaranteed accuracy. Subdivision strategies can take the information of the evaluated points into account leading to irregular shaped subsets. This study focuses on the passive generation of spatial subdivisions aiming at evaluating points on a predefined grid. The efficiency measure is in terms of the complete tree size, or worst case BnB scenario, with a termination criterion on the subset size. Longest edge bisection is used as a benchmark. It is shown that taking the grid for a given termination tolerance into account, other general partitions exist that improve the BnB upper bound on the number of evaluated points and subsets

On trajectory optimization of an electric vehicle

The efficient control of electrical vehicles may contribute to sustainable use of energy. In recent studies, a model has been analyzed and several algorithms based on branch and bound have been presented. In this work, we discuss a reformulated model on the control of an electric vehicle based on the minimization of the energy consumption during an imposed displacement. We will show that similar results can be obtained by applying standard software. Moreover, this paper shows that the specified control problem can be handled from a dynamic programming perspective.This paper has been supported by The Spanish Ministry (RTI2018-095993) in part financed by the European Regional Development Fund (ERDF) and by FCT – Fundação para a Ciência e Tecnologia within the Project Scope: UID/CEC/00319/2019

Uncertainty from Model Calibration: Applying a New Method to Transport Energy Demand Modelling

Uncertainties in energy demand modelling originate from both limited understanding of the real-world system and a lack of data for model development, calibration and validation. These uncertainties allow for the development of different models, but also leave room for different calibrations of a single model. Here, an automated model calibration procedure was developed and tested for transport sector energy use modelling in the TIMER 2.0 global energy model. This model describes energy use on the basis of activity levels, structural change and autonomous and priceinduced energy efficiency improvements. We found that the model could reasonably reproduce historic data under different sets of parameter values, leading to different projections of future energy demand levels. Projected energy use for 2030 shows a range of 44–95% around the best-fit projection. Two different model interpretations of the past can generally be distinguished: (1) high useful energy intensity and major energy efficiency improvements or (2) low useful energy intensity and little efficiency improvement. Generally, the first lead to higher future energy demand levels than the second, but model and insights do not provide decisive arguments to attribute a higher likelihood to one of the alternatives.Delft Center for Systems and ControlMechanical, Maritime and Materials Engineerin

Models for Hyperspectral Image Analysis: From Unmixing to Object-Based Classification

International audienceThe recent advances in hyperspectral remote sensing technology allow the simultaneous acquisition of hundreds of spectral wavelengths for each image pixel. This rich spectral information of the hyperspectral data makes it possible to discriminate different physical substances, leading to a potentially more accurate classification and thus opening the door to numerous new applications. Throughout the history of remote sensing research, numerous methods for hyperspectral image analysis have been presented. Depending on the spatial resolution of the images, specific mathematical models must be designed to effectively analyze the imagery. Some of these models operate at a sub-pixel level, trying to decompose a mixed spectral signature into its pure constituents, while others operate at a pixel or even object level, seeking to assign unique labels to every pixel or object in the scene. The spectral mixing of the measurements and the high dimensionality of the data are some of the challenging features of hyperspectral imagery. This chapter presents an overview of unmixing and classification methods, intended to address these challenges for accurate hyperspectral data analysis