Robust and Constrained Optimization: Methods and Applications

Dewey Clark (Editor)

Series: Mathematics Research Developments
BISAC: MAT042000




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In recent years, the volume of available data has grown exponentially and paved the way for new models in decision-making, particularly decision making under uncertainty. Thus, the opening chapter of Robust and Constrained Optimization: Methods and Applications introduces different robust models induced by three well-known data-driven uncertainty sets: distributional, clustering-oriented, and cutting hyperplanes uncertainty sets.
Following this, the authors describe a model of an uncertain vector optimization problem and define robust solutions. Scalarization and vectorization techniques are proposed as efficient ways to compute robust solutions.
In one study, a rain-fall optimization algorithm has been applied as a new naturally-inspired algorithm based on the behavior of raindrops. This algorithm has been developed with the goal of finding a simpler and more effective search algorithm to optimize multi-dimensional numerical test functions. The process considers the numerical differential of the cost function rather than the mathematical computation of the gradient.
The authors examine the preconditioned iterative solution of a particular type of linear systems, mainly involving matrices of a two-by-two block form with square matrix blocks. Such systems arise in the finite element solution of optimal control problems for partial differential equations in various applications.
Finally, it is shown how various metaheuristic algorithms (including memetic, interval, and random search optimization methods) can be applied to solve different types of optimal control problems (e.g., satellite stabilization, solar sail control, interception problems). Hybrid global optimization methods, which combine strategies from several different metaheuristic random search algorithms, are suggested in an attempt to improve accuracy of the obtained solution. (Imprint: Nova)


Chapter 1. Data Driven Robust Optimization
(Moahammad Namakshenas and Mir Saman Pishvaee, School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran)

Chapter 2. Robust Approaches to Uncertain Vector Optimization Problems
(Elisabeth Köbis. Martin-Luther-University Halle-Wittenberg, Faculty of Natural Sciences II, Institute of Mathematics, Halle, Germany)

Chapter 3. A Rain-Fall Inspired Optimization Algorithm for Optimal Load Dispatch in Power System
(S. Hr. Aghay Kaboli and A. K. Alqallaf, University Malaya Power Energy Dedicated Advanced Centre (UMPEDAC), UM, Kuala Lumpur, Malaysia, and others)

Chapter 4. Preconditioned Iterative Solution Methods for Linear Systems Arising in PDE-Constrained Optimization
(Owe Axelsson, Maya Neytcheva and János Karátson, Institute of Geonics, Czech Academy of Sciences, Ostrava, Czech Republic, and others)

Chapter 5. Application of Metaheuristic Algorithms of Global Constrained Optimization to Optimal Open Loop Control Problems
(A. Panteleev and V. Panovskiy, Moscow Aviation Institute, Moscow, Russia


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