Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such ...problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution.
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special ...structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra.
Here is a hands-on treatment of the subject of optimization, recommended for use by industry professionals, scientists, and students interested in optimization algorithms and their various ...applications. It provides a complete teaching package with MATLAB exercises and online solutions to end-of-chapter problems.
Optimal Transport Villani, Cédric
2009, 2008, 2008-09-24, Volume:
338
eBook
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th ...century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.
Discrete optimization problems are everywhere, from traditional operations research planning (scheduling, facility location and network design); to computer science databases; to advertising issues ...in viral marketing. Yet most such problems are NP-hard; unless P = NP, there are no efficient algorithms to find optimal solutions. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first section is devoted to a single algorithmic technique applied to several different problems, with more sophisticated treatment in the second section. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithm courses, it will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems.
In the design of low-energy buildings, mathematical optimisation has proven to be a powerful tool for minimising energy consumption. Simulation-based optimisation methods are widely employed due to ...the nonlinear thermal behaviour of buildings. However, finding high-quality solutions with reasonable computational cost remains a significant challenge in the building industry.
In this paper, Ant Colony Optimisation for continuous domain (ACOR) is developed and applied to optimise a commercial building in Australia. The results for a typical commercial building showed that optimisation can achieve an additional energy savings of more than 11.4%, even after some common energy saving measures were implemented (e.g. double pane windows). The performance of ACOR was compared to three benchmark optimisation algorithms: Nelder-Mead (NM) algorithm, Particle Swarm Optimisation with Inertia Weight (PSOIW) and the hybrid Particle Swarm Optimisation and Hooke-Jeeves (PSO-HJ). This comparison showed that ACOR was able to consistently find better solutions in less time than the benchmark algorithms. The findings demonstrate that ACOR can further facilitate the design of low-energy buildings.
The design of permanent magnet synchronous motor (PMSM) is a constrained multi-objective problem, and there are often conflicts between the goals. Aiming at the complexity of PMSM optimisation and a ...large number of variables, multi-objective optimisation design of PMSM using a multi-objective comprehensive teaching algorithm (MCTA) is proposed. This algorithm is improved based on the teaching–learning-based optimisation algorithm and can better adapt to large-scale sample space and multivariate optimisation. Also, based on a magnetic equivalent circuit, a static electromagnetic model of the radial magnetic field PMSM is derived, and the design requirements and goals of the PMSM are analysed. In the two PMSM multi-objective optimisation calculation processes, the optimal solution was calculated based on the composite fitness function and Pareto front, respectively. The results of the MCTA were compared with other natural optimisation algorithms. Finally, according to the optimisation results of two sets of experiments, the correctness of the optimal solution of the algorithm was verified by finite element analysis and actual measurement of the prototype. The analysis of results shows the effectiveness, simplicity, and inspiration of MCTA in the PMSM multi-objective structure optimisation design.
Wave energy technologies have the potential to play a significant role in the supply of renewable energy worldwide. One of the most promising designs for wave energy converters (WECs) are fully ...submerged buoys. In this paper, we explore the optimisation of WEC arrays consisting of three-tether buoys.
Such arrays can be optimised for total energy output by adjusting the relative positions of buoys in a wave farm. As there are complex hydrodynamic interactions among WECs, the evaluation of each parameter setting is computationally expensive and thus limits the feasible number of full model evaluations that can be made. Furthermore, these WEC interactions make up a non-convex, multi-modal (with multiple local-optima), continuous and constrained optimisation problem. This problem is challenging to solve using optimisation methods. To tackle the challenge of optimising the positions of WECs in a wave farm, we propose a novel multi-swarm cooperative co-evolution algorithm which consists of three meta-heuristics: the multi verse optimiser (MVO) algorithm, the equilibrium optimisation (EO) method, and the moth flame optimisation (MFO) approach with a backtracking strategy, we introduce a fast, effective new surrogate model to speed up the process of optimisation.
To assess the effectiveness of our proposed approach, 11 state-of-the-art bio-inspired algorithms and three recent hybrid heuristic techniques were compared in six real wave situations located on the coasts of Australia, with two wave farm sizes (four and nine WECs).
The experimental study presented in this paper shows that our hybrid cooperative framework exhibited the best performance in terms of the quality of obtained solutions, computational efficiency, and convergence speed compared with other 14 state-of-the-art meta-heuristics. Furthermore, we found that the power output of the best-found 9-buoy arrangements were higher than that of perpendicular layouts at at 4.15%, 3.29%, 3.62%, 9.2%, 5.74%, and 2.43% for the Perth, Adelaide, Sydney, Tasmania, Brisbane, and Darwin wave sites, respectively. Our investigations reveal that the best-found arrangement at the Tasmania wave site was able to absorb the highest level of wave power relative to the other locations.
•A new Multi-swarm Cooperative optimisation framework is proposed to optimise wave farms performance.•A new fast surrogate model is developed to speed up expensive optimisation process of wave farm.•To improve the placement of converters, a symmetrical backtracking search algorithm is proposed.•To handle the infeasible wave converters layout during the optimisation, a new and effective repair function is developed.•The proposed optimiser enhances significantly the total power output at six wave farms compared with previous methods.
This book, a result of the author's teaching and research experience in various universities and institutes over the past ten years, can be used as a textbook for an optimization course for graduates ...and senior undergraduates. It systematically describes optimization theory and several powerful methods, including recent results. For most methods, the authors discuss an idea s motivation, study the derivation, establish the global and local convergence, describe algorithmic steps, and discuss the numerical performance. The book deals with both theory and algorithms of optimization concurrently. It also contains an extensive bibliography. Finally, apart from its use for teaching, Optimization Theory and Methods will be very beneficial as a research reference.
This book is devoted to vector or multiple criteria approaches in optimization. Topics covered include: vector optimization, vector variational inequalities, vector variational principles, vector ...minmax inequalities and vector equilibrium problems. In particular, problems with variable ordering relations and set-valued mappings are treated. The nonlinear scalarization method is extensively used throughout the book to deal with various vector-related problems. The results presented are original and should be interesting to researchers and graduates in applied mathematics and operations research. Readers will benefit from new methods and ideas for handling multiple criteria decision problems.
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