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.
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.
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.
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.
A guide to modern optimization applications and techniques in newly emerging areas spanning optimization, data science, machine intelligence, engineering, and computer sciences Optimization ...Techniques and Applications with Examples introduces the fundamentals of all the commonly used techniquesin optimization that encompass the broadness and diversity of the methods (traditional and new) and algorithms. The author—a noted expert in the field—covers a wide range of topics including mathematical foundations, optimization formulation, optimality conditions, algorithmic complexity, linear programming, convex optimization, and integer programming. In addition, the book discusses artificial neural network, clustering and classifications, constraint- handling, queueing theory, support vector machine and multi-objective optimization, evolutionary computation, nature-inspired algorithms and many other topics. Designed as a practical resource, all topics are explained in detail with step-by-step examples to show how each method works. The book's exercises test the acquired knowledge that can be potentially applied to real problem solving. By taking an informal approach to the subject, the author helps readers to rapidly acquire the basic knowledge in optimization, operational research, and applied data mining. This important resource: * Offers an accessible and state-of-the-art introduction to the main optimization techniques * Contains both traditional optimization techniques and the most current algorithms and swarm intelligence-based techniques * Presents a balance of theory, algorithms, and implementation * Includes more than 100 worked examples with step-by-step explanations Written for upper undergraduates and graduates in a standard course on optimization, operations research and data mining, Optimization Techniques and Applications with Examples is a highly accessible guide to understanding the fundamentals of all the commonly used techniquesin optimization.
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•This paper examines various aerodynamic optimisation methods.•Benefits and drawback of architectures are discussed relating to aerodynamic optimisation.•Difficulties and ...applicability of algorithms to different design criteria are highlighted.
Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners.
•Three binary versions of Grasshopper Optimization Algorithm (BGOA) are proposed.•Wrapper-based feature selection techniques are proposed using the BGOA algorithms.•The proposed algorithms are ...benchmarked on 18 standard UCI datasets.•The results are compared with 10 algorithms.•The results show the merits of the proposed algorithms and feature selection methods.
Feature Selection (FS) is a challenging machine learning-related task that aims at reducing the number of features by removing irrelevant, redundant and noisy data while maintaining an acceptable level of classification accuracy. FS can be considered as an optimisation problem. Due to the difficulty of this problem and having a large number of local solutions, stochastic optimisation algorithms are promising techniques to solve this problem. As a seminal attempt, binary variants of the recent Grasshopper Optimisation Algorithm (GOA) are proposed in this work and employed to select the optimal feature subset for classification purposes within a wrapper-based framework. Two mechanisms are employed to design a binary GOA, the first one is based on Sigmoid and V-shaped transfer functions, and will be indicated by BGOA-S and BGOA-V, respectively. While the second mechanism uses a novel technique that combines the best solution obtained so far. In addition, a mutation operator is employed to enhance the exploration phase in BGOA algorithm (BGOA-M). The proposed methods are evaluated using 25 standard UCI datasets and compared with 8 well-regarded metaheuristic wrapper-based approaches, and six well known filter-based (e.g., correlation FS) approaches. The comparative results show the superior performance of the BGOA and BGOA-M methods compared to other similar techniques in the literature.
In this article, we investigate distributed convex optimization with both inequality and equality constraints, where the objective function can be a general nonsmooth convex function and all the ...constraints can be both sparsely and densely coupling. By strategically integrating ideas from primal-dual, proximal, and virtual-queue optimization methods, we develop a novel distributed algorithm, referred to as IPLUX, to address the problem over a connected, undirected graph. We show that IPLUX achieves an <inline-formula><tex-math notation="LaTeX">O(1/k)</tex-math></inline-formula> rate of convergence in terms of optimality and feasibility, which is stronger than the convergence results of the alternative methods and eliminates the standard assumption on the compactness of the feasible region. Finally, IPLUX exhibits faster convergence and higher efficiency than several state-of-the-art methods in the simulation.
At depots with refined oil shortage, arranging a reasonable distribution scheme with limited supply affects operation costs, demand satisfaction rate of gasoline stations (hereafter, 'station ...satisfaction'), and overtime penalty. This study considers the refined oil distribution problem with shortages using a multi-objective optimisation approach from the perspective of decision makers of oil marketing companies. The modelling and solving process involves (i) formulation of a crisp multi-depot vehicle routing model with limited supply (MDVRPLS) which considers station priority and soft time windows, (ii) development of a robust optimisation model (ROM) to manage uncertainty in demand, and (iii) the proposal of a multi-objective particle swarm optimisation (MOPSO)algorithm. Results of numerical experiments show that (i) the crisp model can better balance operation costs, station satisfaction, and overtime penalty, which produces 3.33% and 4.60% increase in station satisfaction at an increased unit cost and overtime penalty respectively; (ii) ROM successfully addresses uncertainty in demand compared to the crisp model, which requires an additional 8.81% in cost and 12.85% in penalty; and (iii) the MOPSO manages these MDVRPLS models more effectively than other heuristic algorithms. Therefore, applying ROM of refined oil supply shortage to the management significantly improves the efficiency and resists the disturbance caused by external uncertainties, providing scope for efficient distribution of scarce resources.
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