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Iterative optimizers : difficulty measures and benchmarks
Almost every month, a new optimization algorithm is proposed, often accompanied by the claim that it is superior to all those that came before it. However, this claim is generally based on the algorithm's performance on a specific set of test cases, which are not necessarily representative of the types of problems the algorithm will face in real life. This book presents the theoretical analysis and practical methods (along with source codes) necessary to estimate the difficulty of problems in a test set, as well as to build bespoke test sets consisting of problems with varied difficulties. The book formally establishes a typology of optimization problems, from which a reliable test set can be deduced. At the same time, it highlights how classic test sets are skewed in favor of different classes of problems, and how, as a result, optimizers that have performed well on test problems may perform poorly in real life scenarios.
Book
A survey on evolutionary computation for complex continuous optimization
Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.
Journal Article
Optimization algorithms on matrix manifolds
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.
eBook
Robust Optimization
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.
The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations.
An essential book for anyone working on optimization and decision making under uncertainty,Robust Optimizationalso makes an ideal graduate textbook on the subject.
eBook
The Dual-Dimension of Quality of Life: A Philosophical Value Theory Approach to Reconstructing Health Engineering Goals
Health Engineering (HE) has significantly advanced objective health metrics, yet often overlooks the subjective, value-laden dimension of Quality of Life (QoL), creating a gap in achieving genuine human flourishing. This paper addresses this limitation by introducing a Dual-Dimension QoL Model (DD-QoL), which integrates the Objective Functional Dimension (OFD) with the Subjective Value Dimension (SVD). Based on this model, we develop a Value-Sensitive Assessment Framework (VSAF), a distinctive methodological contribution that uses conceptual engineering to shift HE’s primary goal from merely maximizing OFD to optimizing holistic QoL. Through an illustrative example of an AI-assisted care system for Alzheimer’s disease, we qualitatively demonstrate how a VSAF-guided approach can enhance SVD outcomes without compromising OFD. Our primary contribution is a novel, philosophically-grounded framework that provides a supplementary approach for reconstructing HE goals, ensuring that technological progress serves the broader, more profound aim of promoting valuable life experiences
Journal Article
Performance assessment of the metaheuristic optimization algorithms: an exhaustive review
The simulation-driven metaheuristic algorithms have been successful in solving numerous problems compared to their deterministic counterparts. Despite this advantage, the stochastic nature of such algorithms resulted in a spectrum of solutions by a certain number of trials that may lead to the uncertainty of quality solutions. Therefore, it is of utmost importance to use a correct tool for measuring the performance of the diverse set of metaheuristic algorithms to derive an appropriate judgment on the superiority of the algorithms and also to validate the claims raised by researchers for their specific objectives. The performance of a randomized metaheuristic algorithm can be divided into efficiency and effectiveness measures. The efficiency relates to the algorithm’s speed of finding accurate solutions, convergence, and computation. On the other hand, effectiveness relates to the algorithm’s capability of finding quality solutions. Both scopes are crucial for continuous and discrete problems either in single- or multi-objectives. Each problem type has different formulation and methods of measurement within the scope of efficiency and effectiveness performance. One of the most decisive verdicts for the effectiveness measure is the statistical analysis that depends on the data distribution and appropriate tool for correct judgments.
Journal Article