A new Taxonomy of Continuous Global Optimization Algorithms

Surrogate-based optimization, nature-inspired metaheuristics, and hybrid combinations have become state of the art in algorithm design for solving real-world optimization problems. Still, it is difficult for practitioners to get an overview that explains their advantages in comparison to a large number of available methods in the scope of optimization. Available taxonomies lack the embedding of current approaches in the larger context of this broad field. This article presents a taxonomy of the field, which explores and matches algorithm strategies by extracting similarities and differences in their search strategies. A particular focus lies on algorithms using surrogates, nature-inspired designs, and those created by design optimization. The extracted features of components or operators allow us to create a set of classification indicators to distinguish between a small number of classes. The features allow a deeper understanding of components of the search strategies and further indicate the close connections between the different algorithm designs. We present intuitive analogies to explain the basic principles of the search algorithms, particularly useful for novices in this research field. Furthermore, this taxonomy allows recommendations for the applicability of the corresponding algorithms.Comment: 35 pages total, 28 written pages, 4 figures, 2019 Reworked Versio

State-of-the-art in aerodynamic shape optimisation methods

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

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

Novel Memetic Computing Structures for Continuous Optimisation

This thesis studies a class of optimisation algorithms, namely Memetic Computing Structures, and proposes a novel set of promising algorithms that move the first step towards an implementation for the automatic generation of optimisation algorithms for continuous domains. This thesis after a thorough review of local search algorithms and popular meta-heuristics, focuses on Memetic Computing in terms of algorithm structures and design philosophy. In particular, most of the design carried out during my doctoral studies is inspired by the lex parsimoniae, aka Ockham’s Razor. It has been shown how simple algorithms, when well implemented can outperform complex implementations. In order to achieve this aim, the design is always carried out by attempting to identify the role of each algorithmic component/operator. In this thesis, on the basis of this logic, a set of variants of a recently proposed algorithms are presented. Subsequently a novel memetic structure, namely Parallel Memetic Structure is proposed and tested against modern algorithms representing the state of the art in optimisation. Furthermore, an initial prototype of an automatic design platform is also included. This prototype performs an analysis on separability of the optimisation problem and, on the basis of the analysis results, designs some parts of the parallel structure. Promising results are included. Finally, an investigation of the correlation among the variables and problem dimensionality has been performed. An extremely interesting finding of this thesis work is that the degree of correlation among the variables decreases when the dimensionality increases. As a direct consequence of this fact, large scale problems are to some extent easier to handle than problems in low dimensionality since, due to the lack of correlation among the variables, they can effectively be tackled by an algorithm that performs moves along the axes

A prescription of methodological guidelines for comparing bio-inspired optimization algorithms

Bio-inspired optimization (including Evolutionary Computation and Swarm Intelligence) is a growing research topic with many competitive bio-inspired algorithms being proposed every year. In such an active area, preparing a successful proposal of a new bio-inspired algorithm is not an easy task. Given the maturity of this research field, proposing a new optimization technique with innovative elements is no longer enough. Apart from the novelty, results reported by the authors should be proven to achieve a significant advance over previous outcomes from the state of the art. Unfortunately, not all new proposals deal with this requirement properly. Some of them fail to select appropriate benchmarks or reference algorithms to compare with. In other cases, the validation process carried out is not defined in a principled way (or is even not done at all). Consequently, the significance of the results presented in such studies cannot be guaranteed. In this work we review several recommendations in the literature and propose methodological guidelines to prepare a successful proposal, taking all these issues into account. We expect these guidelines to be useful not only for authors, but also for reviewers and editors along their assessment of new contributions to the field.This work was supported by grants from the Spanish Ministry of Science (TIN2016-8113-R, TIN2017-89517-P and TIN2017-83132-C2- 2-R) and Universidad Politécnica de Madrid (PINV-18-XEOGHQ-19- 4QTEBP). Eneko Osaba and Javier Del Ser-would also like to thank the Basque Government for its funding support through the ELKARTEK and EMAITEK programs. Javier Del Ser-receives funding support from the Consolidated Research Group MATHMODE (IT1294-19) granted by the Department of Education of the Basque Government