Nature-inspired algorithms for solving some hard numerical problems

Optimisation is a branch of mathematics that was developed to find the optimal solutions, among all the possible ones, for a given problem. Applications of optimisation techniques are currently employed in engineering, computing, and industrial problems. Therefore, optimisation is a very active research area, leading to the publication of a large number of methods to solve specific problems to its optimality. This dissertation focuses on the adaptation of two nature inspired algorithms that, based on optimisation techniques, are able to compute approximations for zeros of polynomials and roots of non-linear equations and systems of non-linear equations. Although many iterative methods for finding all the roots of a given function already exist, they usually require: (a) repeated deflations, that can lead to very inaccurate results due to the problem of accumulating rounding errors, (b) good initial approximations to the roots for the algorithm converge, or (c) the computation of first or second order derivatives, which besides being computationally intensive, it is not always possible. The drawbacks previously mentioned served as motivation for the use of Particle Swarm Optimisation (PSO) and Artificial Neural Networks (ANNs) for root-finding, since they are known, respectively, for their ability to explore high-dimensional spaces (not requiring good initial approximations) and for their capability to model complex problems. Besides that, both methods do not need repeated deflations, nor derivative information. The algorithms were described throughout this document and tested using a test suite of hard numerical problems in science and engineering. Results, in turn, were compared with several results available on the literature and with the well-known Durand–Kerner method, depicting that both algorithms are effective to solve the numerical problems considered.A Optimização é um ramo da matemática desenvolvido para encontrar as soluções óptimas, de entre todas as possíveis, para um determinado problema. Actualmente, são várias as técnicas de optimização aplicadas a problemas de engenharia, de informática e da indústria. Dada a grande panóplia de aplicações, existem inúmeros trabalhos publicados que propõem métodos para resolver, de forma óptima, problemas específicos. Esta dissertação foca-se na adaptação de dois algoritmos inspirados na natureza que, tendo como base técnicas de optimização, são capazes de calcular aproximações para zeros de polinómios e raízes de equações não lineares e sistemas de equações não lineares. Embora já existam muitos métodos iterativos para encontrar todas as raízes ou zeros de uma função, eles usualmente exigem: (a) deflações repetidas, que podem levar a resultados muito inexactos, devido ao problema da acumulação de erros de arredondamento a cada iteração; (b) boas aproximações iniciais para as raízes para o algoritmo convergir, ou (c) o cálculo de derivadas de primeira ou de segunda ordem que, além de ser computacionalmente intensivo, para muitas funções é impossível de se calcular. Estas desvantagens motivaram o uso da Optimização por Enxame de Partículas (PSO) e de Redes Neurais Artificiais (RNAs) para o cálculo de raízes. Estas técnicas são conhecidas, respectivamente, pela sua capacidade de explorar espaços de dimensão superior (não exigindo boas aproximações iniciais) e pela sua capacidade de modelar problemas complexos. Além disto, tais técnicas não necessitam de deflações repetidas, nem do cálculo de derivadas. Ao longo deste documento, os algoritmos são descritos e testados, usando um conjunto de problemas numéricos com aplicações nas ciências e na engenharia. Os resultados foram comparados com outros disponíveis na literatura e com o método de Durand–Kerner, e sugerem que ambos os algoritmos são capazes de resolver os problemas numéricos considerados

Understanding Optimisation Processes with Biologically-Inspired Visualisations

Evolutionary algorithms (EAs) constitute a branch of artificial intelligence utilised to evolve solutions to solve optimisation problems abound in industry and research. EAs often generate many solutions and visualisation has been a primary strategy to display EA solutions, given that visualisation is a multi-domain well-evaluated medium to comprehend extensive data. The endeavour of visualising solutions is inherent with challenges resulting from high dimensional phenomenons and the large number of solutions to display. Recently, scholars have produced methods to mitigate some of these known issues when illustrating solutions. However, one key consideration is that displaying the final subset of solutions exclusively (rather than the whole population) discards most of the informativeness of the search, creating inadequate insight into the black-box EA. There is an unequivocal knowledge gap and requirement for methods which can visualise the whole population of solutions from an optimiser and subjugate the high-dimensional problems and scaling issues to create interpretability of the EA search process. Furthermore, a requirement for explainability in evolutionary computing has been demanded by the evolutionary computing community, which could take the form of visualisations, to support EA comprehension much like the support explainable artificial intelligence has brought to artificial intelligence. In this thesis, we report novel visualisation methods that can be used to visualise large and high-dimensional optimiser populations with the aim of creating greater interpretability during a search. We consider the nascent intersection of visualisation and explainability in evolutionary computing. The potential high informativeness of a visualisation method from an early chapter of this work forms an effective platform to develop an explainability visualisation method, namely the population dynamics plot, to attempt to inject explainability into the inner workings of the search process. We further support the visualisation of populations using machine learning to construct models which can capture the characteristics of an EA search and develop intelligent visualisations which use artificial intelligence to potentially enhance and support visualisation for a more informative search process. The methods developed in this thesis are evaluated both quantitatively and qualitatively. We use multi-feature benchmark problems to show the method’s ability to reveal specific problem characteristics such as disconnected fronts, local optima and bias, as well as potentially creating a better understanding of the problem landscape and optimiser search for evaluating and comparing algorithm performance (we show the visualisation method to be more insightful than conventional metrics like hypervolume alone). One of the most insightful methods developed in this thesis can produce a visualisation requiring less than 1% of the time and memory necessary to produce a visualisation of the same objective space solutions using existing methods. This allows for greater scalability and the use in short compile time applications such as online visualisations. Predicated by an existing visualisation method in this thesis, we then develop and apply an explainability method to a real-world problem and evaluate it to show the method to be highly effective at explaining the search via solutions in the objective spaces, solution lineage and solution variation operators to compactly comprehend, evaluate and communicate the search of an optimiser, although we note the explainability properties are only evaluated against the author’s ability and could be evaluated further in future work with a usability study. The work is then supported by the development of intelligent visualisation models that may allow one to predict solutions in optima (importantly local optima) in unseen problems by using a machine learning model. The results are effective, with some models able to predict and visualise solution optima with a balanced F1 accuracy metric of 96%. The results of this thesis provide a suite of visualisations which aims to provide greater informativeness of the search and scalability than previously existing literature. The work develops one of the first explainability methods aiming to create greater insight into the search space, solution lineage and reproductive operators. The work applies machine learning to potentially enhance EA understanding via visualisation. These models could also be used for a number of applications outside visualisation. Ultimately, the work provides novel methods for all EA stakeholders which aims to support understanding, evaluation and communication of EA processes with visualisation

Parallel evolutionary programming techniques for strategy optimisation in air combat scenarios

Air combat between fighter missiles and aircraft can be categorised as a pursuit-evasion problem. One aircraft acts as a pursuer and the other as an evader. Generally, the pursuer will try to capture the evader as quickly as possible and the evader tries to evade capture for as long as possible. For an experienced human pilot, it is trivial to discuss this methodology, but to simulate it, the mathematics involved is very complex and difficult to implement in a computer environment. Classical methods, though very accurate in their analysis, are not suited to solve a complex 6DOF pursuit-evasion problem and they have limitations in representing real-world problems such as discontinuities, discrete, stochastic, chaotic, temporal information or lack of information. In this thesis, evolutionary programming (EP) is applied to determine the optimum maneuvering strategy for an aircraft (evader) to avoid interception by an incoming missile (pursuer). EP is a class of algorithms known as Evolutionary Algorithm (EA). EA has an ability to find an optimal solution in a complex problem which involves discontinuities, discrete, nondifferential parameters and noise. In addition, the methodology was implemented on parallel computer architecture to improve the computing time and expanding the search space. A sensitivity analysis was carried out to determine the best configuration and to understand the effect of parameters, such as number of processors, population size, number of generations, etc., on the results. The effects of sensor and instrument errors were also considered. The method enabled feasible solutions to be found in a relatively short period of time. However, the ability to search for feasible solutions is dependent on various parameters such as initial conditions, aircraft configurations and aerodynamic constraints. It is concluded that, in general, EP is able to determine feasible maneuvering strategies for an evader to avoid interception with and without instrument errors. The methodology has the potential to be used as a training tool for pilots in air combat or as an intelligent engagement strategy for autonomous systems, such as Unmanned Air Combat Vehicles (UCAV)

Numerical and Evolutionary Optimization 2020

This book was established after the 8th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others. This volume is intended to serve as a useful reference for mathematicians, engineers, and computer scientists to explore current issues and solutions emerging from these mathematical and computational methods and their applications

Machine learning assisted optimization with applications to diesel engine optimization with the particle swarm optimization algorithm

A novel approach to incorporating Machine Learning into optimization routines is presented. An approach which combines the benefits of ML, optimization, and meta-model searching is developed and tested on a multi-modal test problem; a modified Rastragin\u27s function. An enhanced Particle Swarm Optimization method was derived from the initial testing. Optimization of a diesel engine was carried out using the modified algorithm demonstrating an improvement of 83% compared with the unmodified PSO algorithm. Additionally, an approach to enhancing the training of ML models by leveraging Virtual Sensing as an alternative to standard multi-layer neural networks is presented. Substantial gains were made in the prediction of Particulate matter, reducing the MMSE by 50% and improving the correlation R^2 from 0.84 to 0.98. Improvements were made in models of PM, NOx, HC, CO, and Fuel Consumption using the method, while training times and convergence reliability were simultaneously improved over the traditional approach

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

Multi-Objective and Multi-Attribute Optimisation for Sustainable Development Decision Aiding

Optimization is considered as a decision-making process for getting the most out of available resources for the best attainable results. Many real-world problems are multi-objective or multi-attribute problems that naturally involve several competing objectives that need to be optimized simultaneously, while respecting some constraints or involving selection among feasible discrete alternatives. In this Reprint of the Special Issue, 19 research papers co-authored by 88 researchers from 14 different countries explore aspects of multi-objective or multi-attribute modeling and optimization in crisp or uncertain environments by suggesting multiple-attribute decision-making (MADM) and multi-objective decision-making (MODM) approaches. The papers elaborate upon the approaches of state-of-the-art case studies in selected areas of applications related to sustainable development decision aiding in engineering and management, including construction, transportation, infrastructure development, production, and organization management