Heuristic procedures for improving the predictability of a genetic programming financial forecasting algorithm

Financial forecasting is an important area in computational finance. Evolutionary Dynamic Data Investment Evaluator (EDDIE) is an established genetic programming (GP) financial forecasting algorithm, which has successfully been applied to a number of international financial datasets. The purpose of this paper is to further improve the algorithm’s predictive performance, by incorporating heuristics in the search. We propose the use of two heuristics: a sequential covering strategy to iteratively build a solution in combination with the GP search and the use of an entropy-based dynamic discretisation procedure of numeric values. To examine the effectiveness of the proposed improvements, we test the new EDDIE version (EDDIE 9) across 20 datasets and compare its predictive performance against three previous EDDIE algorithms. In addition, we also compare our new algorithm’s performance against C4.5 and RIPPER, two state-of-the-art classification algorithms. Results show that the introduction of heuristics is very successful, allowing the algorithm to outperform all previous EDDIE versions and the well-known C4.5 and RIPPER algorithms. Results also show that the algorithm is able to return significantly high rates of return across the majority of the datasets

Algorithms in future capital markets: A survey on AI, ML and associated algorithms in capital markets

This paper reviews Artificial Intelligence (AI), Machine Learning (ML) and associated algorithms in future Capital Markets. New AI algorithms are constantly emerging, with each 'strain' mimicking a new form of human learning, reasoning, knowledge, and decisionmaking. The current main disrupting forms of learning include Deep Learning, Adversarial Learning, Transfer and Meta Learning. Albeit these modes of learning have been in the AI/ML field more than a decade, they now are more applicable due to the availability of data, computing power and infrastructure. These forms of learning have produced new models (e.g., Long Short-Term Memory, Generative Adversarial Networks) and leverage important applications (e.g., Natural Language Processing, Adversarial Examples, Deep Fakes, etc.). These new models and applications will drive changes in future Capital Markets, so it is important to understand their computational strengths and weaknesses. Since ML algorithms effectively self-program and evolve dynamically, financial institutions and regulators are becoming increasingly concerned with ensuring there remains a modicum of human control, focusing on Algorithmic Interpretability/Explainability, Robustness and Legality. For example, the concern is that, in the future, an ecology of trading algorithms across different institutions may 'conspire' and become unintentionally fraudulent (cf. LIBOR) or subject to subversion through compromised datasets (e.g. Microsoft Tay). New and unique forms of systemic risks can emerge, potentially coming from excessive algorithmic complexity. The contribution of this paper is to review AI, ML and associated algorithms, their computational strengths and weaknesses, and discuss their future impact on the Capital Markets

Evolutionary computation for trading systems

2007/2008Evolutionary computations, also called evolutionary algorithms, consist of several heuristics, which are able to solve optimization tasks by imitating some aspects of natural evolution. They may use different levels of abstraction, but they are always working on populations of possible solutions for a given task. The basic idea is that if only those individuals of a population which meet a certain selection criteria reproduce, while the remaining individuals die, the population will converge to those individuals that best meet the selection criteria. If imperfect reproduction is added the population can begin to explore the search space and will move to individuals that have an increased selection probability and that hand down this property to their descendants. These population dynamics follow the basic rule of the Darwinian evolution theory, which can be described in short as the “survival of the fittest”. Although evolutionary computations belong to a relative new research area, from a computational perspective they have already showed some promising features such as: • evolutionary methods reveal a remarkable balance between efficiency and efficacy; • evolutionary computations are well suited for parameter optimisation; • this type of algorithms allows a wide variety of extensions and constraints that cannot be provided in traditional methods; • evolutionary methods are easily combined with other optimization techniques and can also be extended to multi-objective optimization. From an economic perspective, these methods appear to be particularly well suited for a wide range of possible financial applications, in particular in this thesis I study evolutionary algorithms • for time series prediction; • to generate trading rules; • for portfolio selection. It is commonly believed that asset prices are not random, but are permeated by complex interrelations that often translate in assets mispricing and may give rise to potentially profitable opportunities. Classical financial approaches, such as dividend discount models or even capital asset pricing theories, are not able to capture these market complexities. Thus, in the last decades, researchers have employed intensive econometric and statistical modeling that examine the effects of a multitude of variables, such as price- earnings ratios, dividend yields, interest rate spreads and changes in foreign exchange rates, on a broad and variegated range of stocks at the same time. However, these models often result in complex functional forms difficult to manage or interpret and, in the worst case, are solely able to fit a given time series but are useless to predict it. Parallelly to quantitative approaches, other researchers have focused on the impact of investor psychology (in particular, herding and overreaction) and on the consequences of considering informed signals from management and analysts, such as share repurchases and analyst recommendations. These theories are guided by intuition and experience, and thus are difficult to be translated into a mathematical environment. Hence, the necessity to combine together these point of views in order to develop models that examine simultaneously hundreds of variables, including qualitative informations, and that have user friendly representations, is urged. To this end, the thesis focuses on the study of methodologies that satisfy these requirements by integrating economic insights, derived from academic and professional knowledge, and evolutionary computations. The main task of this work is to provide efficient algorithms based on the evolutionary paradigm of biological systems in order to compute optimal trading strategies for various profit objectives under economic and statistical constraints. The motivations for constructing such optimal strategies are: i) the necessity to overcome data-snooping and supervisorship bias in order to learn to predict good trading opportunities by using market and/or technical indicators as features on which to base the forecasting; ii) the feasibility of using these rules as benchmark for real trading systems; iii) the capability of ranking quantitatively various markets with respect to their profitability according to a given criterion, thus making possible portfolio allocations. More precisely, I present two algorithms that use artificial expert trading systems to predict financial time series, and a procedure to generate integrated neutral strategies for active portfolio management. The first algorithm is an automated procedure that simultaneously selects variables and detect outliers in a dynamic linear model using information criteria as objective functions and diagnostic tests as constraints for the distributional properties of errors. The novelties are the automatic implementation of econometric conditions in the model selection step, making possible a better exploration of the solution space on one hand, and the use of evolutionary computations to efficiently generate a reduction procedure from a very large number of independent variables on the other hand. In the second algorithm, the novelty is given by the definition of evolutionary learning in financial terms and its use in a multi-objective genetic algorithm in order to generate technical trading systems. The last tool is based on a trading strategy on six assets, where future movements of each variable are obtained by an evolutionary procedure that integrates various types of financial variables. The contribution is given by the introduction of a genetic algorithm to optimize trading signals parameters and the way in which different informations are represented and collected. In order to compare the contribution of this work to “classical” techniques and theories, the thesis is divided into three parts. The first part, titled Background, collects Chapters 2 and 3. Its purpose is to provide an introduction to search/optimization evolutionary techniques on one hand, and to the theories that relate the predictability in financial markets with the concept of efficiency proposed over time by scholars on the other hand. More precisely, Chapter 2 introduces the basic concepts and major areas of evolutionary computation. It presents a brief history of three major types of evolutionary algorithms, i.e. evolution strategies, evolutionary programming and genetic algorithms, and points out similarities and differences among them. Moreover it gives an overview of genetic algorithms and describes classical and genetic multi-objective optimization techniques. Chapter 3 first presents an overview of the literature on the predictability of financial time series. In particular, the extent to which the efficiency paradigm is affected by the introduction of new theories, such as behavioral finance, is described in order to justify the market forecasting methodologies developed by practitioners and academics in the last decades. Then, a description of the econometric and financial techniques that will be used in conjunction with evolutionary algorithms in the successive chapters is provided. Special attention is paid to economic implications, in order to highlight merits and shortcomings from a practitioner perspective. The second part of the thesis, titled Trading Systems, is devoted to the description of two procedures I have developed in order to generate artificial trading strategies on the basis of evolutionary algorithms, and it groups Chapters 4 and 5. In particular, chapter 4 presents a genetic algorithm for variable selection by minimizing the error in a multiple regression model. Measures of errors such as ME, RMSE, MAE, Theil’s inequality coefficient and CDC are analyzed choosing models based on AIC, BIC, ICOMP and similar criteria. Two components of penalty functions are taken in analysis- level of significance and Durbin Watson statistics. Asymptotic properties of functions are tested on several financial variables including stocks, bonds, returns, composite prices indices from the US and the EU economies. Variables with outliers that distort the efficiency and consistency of estimators are removed to solve masking and smearing problems that they may cause in estimations. Two examples complete the chapter. In both cases, models are designed to produce short-term forecasts for the excess returns of the MSCI Europe Energy sector on the MSCI Europe index and a recursive estimation- window is used to shed light on their predictability performances. In the first application the data-set is obtained by a reduction procedure from a very large number of leading macro indicators and financial variables stacked at various lags, while in the second the complete set of 1-month lagged variables is considered. Results show a promising capability to predict excess sector returns through the selection, using the proposed methodology, of most valuable predictors. In Chapter 5 the paradigm of evolutionary learning is defined and applied in the context of technical trading rules for stock timing. A new genetic algorithm is developed by integrating statistical learning methods and bootstrap to a multi-objective non dominated sorting algorithm with variable string length, making possible to evaluate statistical and economic criteria at the same time. Subsequently, the chapter discusses a practical case, represented by a simple trading strategy where total funds are invested in either the S&P 500 Composite Index or in 3-month Treasury Bills. In this application, the most informative technical indicators are selected from a set of almost 5000 signals by the algorithm. Successively, these signals are combined into a unique trading signal by a learning method. I test the expert weighting solution obtained by the plurality voting committee, the Bayesian model averaging and Boosting procedures with data from the the S&P 500 Composite Index, in three market phases, up-trend, down- trend and sideways-movements, covering the period 2000–2006. In the third part, titled Portfolio Selection, I explain how portfolio optimization models may be constructed on the basis of evolutionary algorithms and on the signals produced by artificial trading systems. First, market neutral strategies from an economic point of view are introduced, highlighting their risks and benefits and focusing on their quantitative formulation. Then, a description of the GA-Integrated Neutral tool, a MATLAB set of functions based on genetic algorithms for active portfolio management, is given. The algorithm specializes in the parameter optimization of trading signals for an integrated market neutral strategy. The chapter concludes showing an application of the tool as a support to decisions in the Absolute Return Interest Rate Strategies sub-fund of Generali Investments.Gli “algoritmi evolutivi”, noti anche come “evolutionary computations” comprendono varie tecniche di ottimizzazione per la risoluzione di problemi, mediante alcuni aspetti suggeriti dall’evoluzione naturale. Tali metodologie sono accomunate dal fatto che non considerano un’unica soluzione alla volta, bens`ı trattano intere popolazioni di possibili soluzioni per un dato problema. L’idea sottostante `e che, se un algoritmo fa evolvere solamente gli individui di una data popolazione che soddisfano a un certo criterio di selezione, e lascia morire i restanti, la popolazione converger`a agli individui che meglio soddisfano il criterio di selezione. Con una selezione non ottimale, cio`e una che ammette pure soluzioni sub-ottimali, la popolazione rappresenter` a meglio l’intero spazio di ricerca e sar`a in grado di individuare in modo pi`u consistente gli individui migliori da far evolvere. Queste dinamiche interne alle popolazioni seguono i principi Darwiniani dell’evoluzione, che si possono sinteticamente riassumere nella dicitura “la sopravvivenza del più adatto”. Sebbene gli algoritmi evolutivi siano un’area di ricerca relativamente nuova, dal punto di vista computazionale hanno dimostrato alcune caratteristiche interessanti fra cui le seguenti: • permettono un notevole equilibrio tra efficienza ed efficacia; • sono particolarmente indicati per la configurazione dei parametri in problemi di ottimizzazione; • consentono una flessibilit`a nella definizione matematica dei problemi e dei vincoli che non si trova nei metodi tradizionali; • possono facilmente essere integrati con altre tecniche di ottimizzazione ed essere essere modificati per risolvere problemi multi-obiettivo. Dal un punto di vista economico, l’applicazione di queste procedure pu`o risultare utile specialmente in campo finanziario. In particolare, nella mia tesi ho studiato degli algoritmi evolutivi per • la previsione di serie storiche finanziarie; • la costruzione di regole di trading; • la selezione di portafogli. Da un punto di vista pi`u ampio, lo scopo di questa ricerca `e dunque l’analisi dell’evoluzione e della complessit`a dei mercati finanziari. In tal senso, dal momento che i prezzi non seguono andamenti puramente casuali, ma sono governati da un insieme molto articolato di eventi correlati, i modelli e le teorie classiche, come i dividend discount model e le varie capital asset pricing theories, non sono pi`u sufficienti per determinare potenziali opportunit`a di profitto. A tal fine, negli ultimi decenni, alcuni ricercatori hanno sviluppato una vasta gamma di modelli econometrici e statistici in grado di esaminare contemporaneamente le relazioni e gli effetti di centinaia di variabili, come ad esempio, price-earnings ratios, dividendi, differenziali fra tassi di interesse e variazioni dei tassi di cambio, per una vasta gamma di assets. Comunque, questo approccio, che fa largo impiego di strumenti di calcolo, spesso porta a dei modelli troppo complicati per essere gestiti o interpretati, e, nel peggiore dei casi, pur essendo ottimi per descrivere situazioni passate, risultano inutili per fare previsioni. Parallelamente a questi approcci quantitativi, si `e manifestato un grande interesse sulla psicologia degli investitori e sulle conseguenze derivanti dalle opinioni di esperti e analisti nelle dinamiche del mercato. Questi studi sono difficilmente traducibili in modelli matematici e si basano principalmente sull’intuizione e sull’esperienza. Da qui la necessit` a di combinare insieme questi due punti di vista, al fine di sviluppare modelli che siano in grado da una parte di trattare contemporaneamente un elevato numero di variabili in modo efficiente e, dall’altra, di incorporare informazioni e opinioni qualitative. La tesi affronta queste tematiche integrando le conoscenze economiche, sia accademiche che professionali, con gli algoritmi evolutivi. Pi`u pecisamente, il principale obiettivo di questo lavoro `e lo sviluppo di algoritmi efficienti basati sul paradigma dell’evoluzione dei sistemi biologici al fine di determinare strategie di trading ottimali in termini di profitto e di vincoli economici e statistici. Le ragioni che motivano lo studio di tali strategie ottimali sono: i) la necessit`a di risolvere i problemi di data-snooping e supervivorship bias al fine di ottenere regole di investimento vantaggiose utilizzando indicatori di mercato e/o tecnici per la previsione; ii) la possibilità di impiegare queste regole come benchmark per sistemi di trading reali; iii) la capacit`a di individuare gli asset pi`u vantaggiosi in termini di profitto, o di altri criteri, rendendo possibile una migliore allocazione di risorse nei portafogli. In particolare, nella tesi descrivo due algoritmi che impiegano sistemi di trading artificiali per predire serie storiche finanziarie e una procedura di calcolo per strategie integrate neutral market per la gestione attiva di portafogli. Il primo algoritmo `e una procedura automatica che seleziona le variabili e simultaneamente determina gli outlier in un modello dinamico lineare utilizzando criteri informazionali come funzioni obiettivo e test diagnostici come vincoli per le caratteristiche delle distribuzioni degli errori. Le novit`a del metodo sono da una parte l’implementazione automatica di condizioni econometriche nella fase di selezione, consentendo una migliore analisi dello EVOLUTIONARY COMPUTATIONS FOR TRADING SYSTEMS 3 spazio delle soluzioni, e dall’altra parte, l’introduzione di una procedura di riduzione evolutiva capace di riconoscere in modo efficiente le variabili pi`u informative. Nel secondo algoritmo, le novità sono costituite dalla definizione dell’apprendimento evolutivo in termini finanziari e dall’applicazione di un algoritmo genetico multi-obiettivo per la costruzione di sistemi di trading basati su indicatori tecnici. L’ultimo metodo proposto si basa su una strategia di trading su sei assets, in cui le dinamiche future di ciascuna variabile sono ottenute impiegando una procedura evolutiva che integra diverse tipologie di variabili finanziarie. Il contributo è dato dall’impiego di un algoritmo genetico per ottimizzare i parametri negli indicatori tecnici e dal modo in cui le differenti informazioni sono presentate e collegate. La tesi `e organizzata in tre parti. La prima parte, intitolata Background, comprende i Capitoli 2 e 3, ed è intesa a fornire un’introduzione alle tecniche di ricerca/ottimizzazione su base evolutiva da una parte, e alle teorie che si occupano di efficienza e prevedibilit`a dei mercati finanziari dall’altra. Più precisamente, il Capitolo 2 introduce i concetti base e i maggiori campi di studio della computazione evolutiva. In tal senso, si dà una breve presentazione storica di tre dei maggiori tipi di algoritmi evolutivi, ciò e le strategie evolutive, la programmazione evolutiva e gli algoritmi genetici, evidenziandone caratteri comuni e differenze. Il capitolo si chiude con una panoramica sugli algoritmi genetici e sulle tecniche classiche e genetiche di ottimizzazione multi-obiettivo. Il Capitolo 3 affronta nel dettaglio la problematica della prevedibilit`a delle serie storiche finanziarie mettendo in luce, in particolare, quanto il paradigma dell’efficienza sia influenzato dalle pi`u recenti teorie finanziarie, come ad esempio la finanza comportamentale. Lo scopo è quello di dare una giustificazione su basi teoriche per le metodologie di previsione sviluppate nella tesi. Segue una descrizione dei metodi econometrici e di analisi tecnica che nei capitoli successivi verrano impiegati assieme agli algoritmi evolutivi. Una particolare attenzione è data alle implicazioni economiche, al fine di evidenziare i loro meriti e i loro difetti da un punto di vista pratico. La seconda parte, intitolata Trading Systems, raggruppa i Capitoli 4 e 5 ed è dedicata alla descrizione di due procedure che ho sviluppato per generare sistemi di trading artificiali sulla base di algoritmi evolutivi. In particolare, il Capitolo 4 presenta un algortimo genetico per la selezione di variabili attraverso la minimizzazione dell’errore in un modello di regressione multipla. Misure di errore, quali il ME, il RMSE, il MAE, il coefficiente di Theil e il CDC sono analizzate a partire da modelli selezionati sulla scorta di criteri informazionali, come ad esempio AIC, BIC, ICOMP. A livello di vincoli diagnostici, ho considerato una funzione di penalità a due componenti e la statistica di Durbin Watson. Il programma impiega variabili finanziarie di vario tipo, come rendimenti di titoli, bond e prezzi di indici composti ottenuti dalle economie Statunitense ed Europea. Nel caso le serie storiche 4 MASSIMILIANO KAUCIC considerate presentino outliers che distorcono l’efficienza e la consistenza degli stimatori, l’algoritmo `e in grado di individuarle e rimuoverle dalla serie, risolvendo il problema di masking and smearing. Il capitolo si conclude con due applicazioni, in cui i modelli sono progettati per produrre previsioni di breve periodo per l’extra rendimento del settore MSCI Europe Energy sull’indice MSCI Europe e una procedura di tipo recursive estimation-window è utilizzata per evidenziarne le performance previsionali. Nel primo esempio, l’insieme dei dati `e ottenuto estraendo le variabili di interesse da un considerevole numero di indicatori di tipo macro e da variabili finanziarie ritardate rispetto alla variabile dipendente. Nel secondo esempio ho invece considerato l’intero insieme di variabili ritardate di 1 mese. I risultati mostrano una notevole capacità previsiva per l’extra rendimento, individuando gli indicatori maggiormente informativi. Nel Capitolo 5, il concetto di apprendimento evolutivo viene definito ed applicato alla costruzione di regole di trading su indicatori tecnici per lo stock timing. In tal senso, ho sviluppato un algoritmo che integra metodi di apprendimento statistico e di boostrap con un particolare algoritmo multi-obiettivo. La procedura derivante è in grado di valutare contemporaneamente criteri economici e statistici. Per descrivere il suo funzionamento, ho considerato un semplice esempio di trading in cui tutto il capitale è investito in un indice (che nel caso trattato è l’indice S&P 500 Composite) o in un titolo a basso rischio (nell’esempio, i Treasury Bills a 3 mesi). Il segnale finale di trading `e il risultato della selezione degli indicatori tecnici pi`u informativi a partire da un insieme di circa 5000 indicatori e la loro conseguente integrazione mediante un metodo di apprendimento (il plurality voting committee, il bayesian model averaging o il Boosting). L’analisi è stata condotta sull’intervallo temporale dal 2000 al 2006, suddiviso in tre sottoperiodi: il primo rappresenta l’indice in un

Time series forecasting for dynamic environments: The DyFor Genetic Program model

Copyright © 2007 IEEESeveral studies have applied genetic programming (GP) to the task of forecasting with favorable results. However, these studies, like those applying other techniques, have assumed a static environment, making them unsuitable for many real-world time series which are generated by varying processes. This study investigates the development of a new ldquodynamicrdquo GP model that is specifically tailored for forecasting in nonstatic environments. This dynamic forecasting genetic program (DyFor GP) model incorporates features that allow it to adapt to changing environments automatically as well as retain knowledge learned from previously encountered environments. The DyFor GP model is tested for forecasting efficacy on both simulated and actual time series including the U.S. Gross Domestic Product and Consumer Price Index Inflation. Results show that the performance of the DyFor GP model improves upon that of benchmark models for all experiments. These findings highlight the DyFor GP's potential as an adaptive, nonlinear model for real-world forecasting applications and suggest further investigations.Neal Wagner, Zbigniew Michalewicz, Moutaz Khouja, and Rob Roy McGrego

Robust aircraft trajectory optimization under meteorological uncertainty

Mención Internacional en el título de doctorThe Air Traffic Management (ATM) system in the busiest airspaces in the world is currently being overhauled to deal with multiple capacity, socioeconomic, and environmental challenges. One major pillar of this process is the shift towards a concept of operations centered on aircraft trajectories (called Trajectory-Based Operations or TBO in Europe) instead of rigid airspace structures. However, its successful implementation (and, thus, the realization of the associated improvements in ATM performance) rests on appropriate understanding and management of uncertainty. Due to its complex socio-technical structure, the design and operations of the ATM system are heavily impacted by uncertainty, proceeding from multiple sources and propagating through the interconnections between its subsystems. One major source of ATM uncertainty is weather. Due to its nonlinear and chaotic nature, a number of meteorological phenomena of interest cannot be forecasted with complete accuracy at arbitrary lead times, which leads to uncertainty or disruption in individual air and ground operations that propagates to all ATM processes. Therefore, in order to achieve the goals of SESAR and similar programs, it is necessary to deal with meteorological uncertainty at multiple scales, from the trajectory prediction and planning processes to flow and traffic management operations. This thesis addresses the problem of single-aircraft flight planning considering two important sources of meteorological uncertainty: wind prediction error and convective activity. As the actual wind field deviates from its forecast, the actual trajectory will diverge in time from the planned trajectory, generating uncertainty in arrival times, sector entry and exit times, and fuel burn. Convective activity also impacts trajectory predictability, as it leads pilots to deviate from their planned route, creating challenging situations for controllers. In this work, we aim to develop algorithms and methods for aircraft trajectory optimization that are able to integrate information about the uncertainty in these meteorological phenomena into the flight planning process at both pre-tactical (before departure) and tactical horizons (while the aircraft is airborne), in order to generate more efficient and predictable trajectories. To that end, we frame flight planning as an optimal control problem, modeling the motion of the aircraft with a point-mass model and the BADA performance model. Optimal control methods represent a flexible and general approach that has a long history of success in the aerospace field. As a numerical scheme, we use direct methods, which can deal with nonlinear systems of moderate and high-dimensional state spaces in a computationally manageable way. Nevertheless, while this framework is well-developed in the context of deterministic problems, the techniques for the solution of practical optimal control problems under uncertainty are not as mature, and the methods proposed in the literature are not applicable to the flight planning problem as it is now understood. The first contribution of this thesis addresses this challenge by introducing a framework for the solution of general nonlinear optimal control problems under parametric uncertainty. It is based on an ensemble trajectory scheme, where the trajectories of the system under multiple scenarios are considered simultaneously within the same dynamical system and the uncertain optimal control problem is turned into a large conventional optimal control problem that can be then solved by standard, well-studied direct methods in optimal control. We then employ this approach to solve the robust flight plan optimization problem at the planning horizon. In order to model uncertainty in the wind and estimating the probability of convective conditions, we employ Ensemble Prediction System (EPS) forecasts, which are composed by multiple predictions instead of a single deterministic one. The resulting method can be used to optimize flight plans for maximum expected efficiency according to the cost structure of the airline; additionally, predictability and exposure to convection can be incorporated as additional objectives. The inherent tradeoffs between these objectives can be assessed with this methodology. The second part of this thesis presents a solution for the rerouting of aircraft in uncertain convective weather scenarios at the tactical horizon. The uncertain motion of convective weather cells is represented with a stochastic model that has been developed from the output of a deterministic satellite-based nowcast product, Rapidly Developing Thunderstorms (RDT). A numerical optimal control framework, based on the pointmass model with the addition of turn dynamics, is employed for optimizing efficiency and predictability of the proposed trajectories in the presence of uncertainty about the future evolution of the storm. Finally, the optimization process is initialized by a randomized heuristic procedure that generates multiple starting points. The combined framework is able to explore and as exploit the space of solution trajectories in order to provide the pilot or the air traffic controller with a set of different suggested avoidance trajectories, as well as information about their expected cost and risk. The proposed methods are tested on example scenarios based on real data, showing how different user priorities lead to different flight plans and what tradeoffs are then present. These examples demonstrate that the solutions described in this thesis are adequate for the problems that have been formulated. In this way, the flight planning process can be enhanced to increase the efficiency and predictability of individual aircraft trajectories, which would lead to higher predictability levels of the ATM system and thus improvements in multiple performance indicators.El sistema de gestión del tráfico aéreo (Air Traffic Management, ATM) en los espacios aéreos más congestionados del mundo está siendo reformado para lidiar con múltiples desafíos socioeconómicos, medioambientales y de capacidad. Un pilar de este proceso es el gradual reemplazo de las estructuras rígidas de navegación, basadas en aerovías y waypoints, hacia las operaciones basadas en trayectorias. No obstante, la implementación exitosa de este concepto y la realización de las ganancias esperadas en rendimiento ATM requiere entender y gestionar apropiadamente la incertidumbre. Debido a su compleja estructura socio-técnica, el diseño y operaciones del sistema ATM se encuentran marcadamente influidos por la incertidumbre, que procede de múltiples fuentes y se propaga por las interacciones entre subsistemas y operadores humanos. Uno de los principales focos de incertidumbre en ATM es la meteorología. Debido a su naturaleza no-linear y caótica, muchos fenómenos de interés no pueden ser pronosticados con completa precisión en cualquier horizonte temporal, lo que crea disrupción en las operaciones en aire y tierra que se propaga a otros procesos de ATM. Por lo tanto, para lograr los objetivos de SESAR e iniciativas análogas, es imprescindible tener en cuenta la incertidumbre en múltiples escalas espaciotemporales, desde la predicción de trayectorias hasta la planificación de flujos y tráfico. Esta tesis aborda el problema de la planificación de vuelo de aeronaves individuales considerando dos fuentes importantes de incertidumbre meteorológica: el error en la predicción del viento y la actividad convectiva. Conforme la realización del viento se desvía de su previsión, la trayectoria real se desviará temporalmente de la planificada, lo que implica incertidumbre en tiempos de llegada a sectores y aeropuertos y en consumo de combustible. La actividad convectiva también tiene un impacto en la predictibilidad de las trayectorias, puesto que obliga a los pilotos a desviarse de sus planes de vuelo para evitarla, cambiado así la situación de tráfico. En este trabajo, buscamos desarrollar métodos y algoritmos para la optimización de trayectorias que puedan integrar información sobre la incertidumbre en estos fenómenos meteorológicos en el proceso de diseño de planes de vuelo en horizontes de planificación (antes del despegue) y tácticos (durante el vuelo), con el objetivo de generar trayectorias más eficientes y predecibles. Con este fin, formulamos la planificación de vuelo como un problema de control óptimo, modelando la dinámica del avión con un modelo de masa puntual y el modelo de rendimiento BADA. El control óptimo es un marco flexible y general con un largo historial de éxito en el campo de la ingeniería aeroespacial. Como método numérico, empleamos métodos directos, que son capaces de manejar sistemas dinámicos de alta dimensión con costes computacionales moderados. No obstante, si bien esta metodología es madura en contextos deterministas, la solución de problemas prácticas de control óptimo bajo incertidumbre en la literatura no está tan desarrollada, y los métodos propuestos en la literatura no son aplicables al problema de interés. La primera contribución de esta tesis hace frente a este reto mediante la introducción de un marco numérico para la resolución de problemas generales de control óptimo no-lineal bajo incertidumbre paramétrica. El núcleo de este método es un esquema de conjunto de trayectorias, en el que las trayectorias del sistema dinámico bajo múltiples escenarios son consideradas de forma simultánea, y el problema de control óptimo bajo incertidumbre es así transformado en un problema convencional que puede ser tratado mediante métodos existentes en control óptimo. A continuación, empleamos este método para resolver el problema de la planificación de vuelo robusta. La incertidumbre en el viento y la probabilidad de ocurrencia de condiciones convectivas son modeladas mediante el uso de previsiones de conjunto o ensemble, compuestas por múltiples predicciones en lugar de una única previsión determinista. Este método puede ser empleado para maximizar la eficiencia esperada de los planes de vuelo de acuerdo a la estructura de costes de la aerolínea; además, la predictibilidad de la trayectoria y la exposición a la convección pueden ser incorporadas como objetivos adicionales. El trade-off entre estos objetivos puede ser evaluado mediante la metodología propuesta. La segunda parte de la tesis presenta una solución para reconducir aviones en escenarios tormentosos en un horizonte táctico. La evolución de las células convectivas es representada con un modelo estocástico basado en las proyecciones de Rapidly Developing Thunderstorms (RDT), un sistema determinista basado en imágenes de satélite. Este modelo es empleado por un método de control óptimo numérico, basado en un modelo de masa puntual en el que se modela la dinámica de viraje, con el objetivo de maximizar la eficiencia y predictibilidad de la trayectoria en presencia de incertidumbre sobre la evolución futura de las tormentas. Finalmente, el proceso de optimizatión es inicializado por un método heurístico aleatorizado que genera múltiples puntos de inicio para las iteraciones del optimizador. Esta combinación permite explorar y explotar el espacio de trayectorias solución para proporcionar al piloto o al controlador un conjunto de trayectorias propuestas, así como información útil sobre su coste y el riesgo asociado. Los métodos propuestos son probados en escenarios de ejemplo basados en datos reales, ilustrando las diferentes opciones disponibles de acuerdo a las prioridades del planificador y demostrando que las soluciones descritas en esta tesis son adecuadas para los problemas que se han formulado. De este modo, es posible enriquecer el proceso de planificación de vuelo para incrementar la eficiencia y predictibilidad de las trayectorias individuales, lo que contribuiría a mejoras en el rendimiento del sistema ATM.These works have been financially supported by Universidad Carlos III de Madrid through a PIF scholarship; by Eurocontrol, through the HALA! Research Network grant 10-220210-C2; by the Spanish Ministry of Economy and Competitiveness (MINECO)'s R&D program, through the OptMet project (TRA2014-58413-C2-2-R); and by the European Commission's SESAR Horizon 2020 program, through the TBO-Met project (grant number 699294).Programa de Doctorado en Mecánica de Fluidos por la Universidad Carlos III de Madrid; la Universidad de Jaén; la Universidad de Zaragoza; la Universidad Nacional de Educación a Distancia; la Universidad Politécnica de Madrid y la Universidad Rovira iPresidente: Damián Rivas Rivas.- Secretario: Xavier Prats Menéndez.- Vocal: Benavar Sridha

Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

COMISEF Working Papers Series WPS-028 08/02/2010 URL: http://comisef.eu/files/wps028.pd

A system to predict the S&P 500 using a bio-inspired algorithm

The goal of this research was to develop an algorithmic system capable of predicting the directional trend of the S&P 500 financial index. The approach I have taken was inspired by the biology of the human retina. Extensive research has been published attempting to predict different financial markets using historical data, testing on an in-sample and trend basis with many employing sophisticated mathematical techniques. In reviewing and evaluating these in-sample methodologies, it became evident that this approach was unable to achieve sufficiently reliable prediction performance for commercial exploitation. For these reasons, I moved to an out-of-sample strategy and am able to predict tomorrow’s (t+1) directional trend of the S&P 500 at 55.1%. The key elements that underpin my bio-inspired out-of-sample system are: Identification of 51 financial market data (FMD) inputs, including other indices, currency pairs, swap rates, that affect the 500 component companies of the S&P 500. The use of an extensive historical data set, comprising the actual daily closing prices of the chosen 51 FMD inputs and S&P 500. The ability to compute this large data set in a time frame of less than 24 hours. The data set was fed into a linear regression algorithm to determine the predicted value of tomorrow’s (t+1) S&P 500 closing price. This process was initially carried out in MatLab which proved the concept of my approach, but (3) above was not met. In order to successfully meet the requirement of handling such a large data set to complete the prediction target on time, I decided to adopt a novel graphics processing unit (GPU) based computational architecture. Through extensive optimisation of my GPU engine, I was able to achieve a sufficient speed up of 150x to meet (3). In achieving my optimum directional trend of 55.1%, an extensive range of tests exploring a number of trade offs were carried out using an 8 year data set. The results I have obtained will form the basis of a commercial investment fund. It should be noted that my algorithm uses financial data of the past 60-days, and as such would not be able to predict rapid market changes such as a stock market crash

Machining Performance Analysis in End Milling: Predicting Using ANN and a Comparative Optimisation Study of ANN/BB-BC and ANN/PSO

End milling machining performance indicators such as surface roughness, tool wear and machining time are the principally indicators of machine tool industrial productivity, cost and competitiveness. Since accurate predictions and optimisations are necessary for control purposes, new merit-driven approaches are for good results. The aim of this work is two folds: prediction of machining performance for surface roughness, tool wear and machining time with ANN and the optimisation of these performance indicators using the combined models of ANN-BB-BC and ANN-PSO. However, the optimisation platform is hinged on the fuzzy goal programming model, which facilitates comparisons between the performance of the BB-BC and the PSO algorithms. To demonstrate the approach, optimal tool wear and surface roughness were obtained from a fuzzy goal programme, then converted to a bi-objective non-linear programming model, and solved with the BB-BC and the PSO algorithms. The outputs of the artificial neural network (ANN) were integrated with the optimisation models. The effectiveness of the method was ascertained using extensive literature data. Thus, prediction and optimisation of complex end milling parameters was attained using appropriate selection of parameters with high quality outputs, enhanced by precise prediction and optimisation tools in this proposed approach

Machine Learning and Finance: A Review using Latent Dirichlet Allocation Technique (LDA)

The aim of this paper is provide a first comprehensive structuring of the literature applying machine learning to finance. We use a probabilistic topic modelling approach to make sense of this diverse body of research spanning across the disciplines of finance, economics, computer sciences, and decision sciences. Through the topic modelling approach, a Latent Dirichlet Allocation Technique (LDA), we can extract the 14 coherent research topics that are the focus of the 6,148 academic articles during the years 1990-2019 analysed. We first describe and structure these topics, and then further show how the topic focus has evolved over the last two decades. Our study thus provides a structured topography for finance researchers seeking to integrate machine learning research approaches in their exploration of finance phenomena. We also showcase the benefits to finance researchers of the method of probabilistic modelling of topics for deep comprehension of a body of literature, especially when that literature has diverse multi-disciplinary actors