A Bayesian approach to portfolios selection in multicriteria group decision making

In the a-posteriori approach to multicriteria decision making the idea is to first find a set of interesting (usually non-dominated) decision alternatives and then let the decision maker select among these. Often an additional demand is to limit the size of alternatives to a small number of solutions. In this case, it is important to state preferences on sets. In previous work it has been shown that independent normalization of objective functions (using for instance desirability functions) combined with the hypervolume indicator can be used to formulate such set-preferences. A procedure to compute and to maximize the probability that a set of solutions contains at least one satisfactory solution is established. Moreover, we extend the model to the scenario of multiple decision makers. For this we compute the probability that at least one solution in a given set satisfies all decision makers. First, the information required a-priori from the decision makers is considered. Then, a computational procedure to compute the probability for a single set to contain a solution, which is acceptable to all decision makers, is introduced. Thereafter, we discuss how the computational effort can be reduced and how the measure can be maximized. Practical examples for using this in database queries will be discussed, in order to show how this approach relates to applications

The segmentation issue: general stopping criteria and specific design considerations for practical application of evolutionary algorithms

Segmentation is a tool presented for representation and approximation of data, according to a set of appropriate models. These procedures have applications to many different domains, such as time series analysis, polygonal approximation, Air Traffic Control,... Different heuristic and metaheuristic proposals have been introduced to deal with this issue. This thesis provides a novel multiobjective evolutionary method, analyzing the required general tools for the application evolutionary algorithms to real problems and the specific modifications required over the different steps of general proposals to adapt them to the segmentation domain. An introduction to the domain is presented by means of the design of a specific heuristic for segmentation of Air Traffic Control (ATC) data. This domain has a series of characteristics which make it difficult to be faced with traditional techniques: noisy data and a large number of measurements. The proposal works on two phases, using a pre-segmentation which introduces available domain information and applying a standard technique over this initial technique's results. Its results according to the presented domain, tested with a set of eight different representative trajectories, show competitive advantages compared to general approaches, which oversegmentate noisy data and, in some cases, exhibit poor scalability. This heuristic proposal shows the costly process of adapting available approaches and designing specific ones, along with the multi-objective nature of the problem, which requires the use of quality indicators for a proper comparison process. Applying evolutionary algorithms to segmentation provides several advantages, highlighting the fact that the problem dependance of heuristics make it costly to adapt these heuristics to new domains, as introduced by the designed heuristic to ATC. However, the practical application of these algorithms requires the study of a topic which has received little research effort from the community: stopping criteria. An evolutionary approach should contain a dynamic procedure which can determine when stagnation has taken place and stop the algorithm accordingly (as opposed to a-priori cost budgets, either in function evaluations or generations, which are usually applied for test datasets). Stopping criteria have been faced for single and multi-objective cases in this thesis. Single-objective stopping criteria have been approached proposing an active role of the stopping criteria, actively increasing the diversity in the variable space while tracking the updates in the fitness function. Thus, the algorithm reuses the information obtained for the stopping decision and feeds it to a stopping prevention mechanism in order to prevent problematic situations such as early convergence. The presented algorithm has been tested according to a set of 27 different functions, with different characteristics regarding their dimensionality, search space, local minima... The results show that the introduced mechanisms enhance the robustness of the results, due to the improved exploration and the early convergence prevention. Multi-objective stopping criteria are faced with the use of progress indicators (comparison measures of the quality of the evolution results at different generations) and an associated data gathering tool. The final proposal uses three different progress indicators, (hypervolume, epsilon and Mutual Dominance Rate) and considers them jointly according to a decision fusion architecture. The stagnation analysis is based on the least squares regression parameters of the indicators values, including a normality analysis as well. The online nature of these algorithms is highlighted, preventing the recomputation of the indicators values which were present in other available alternatives, and also focusing on the simplicity of the final proposal, in order to reduce the cost of introducing it into available algorithms. The proposal has been tested with instances of the DTLZ algorithm family, obtaining satisfactory stops with a standard set of configuration values for the technique. However, there is a lack of quantitative measures to determine the objective quality of a stop and to properly compare its value to other alternatives. The multi-objective nature of the segmentation problem is analyzed to propose a multiobjective evolutionary algorithm (MOEA) to deal with it. This nature is analyzed according to a selection of available approaches, highlighting the difficulties which had to be faced in the parameter configuration in order to guide the processes to the desired solution values. A multi-objective a-posteriori approach such as the one presented allows the decision maker to choose from the front of possible final solutions the one which suits him best, simplifying this process. The presented approach chooses SPEA2 as its underlying MOEA, analyzing different representation and initialization proposals. The results have been validated against a representative set of heuristic and metaheuristic techniques, using three widely extended curves from the polygonal approximation domain (chromosome, leaf and semicircle), obtaining statistically better results for almost all the different test cases. This initial MOEA approach had unresolved issues, such as the archiving technique complexity order, and also lacked the proper specific design considerations to adapt it to the application domain. These issues have been faced according to different improvements. First of all, an alternative representation is proposed, including partial fitness information and associated fitness-aware transformation operators (transformation operators which compute children fitness values according to their changes and the parents partial values). A novel archiving procedure is introduced according to the bi-objective nature of the domain, being one of them discrete. This leads to a relaxed Pareto dominance check, named epsilon glitches. Multi-objective local search versions of the traditional algorithms are proposed and tested for the initialization of the algorithm, along with the stopping criterion proposal which has also been adapted to the problem characteristics. The archive size in this case is big enough to contain all the different individuals in the optimal front, such that quality assessment is simplified and a simpler mechanism can be introduced to detect stagnation, according to the improvements in each of the possible individuals. The final evolutionary proposal is scalable, requires few configuration parameters and introduces an efficient dynamic stopping criterion. Its results have been tested against the original technique and the set of heuristic and metaheuristic techniques previously used, including the three original curves and also more complex versions of them (obtained with an introduced generation mechanism according to these original shapes). Even though the stopping results are very satisfactory, the obtained results are slightly worse than the original MOEA for the three simpler problem instances with the established configuration parameters (as was expected, due to the computational effort of the a-priori established number of generations and population size, based on the analysis of the algorithm's results). However, the comparison versus the alternative techniques stills shows the same statistically better results, and its reduced computational cost allows its application to a wider set of problems.La segmentación es una técnica creada para la representación y la aproximación de conjuntos de datos a través de un conjunto de modelos apropiados. Estos procedimientos tienen aplicaciones para múltiples dominios distintos, como el análisis de series temporales, la aproximación poligonal o el Control de Tráfico Aéreo. Se han hecho múltiples propuestas tanto de carácter heurístico como metaheurístico para lidiar con este problema. Esta tesis proporciona un nuevo método evolutivo multiobjetivo, analizando las herramientas generales necesarias para la aplicación de algoritmos evolutivos a problemas reales y las modificaciones específicas necesarias sobre los distintos pasos de las propuestas genéricas para adaptarlos al dominio de la segmentación. Se presenta una introducción al dominio mediante el diseño de una heurística específica para la segmentación de datos procedentes del Control de Tráfico Aéreo (CTA). Este dominio tiene una serie de características que dificultan la aplicación de técnicas tradicionales: datos con ruido y un gran número de muestras. La propuesta realizada funciona de acuerdo a dos fases, utilizando una presegmentación que introduce información del dominio disponible para posteriormente aplicar una técnica estándar sobre los resultados de esta técnica inicial. Sus resultados para el dominio presentado, probado con un conjunto de ocho trayectorias representativas distintas, presentan ventajas competitivas frente a los enfoques generales, que sobresegmentan los datos con ruido y, en algunos casos, presentan una mala escalabilidad. Esta propuesta heurística muestra el costoso proceso que implica adaptar los enfoques existentes o el diseño de otros nuevos, junto a la naturaleza multiobjectivo del problema, que precisa del uso de indicadores de calidad para realizar un proceso de comparación apropiado. La aplicación de algoritmos evolutivos a la segmentación tiene múltiples ventajas, destacando el hecho de la dependencia existente entre las heurísticas y el problema específico para el que han sido diseñadas, lo que hace que su adaptación a nuevos dominios sea costosa, como se ha introducido a través de la propuesta heurística para CTA. A pesar de ello, la aplicación práctica de estos algoritmos requiere el estudio de una faceta que ha recibido poca atención por parte de la comunidad desde el punto de vista de la investigación: los criterios de parada. Un enfoque evolutivo debería tener una técnica dinámica que pueda detectar cuando se ha producido el estancamiento del proceso, y parar el algoritmo de acuerdo a ello (de manera opuesta a los criterios a-priori que establecen un coste predeterminado, expresado como número de evaluaciones o de generaciones, y que son habitualmente aplicados para los conjuntos de datos de prueba). Los criterios de parada se han afrontado tanto desde el caso de un único objetivo como desde el caso multiobjectivo en esta tesis. Los criterios de parada para un único objetivo se han abordado proponiendo un rol activo para el criterio, aumentando la diversidad en el espacio de variables de una manera activa, mientras se monitorizan los cambios en la función objetivo. De esta manera, el algoritmo reutiliza la información obtenida para la decisión de parada y la inserta en un mecanismo de prevención de la parada con la finalidad de prevenir situaciones problemáticas como la convergencia temprana. El algoritmo presentado se ha probado sobre un conjunto de 27 funciones distintas, con diferentes características respecto a su dimensionalidad, espacio de búsqueda, mínimos locales... Los resultados muestran que los mecanismos introducidos mejoran la robustez de los resultados, haciendo uso de la exploración mejorada y la prevención de la convergencia temprana. Los criterios de parada multiobjetivo se han planteado con el uso de indicadores de avance (medidas comparativas de la calidad de los resultados de la evolución en diferentes generaciones) y una herramienta de recolección de datos asociada. La propuesta final utiliza tres indicadores de avance distintos (hypervolumen, epsilon y ratio de dominancia mutua) y los considera de una manera conjunta de acuerdo a una arquitectura de fusión de decisiones. El análisis del estancamiento se basa en los parámetros de una regresión de mínimos cuadrados sobre los valores de los indicadores, incluyendo asimismo un análisis de normalidad. Se recalca la naturaleza online de estos algoritmos, evitando el recálculo de los valores de los indicadores que estaba presente en otras alternativas disponibles, y también focalizándose en la simplicidad de la propuesta final, de manera que se facilite el proceso de introducir el criterio en los algoritmos existentes. La propuesta ha sido probada con instancias de la familia de algoritmos DTLZ, obteniendo resultados de parada satisfactorios con un conjunto de valores de configuración estándar para la técnica. Sin embargo, existe una falta de medidas cuantitativas para determinar la calidad objetiva de una parada, así como para comparar de manera apropiada su valor frente al de otras alternativas. La naturaleza multiobjetivo del problema de segmentación se ha analizado para proponer un algoritmo evolutivo multiobjetivo (AEMO) para resolverlo. Esta naturaleza ha sido analizada de acuerdo a una selección de los enfoques disponibles, destacando las dificultades que se tienen que afrontar en la configuración de los parámetros de cara a guiar el proceso hacia los valores de solución deseados. Un enfoque multiobjetivo a-posteriori como el que se ha presentado permite al responsable elegir del frente de posibles soluciones finales aquella que encaja mejor, simplificando este proceso. El enfoque presentado ha elegido SPEA2 como algoritmo de base, analizando diferentes propuestas de inicialización y representación. Los resultados se han validado frente a un conjunto significativo de técnicas heurísticas y metaheurísticas, utilizando tres curvas ampliamente extendidas en el dominio de la segmentación poligonal (cromosoma, hoja y semicírculo), obteniendo resultados estadísticamente mejores para la casi totatilidad de los casos de prueba. Esta propuesta inicial de AEMO presentaba una serie de problemas sin resolver, como el orden de complejidad de la técnica de almacenaje, y además carecía de las consideraciones específicas de diseño para su adaptación al dominio de aplicación. Estos problemas se han afrontado de acuerdo a diferentes mejoras. Por un lado, se ha propuesto una representación alternativa, incluyendo información parcial de la función objetivo y operadores de transformación informados (operadores de transformación que calculan los valores de la función objetivo de los hijos de acuerdo a los cambios realizados y los valores parciales de los padres). Una nueva técnica de almacenaje se ha introducido de acuerdo a la naturaleza biobjetivo del dominio, siendo uno de ellos además discreto. Esta naturaleza ha llevado a la aplicación de una forma relajada de dominancia de Pareto, que hemos denominado pulsos épsilon. Versiones multiobjetivo de los algoritmos tradicionales de búsqueda local han sido propuestas y probadas para la inicialización del algoritmo, junto con la propuesta de criterio de parada, que también ha sido adaptada a las características del problema. En este caso, el tamaño del almacén es suficientemente grande como para almacenar todos los individuos del frente óptimo, de manera que las técnicas de análisis de calidad de los frentes se simplifican, y un mecanismo más sencillo puede ser introducido para detectar el estancamiento, de acuerdo a las mejoras en cada uno de los individuos posibles. La propuesta evolutiva final es escalable, requiere pocos parámetros de configuración e introduce un criterio de parada dinámico y eficiente. Sus resultados se han probado frente a la técnica original y el conjunto de técnicas heurísticas y metaheurísticas previamente utilizadas, incluyendo las tres curvas originales y versiones más complejas de las mismas (obtenidas con un mecanismo de generación incluido de acuerdo a estas tres formas originales). A pesar de que los resultados de parada son muy satisfactorios, los resultados obtenidos son ligeramente peores que el AEMO original para las tres instancias del problema más simples, utilizando el conjunto de parámetros de configuración establecidos (como cabía esperar, dado el coste computacional del número de generaciones y tamaño de la población establecidos a priori, basados en el análisis de los resultados del algoritmo). En cualquier caso, la comparación frente a las técnicas alternativas todavía presenta los mismos resultados estadísticamente mejores, y las mejoras en el coste computacional permiten su aplicación a un mayor conjunto de problemas.Programa Oficial de Doctorado en Ciencia y Tecnología InformáticaPresidente: Pedro Isasi Viñuela.- Secretario: Rafael Martínez Tomás.- Vocal: Javier Segovia Pére

Multi-objective optimisation methods applied to aircraft techno-economic and environmental issues

Engineering methods that couple multi-objective optimisation (MOO) techniques with high fidelity computational tools are expected to minimise the environmental impact of aviation while increasing the growth, with the potential to reveal innovative solutions. In order to mitigate the compromise between computational efficiency and fidelity, these methods can be accelerated by harnessing the computational efficiency of Graphic Processor Units (GPUs). The aim of the research is to develop a family of engineering methods to support research in aviation with respect to the environmental and economic aspects. In order to reveal the non-dominated trade-o_, also known as Pareto Front(PF), among conflicting objectives, a MOO algorithm, called Multi-Objective Tabu Search 2 (MOTS2), is developed, benchmarked relative to state-of-the-art methods and accelerated by using GPUs. A prototype fluid solver based on GPU is also developed, so as to simulate the mixing capability of a microreactor that could potentially be used in fuel-saving technologies in aviation. By using the aforementioned methods, optimal aircraft trajectories in terms of flight time, fuel consumption and emissions are generated, and alternative designs of a microreactor are suggested, so as to assess the trade-offs between pressure losses and the micro-mixing capability. As a key contribution to knowledge, with reference to competitive optimisers and previous cases, the capabilities of the proposed methodology are illustrated in prototype applications of aircraft trajectory optimisation (ATO) and micromixing optimisation with 2 and 3 objectives, under operational and geometrical constraints, respectively. In the short-term, ATO ought to be applied to existing aircraft. In the long-term, improving the micro-mixing capability of a microreactor is expected to enable the use of hydrogen-based fuel. This methodology is also benchmarked and assessed relative to state-of-the-art techniques in ATO and micro-mixing optimisation with known and unknown trade-offs, whereas the former could only optimise 2 objectives and the latter could not exploit the computational efficiency of GPUs. The impact of deploying on GPUs a micro-mixing _ow solver, which accelerates the generation of trade-off against a reference study, and MOTS2, which illustrates the scalability potential, is assessed. With regard to standard analytical function test cases and verification cases in MOO, MOTS2 can handle the multi-modality of the trade-o_ of ZDT4, which is a MOO benchmark function with many local optima that presents a challenge for a state-of-the-art genetic algorithm for ATO, called NSGAMO, based on case studies in the public domain. However, MOTS2 demonstrated worse performance on ZDT3, which is a MOO benchmark function with a discontinuous trade-o_, for which NSGAMO successfully captured the target PF. Comparing their overall performance, if the shape of the PF is known, MOTS2 should be preferred in problems with multi-modal trade-offs, whereas NSGAMO should be employed in discontinuous PFs. The shape of the trade-o_ between the objectives in airfoil shape optimisation, ATO and micro-mixing optimisation was continuous. The weakness of MOTS2 to sufficiently capture the discontinuous PF of ZDT3 was not critical in the studied examples … [cont.]

Scalarized Preferences in Multi-objective Optimization

Multikriterielle Optimierungsprobleme verfügen über keine Lösung, die optimal in jeder Zielfunktion ist. Die Schwierigkeit solcher Probleme liegt darin eine Kompromisslösung zu finden, die den Präferenzen des Entscheiders genügen, der den Kompromiss implementiert. Skalarisierung – die Abbildung des Vektors der Zielfunktionswerte auf eine reelle Zahl – identifiziert eine einzige Lösung als globales Präferenzenoptimum um diese Probleme zu lösen. Allerdings generieren Skalarisierungsmethoden keine zusätzlichen Informationen über andere Kompromisslösungen, die die Präferenzen des Entscheiders bezüglich des globalen Optimums verändern könnten. Um dieses Problem anzugehen stellt diese Dissertation eine theoretische und algorithmische Analyse skalarisierter Präferenzen bereit. Die theoretische Analyse besteht aus der Entwicklung eines Ordnungsrahmens, der Präferenzen als Problemtransformationen charakterisiert, die präferierte Untermengen der Paretofront definieren. Skalarisierung wird als Transformation der Zielmenge in diesem Ordnungsrahmen dargestellt. Des Weiteren werden Axiome vorgeschlagen, die wünschenswerte Eigenschaften von Skalarisierungsfunktionen darstellen. Es wird gezeigt unter welchen Bedingungen existierende Skalarisierungsfunktionen diese Axiome erfüllen. Die algorithmische Analyse kennzeichnet Präferenzen anhand des Resultats, das ein Optimierungsalgorithmus generiert. Zwei neue Paradigmen werden innerhalb dieser Analyse identifiziert. Für beide Paradigmen werden Algorithmen entworfen, die skalarisierte Präferenzeninformationen verwenden: Präferenzen-verzerrte Paretofrontapproximationen verteilen Punkte über die gesamte Paretofront, fokussieren aber mehr Punkte in Regionen mit besseren Skalarisierungswerten; multimodale Präferenzenoptima sind Punkte, die lokale Skalarisierungsoptima im Zielraum darstellen. Ein Drei-Stufen-Algorith\-mus wird entwickelt, der lokale Skalarisierungsoptima approximiert und verschiedene Methoden werden für die unterschiedlichen Stufen evaluiert. Zwei Realweltprobleme werden vorgestellt, die die Nützlichkeit der beiden Algorithmen illustrieren. Das erste Problem besteht darin Fahrpläne für ein Blockheizkraftwerk zu finden, die die erzeugte Elektrizität und Wärme maximieren und den Kraftstoffverbrauch minimiert. Präferenzen-verzerrte Approximationen generieren mehr Energie-effiziente Lösungen, unter denen der Entscheider seine favorisierte Lösung auswählen kann, indem er die Konflikte zwischen den drei Zielen abwägt. Das zweite Problem beschäftigt sich mit der Erstellung von Fahrplänen für Geräte in einem Wohngebäude, so dass Energiekosten, Kohlenstoffdioxidemissionen und thermisches Unbehagen minimiert werden. Es wird gezeigt, dass lokale Skalarisierungsoptima Fahrpläne darstellen, die eine gute Balance zwischen den drei Zielen bieten. Die Analyse und die Experimente, die in dieser Arbeit vorgestellt werden, ermöglichen es Entscheidern bessere Entscheidungen zu treffen indem Methoden angewendet werden, die mehr Optionen generieren, die mit den Präferenzen der Entscheider übereinstimmen

Robust optimization of algorithmic trading systems

GAs (Genetic Algorithms) and GP (Genetic Programming) are investigated for finding robust Technical Trading Strategies (TTSs). TTSs evolved with standard GA/GP techniques tend to suffer from over-fitting as the solutions evolved are very fragile to small disturbances in the data. The main objective of this thesis is to explore optimization techniques for GA/GP which produce robust TTSs that have a similar performance during both optimization and evaluation, and are also able to operate in all market conditions and withstand severe market shocks. In this thesis, two novel techniques that increase the robustness of TTSs and reduce over-fitting are described and compared to standard GA/GP optimization techniques and the traditional investment strategy Buy & Hold. The first technique employed is a robust multi-market optimization methodology using a GA. Robustness is incorporated via the environmental variables of the problem, i.e. variablity in the dataset is introduced by conducting the search for the optimum parameters over several market indices, in the hope of exposing the GA to differing market conditions. This technique shows an increase in the robustness of the solutions produced, with results also showing an improvement in terms of performance when compared to those offered by conducting the optimization over a single market. The second technique is a random sampling method we use to discover robust TTSs using GP. Variability is introduced in the dataset by randomly sampling segments and evaluating each individual on different random samples. This technique has shown promising results, substantially beating Buy & Hold. Overall, this thesis concludes that Evolutionary Computation techniques such as GA and GP combined with robust optimization methods are very suitable for developing trading systems, and that the systems developed using these techniques can be used to provide significant economic profits in all market conditions

Datacenter management for on-site intermittent and uncertain renewable energy sources

Les technologies de l'information et de la communication sont devenues, au cours des dernières années, un pôle majeur de consommation énergétique avec les conséquences environnementales associées. Dans le même temps, l'émergence du Cloud computing et des grandes plateformes en ligne a causé une augmentation en taille et en nombre des centres de données. Pour réduire leur impact écologique, alimenter ces centres avec des sources d'énergies renouvelables (EnR) apparaît comme une piste de solution. Cependant, certaines EnR telles que les énergies solaires et éoliennes sont liées aux conditions météorologiques, et sont par conséquent intermittentes et incertaines. L'utilisation de batteries ou d'autres dispositifs de stockage est souvent envisagée pour compenser ces variabilités de production. De par leur coût important, économique comme écologique, ainsi que les pertes énergétiques engendrées, l'utilisation de ces dispositifs sans intégration supplémentaire est insuffisante. La consommation électrique d'un centre de données dépend principalement de l'utilisation des ressources de calcul et de communication, qui est déterminée par la charge de travail et les algorithmes d'ordonnancement utilisés. Pour utiliser les EnR efficacement tout en préservant la qualité de service du centre, une gestion coordonnée des ressources informatiques, des sources électriques et du stockage est nécessaire. Il existe une grande diversité de centres de données, ayant différents types de matériel, de charge de travail et d'utilisation. De la même manière, suivant les EnR, les technologies de stockage et les objectifs en termes économiques ou environnementaux, chaque infrastructure électrique est modélisée et gérée différemment des autres. Des travaux existants proposent des méthodes de gestion d'EnR pour des couples bien spécifiques de modèles électriques et informatiques. Cependant, les multiples combinaisons de ces deux parties rendent difficile l'extrapolation de ces approches et de leurs résultats à des infrastructures différentes. Cette thèse explore de nouvelles méthodes pour résoudre ce problème de coordination. Une première contribution reprend un problème d'ordonnancement de tâches en introduisant une abstraction des sources électriques. Un algorithme d'ordonnancement est proposé, prenant les préférences des sources en compte, tout en étant conçu pour être indépendant de leur nature et des objectifs de l'infrastructure électrique. Une seconde contribution étudie le problème de planification de l'énergie d'une manière totalement agnostique des infrastructures considérées. Les ressources informatiques et la gestion de la charge de travail sont encapsulées dans une boîte noire implémentant un ordonnancement sous contrainte de puissance. La même chose s'applique pour le système de gestion des EnR et du stockage, qui agit comme un algorithme d'optimisation d'engagement de sources pour répondre à une demande. Une optimisation coopérative et multiobjectif, basée sur un algorithme évolutionnaire, utilise ces deux boîtes noires afin de trouver les meilleurs compromis entre les objectifs électriques et informatiques. Enfin, une troisième contribution vise les incertitudes de production des EnR pour une infrastructure plus spécifique. En utilisant une formulation en processus de décision markovien (MDP), la structure du problème de décision sous-jacent est étudiée. Pour plusieurs variantes du problème, des méthodes sont proposées afin de trouver les politiques optimales ou des approximations de celles-ci avec une complexité raisonnable.In recent years, information and communication technologies (ICT) became a major energy consumer, with the associated harmful ecological consequences. Indeed, the emergence of Cloud computing and massive Internet companies increased the importance and number of datacenters around the world. In order to mitigate economical and ecological cost, powering datacenters with renewable energy sources (RES) began to appear as a sustainable solution. Some of the commonly used RES, such as solar and wind energies, directly depends on weather conditions. Hence they are both intermittent and partly uncertain. Batteries or other energy storage devices (ESD) are often considered to relieve these issues, but they result in additional energy losses and are too costly to be used alone without more integration. The power consumption of a datacenter is closely tied to the computing resource usage, which in turn depends on its workload and on the algorithms that schedule it. To use RES as efficiently as possible while preserving the quality of service of a datacenter, a coordinated management of computing resources, electrical sources and storage is required. A wide variety of datacenters exists, each with different hardware, workload and purpose. Similarly, each electrical infrastructure is modeled and managed uniquely, depending on the kind of RES used, ESD technologies and operating objectives (cost or environmental impact). Some existing works successfully address this problem by considering a specific couple of electrical and computing models. However, because of this combined diversity, the existing approaches cannot be extrapolated to other infrastructures. This thesis explores novel ways to deal with this coordination problem. A first contribution revisits batch tasks scheduling problem by introducing an abstraction of the power sources. A scheduling algorithm is proposed, taking preferences of electrical sources into account, though designed to be independent from the type of sources and from the goal of the electrical infrastructure (cost, environmental impact, or a mix of both). A second contribution addresses the joint power planning coordination problem in a totally infrastructure-agnostic way. The datacenter computing resources and workload management is considered as a black-box implementing a scheduling under variable power constraint algorithm. The same goes for the electrical sources and storage management system, which acts as a source commitment optimization algorithm. A cooperative multiobjective power planning optimization, based on a multi-objective evolutionary algorithm (MOEA), dialogues with the two black-boxes to find the best trade-offs between electrical and computing internal objectives. Finally, a third contribution focuses on RES production uncertainties in a more specific infrastructure. Based on a Markov Decision Process (MDP) formulation, the structure of the underlying decision problem is studied. For several variants of the problem, tractable methods are proposed to find optimal policies or a bounded approximation

Multiobjective genetic programming for financial portfolio management in dynamic environments

Multiobjective (MO) optimisation is a useful technique for evolving portfolio optimisation solutions that span a range from high-return/high-risk to low-return/low-risk. The resulting Pareto front would approximate the risk/reward Efficient Frontier [Mar52], and simplifies the choice of investment model for a given client’s attitude to risk. However, the financial market is continuously changing and it is essential to ensure that MO solutions are capturing true relationships between financial factors and not merely over fitting the training data. Research on evolutionary algorithms in dynamic environments has been directed towards adapting the algorithm to improve its suitability for retraining whenever a change is detected. Little research focused on how to assess and quantify the success of multiobjective solutions in unseen environments. The multiobjective nature of the problem adds a unique feature to be satisfied to judge robustness of solutions. That is, in addition to examining whether solutions remain optimal in the new environment, we need to ensure that the solutions’ relative positions previously identified on the Pareto front are not altered. This thesis investigates the performance of Multiobjective Genetic Programming (MOGP) in the dynamic real world problem of portfolio optimisation. The thesis provides new definitions and statistical metrics based on phenotypic cluster analysis to quantify robustness of both the solutions and the Pareto front. Focusing on the critical period between an environment change and when retraining occurs, four techniques to improve the robustness of solutions are examined. Namely, the use of a validation data set; diversity preservation; a novel variation on mating restriction; and a combination of both diversity enhancement and mating restriction. In addition, preliminary investigation of using the robustness metrics to quantify the severity of change for optimum tracking in a dynamic portfolio optimisation problem is carried out. Results show that the techniques used offer statistically significant improvement on the solutions’ robustness, although not on all the robustness criteria simultaneously. Combining the mating restriction with diversity enhancement provided the best robustness results while also greatly enhancing the quality of solutions

Exact and heuristic approaches for multi-component optimisation problems

Modern real world applications are commonly complex, consisting of multiple subsystems that may interact with or depend on each other. Our case-study about wave energy converters (WEC) for the renewable energy industry shows that in such a multi-component system, optimising each individual component cannot yield global optimality for the entire system, owing to the influence of their interactions or the dependence on one another. Moreover, modelling a multi-component problem is rarely easy due to the complexity of the issues, which leads to a desire for existent models on which to base, and against which to test, calculations. Recently, the travelling thief problem (TTP) has attracted significant attention in the Evolutionary Computation community. It is intended to offer a better model for multicomponent systems, where researchers can push forward their understanding of the optimisation of such systems, especially for understanding of the interconnections between the components. The TTP interconnects with two classic NP-hard problems, namely the travelling salesman problem and the 0-1 knapsack problem, via the transportation cost that non-linearly depends on the accumulated weight of items. This non-linear setting introduces additional complexity. We study this nonlinearity through a simplified version of the TTP - the packing while travelling (PWT) problem, which aims to maximise the total reward for a given travelling tour. Our theoretical and experimental investigations demonstrate that the difficulty of a given problem instance is significantly influenced by adjusting a single parameter, the renting rate, which prompted our method of creating relatively hard instances using simple evolutionary algorithms. Our further investigations into the PWT problem yield a dynamic programming (DP) approach that can solve the problem in pseudo polynomial time and a corresponding approximation scheme. The experimental investigations show that the new approaches outperform the state-of-the-art ones. We furthermore propose three exact algorithms for the TTP, based on the DP of the PWT problem. By employing the exact DP for the underlying PWT problem as a subroutine, we create a novel indicator-based hybrid evolutionary approach for a new bi-criteria formulation of the TTP. This hybrid design takes advantage of the DP approach, along with a number of novel indicators and selection mechanisms to achieve better solutions. The results of computational experiments show that the approach is capable to outperform the state-of-the-art results.Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 201

Matheuristic algorithms for solving multi-objective/stochastic scheduling and routing problems

In der Praxis beinhalten Optimierungsprobleme oft unterschiedliche Ziele, welche optimiert werden sollen. Oft ist es nicht möglich die Ziele zu einem einzelnen Ziel zusammenzufassen. Mehrzieloptimierung beschäftigt sich damit, solche Probleme zu lösen. Wie in der Einzieloptimierung muss eine Lösung alle Nebenbedingungen des Problems erfüllen. Im Allgemeinen sind die Ziele konfligierend, sodass es nicht möglich ist eine einzelne Lösung zu finden welche optimal im Sinne aller Ziele ist. Algorithmen zum Lösen von Mehrziel-Optimierungsproblemen, präsentieren dem Entscheider eine Menge von effizienten Alternativen. Effizienz in der Mehrzieloptimierung ist als Pareto-Optimalität ausgedrückt. Eine Lösung eines Optimierungsproblems ist genau dann Pareto-optimal wenn es keine andere zulässige Lösung gibt, welche in allen Zielen mindestens gleich gut wie die betrachtete Lösung ist und besser in mindestens einem Ziel. In dieser Arbeit werden Mehrziel-Optimierungsprobleme aus zwei unterschiedlichen Anwendungsgebieten betrachtet. Das erste Problem, das Multi-objective Project Selection, Scheduling and Staffing with Learning Problem (MPSSSL), entstammt dem Management in forschungsorientierten Organisationen. Die Entscheider in solchen Organisationen stehen vor der Frage welche Projekte sie aus einer Menge von Projektanträgen auswählen sollen, und wie diese Teilmenge von Projekten (ein Projektportfolio) mit den benötigten Ressourcen ausgestattet werden kann (dies beinhaltet die zeitliche und personelle Planung). Aus unterschiedlichen Gründen ist dieses Problem schwer zu lösen, z.B. (i) die Auswahl von Projekten unter Beachtung der beschränkten Ressourcen ist ein Rucksackproblem (und ist damit NP-schwer) (ii) ob ein Projektportfolio zulässig ist oder nicht hängt davon ab ob, man dafür einen Zeitplan erstellen kann und genügend Mitarbeiter zur Verfügung stehen. Da in diesem Problem die Mitarbeiterzuordnung zu den einzelnen Projekten einbezogen wird, muss der Entscheider Ziele unterschiedlicher Art berücksichtigen. Manche Ziele sind ökonomischer Natur, z.B. die Rendite, andere wiederum beziehen sich auf die Kompetenzentwicklung der einzelnen Mitarbeiter. Ziele, die sich auf die Kompetenzentwicklung beziehen, sollen sicherstellen, dass das Unternehmen auch in Zukunft am Markt bestehen kann. Im Allgemeinen können diese unterschiedlichen Ziele nicht zu einem einzigen Ziel zusammengefasst werden. Daher werden Methoden zur Lösung von Mehrziel-Optimierungsproblemen benötigt. Um MPSSSL Probleme zu lösen werden in dieser Arbeit zwei unterschiedliche hybride Algorithmen betrachtet. Beide kombinieren nämlich Metaheuristiken (i) den Nondominated Sorting Genetic (NSGA-II) Algorithmus, und den (ii)~Pareto Ant Colony (P-ACO) Algorithmus, mit einem exakten Algorithmus zum Lösen von Linearen Programmen kombinieren. Unsicherheit ist ein weiterer wichtiger Aspekt der in der Praxis auftaucht. Unterschiedliche Parameter des Problems können unsicher sein (z.B. der aus einem Projekt erzielte Gewinn oder die Zeit bzw. der Aufwand, der benötigt wird, um die einzelnen Vorgänge eines Projekts abzuschließen). Um in diesem Fall das ``beste'' Projektportfolio zu finden, werden Methoden benötigt, welche stochastische Mehrziel-Optimierungsprobleme lösen können. Zur Lösung der stochastischen Erweiterung (SMPSSSL) des MPSSSL Problems zu lösen, präsentieren wir eine Methode, die den zuvor genannten hybriden NSGA-II Algorithmus mit dem Adaptive Pareto Sampling (APS) Algorithmus kombiniert. APS wird verwendet, um das Zusammenspiel von Simulation und Optimierung zu koordinieren. Zur Steigerung der Performance des Simulationsprozesses, verwenden wir Importance Sampling (IS). Das zweite Problem dieser Arbeit, das Bi-Objective Capacitated Vehicle Routing Problem with Route Balancing (CVRPB), kommt aus dem Bereich Logistik. Wenn man eine Menge von Kunden zu beliefern hat, steht man als Entscheider vor der Frage, wie man die Routen für eine fixe Anzahl von Fahrzeugen (mit beschränkter Kapazität) bestimmt, sodass alle Kunden beliefert werden können. Die Routen aller Fahrzeuge starten und enden dabei immer bei einem Depot. Die Einziel-Variante dieses Problems ist als Capacitated Vehicle Routing Problem (CVRP) bekannt, dessen Ziel es ist die Lösung zu finden, die die Gesamtkosten aller Routen minimiert. Dabei tritt jedoch das Problem auf, dass die Routen der optimalen Lösung sehr unterschiedliche Fahrtzeiten haben können. Unter bestimmten Umständen ist dies jedoch nicht erwünscht. Um dieses Problem zu umgehen, betrachten wir in dieser Arbeit eine Variante des (bezeichnet als CVRPB) CVRP, welche als zweite Zielfunktion die Balanziertheit der einzelnen Routen einbezieht. Zur Lösung von CVRPB Problemen verwenden wir die Adaptive Epsilon-Constraint Method in Kombination mit einem Branch-and-Cut Algorithmus und zwei unterschiedlichen Genetischen Algorithmen (GA), (i) einem Einziel-GA und (ii) dem NSGA-II. In dieser Arbeit werden Optimierungsalgorithmen präsentiert, welche es erlauben, Mehrziel- und stochastische Mehrziel-Optimierungsprobleme zu lösen. Unterschiedliche Algorithmen wurden implementiert und basierend auf aktuellen Performance-Maßen verglichen. Experimente haben gezeigt, dass die entwickelten Methoden gut geeignet sind, die betrachteten Optimierungsprobleme zu lösen. Die hybriden Algorithmen, welche Metaheuristiken mit exakten Methoden kombinieren, waren entweder ausschlaggebend um das Problem zu lösen (im Fall des Project Portfolio Selection Problems) oder konnten die Performance des Lösungsprozesses signifikant verbessern (im Fall des Vehicle Routing Problems).In practice decision problems often include different goals which can hardly be aggregated to a single objective for different reasons. In the field of multi-objective optimization several objective functions are considered. As in single objective optimization a solution has to satisfy all constraints of the problem. In general the goals are conflicting and there will be no solution, that is optimal for all objectives. Algorithms for multi-objective optimization problems provide the decision maker a set of efficient solutions, among which she or he can choose the most suitable alternative. In multi-objective optimization efficiency of a solution is expressed as Pareto-optimality. Pareto-optimality of a solution is defined as the property that no other solution exists that is better than the proposed one in at least one objective and at least equally good in all criteria. The first application that is considered in this thesis, the Multi-objective Project Selection, Scheduling and Staffing with Learning problem (MPSSSL) arises from the field of management in research-centered organizations. Given a set of project proposals the decision makers have to select the ``best'' subset of projects (a project portfolio) and set these up properly (schedule them and provide the necessary resources). This problem is hard to solve for different reasons: (i) selecting a subset of projects considering limited resources is a knapsack-type problem that is known to be NP-hard, and (ii) to determine the feasibility of a given portfolio, the projects have to be scheduled and staff must be assigned to them. As in this problem the assignment of workers is influenced by the decision which portfolio should be selected, the decision maker has to consider goals of different nature. Some objectives are related to economic goals (e.g. return of investment), others are related to the competence development of the workers. Competence oriented goals are motivated by the fact that competencies determine the attainment and sustainability of strategic positions in market competition. In general the objectives cannot be combined to a single objective, therefore methods for solving multi-objective optimization problems are used. To solve the problem we use two different hybrid algorithms that combine metaheuristic algorithms, (i) the Nondominated Sorting Genetic Algorithm (NSGA-II), and (ii) Pareto Ant Colony (P-ACO) algorithm with a linear programming solver as a subordinate. In practice, uncertainty is another typically encountered aspect. Different parameters of the problem can be uncertain (e.g. benefits of a project, or the time and effort required to perform the single activities required by a project). To determine the ``best'' portfolio, methods are needed that are able to handle uncertainty in optimization. To solve the stochastic extension (SMPSSSL) of the MPSSSL problem we present an algorithm that combines the aforementioned NSGA-II algorithm with the Adaptive Pareto Sampling (APS) algorithm. APS is used to handle the interplay between multi-objective optimization and simulation. The performance of the simulation process is increased by using importance sampling (IS). The second problem, the Bi-objective Capacitated Vehicle Routing Problem with Route Balancing (CVRPB) arises from the field of vehicle routing. Given a set of customers, the decision makers have to construct routes for a fixed number of vehicles, each starting and ending at the same depot, such that the demands of all customers can be fulfilled, and the capacity constraints of each vehicle are not violated. The traditional objective of this problem (known as the Capacitated Vehicle Routing Problem (CVRP)) is minimizing the total costs of all routes. A problem that may arise by this approach is that the resulting routes can be very unbalanced (in the sense of drivers workload). To overcome this problem a second objective function that measures the balance of the routes of a solution is introduced. In this work, we use the Adaptive Epsilon-Constraint Method in combination with a branch-and-cut algorithm and two genetic algorithms (i) a single-objective GA and (ii) the multi-objective NSGA-II, to solve the considered problem. Prototypes of different algorithms to solve the problems are developed and their performance is assessed by using state of the art performance measures. The computational experiments show that the developed solution procedures will be well suited to solve the considered optimization problems. The hybrid algorithms combining metaheuristic and exact optimization methods, turned out to be crucial to solve the problem (application to project portfolio selection) or to improve the performance of the solution procedure (application to vehicle routing)