A modified mean-variance-conditional value at risk model of multi-objective portfolio optimization with an application in finance

This research focuses on the development of a portfolio optimization model based on the classic optimization method and a meta-heuristic algorithm. The main goal of a portfolio optimization model is to achieve maximum return with minimum investment risk by allocating capital based on a set of existing assets. Recently, mean-variance models have been improved to mean-variance-CVaR (MVC) model as a multi-objective portfolio optimization (MPO) problem which is difficult to be solved directly and optimally. In this work, a modified MVC model of portfolio optimization is constructed using the weighted sum method (WSM). In this method, each objective function of MVC model is given a weight. The optimization problem is then minimized as a weighted sum of the objective functions. The implementation of WSM enables the MVC model to be transformed from a multi-objective function to one with a single objective function. The modified MVC model is then solved using ant colony optimization (ACO) algorithm. This algorithm solves the MVC model by the number of ant colonies and the number of pheromone, a chemical creating trails for others to follow. The modified MVC model can be used in managing diverse investment portfolio, including stocks on the stock market and currency exchange. The applicability and effectiveness of the proposed method are demonstrated by solving a benchmark problem and a practical investment problem as examples. The data of practical examples are collected from the foreign currency exchange of Bank Negara Malaysia for the years 2012 and 2013. In conclusion, this thesis presented a hybrid optimization algorithm which utilizes a classical approach, WSM and a meta-heuristic approach, ACO to solve an MVC model of portfolio optimization

A variable neighborhood search simheuristic for project portfolio selection under uncertainty

With limited nancial resources, decision-makers in rms and governments face the task of selecting the best portfolio of projects to invest in. As the pool of project proposals increases and more realistic constraints are considered, the problem becomes NP-hard. Thus, metaheuristics have been employed for solving large instances of the project portfolio selection problem (PPSP). However, most of the existing works do not account for uncertainty. This paper contributes to close this gap by analyzing a stochastic version of the PPSP: the goal is to maximize the expected net present value of the inversion, while considering random cash ows and discount rates in future periods, as well as a rich set of constraints including the maximum risk allowed. To solve this stochastic PPSP, a simulation-optimization algorithm is introduced. Our approach integrates a variable neighborhood search metaheuristic with Monte Carlo simulation. A series of computational experiments contribute to validate our approach and illustrate how the solutions vary as the level of uncertainty increases

Population-based algorithms for improved history matching and uncertainty quantification of Petroleum reservoirs

In modern field management practices, there are two important steps that shed light on a multimillion dollar investment. The first step is history matching where the simulation model is calibrated to reproduce the historical observations from the field. In this inverse problem, different geological and petrophysical properties may provide equally good history matches. Such diverse models are likely to show different production behaviors in future. This ties the history matching with the second step, uncertainty quantification of predictions. Multiple history matched models are essential for a realistic uncertainty estimate of the future field behavior. These two steps facilitate decision making and have a direct impact on technical and financial performance of oil and gas companies. Population-based optimization algorithms have been recently enjoyed growing popularity for solving engineering problems. Population-based systems work with a group of individuals that cooperate and communicate to accomplish a task that is normally beyond the capabilities of each individual. These individuals are deployed with the aim to solve the problem with maximum efficiency. This thesis introduces the application of two novel population-based algorithms for history matching and uncertainty quantification of petroleum reservoir models. Ant colony optimization and differential evolution algorithms are used to search the space of parameters to find multiple history matched models and, using a Bayesian framework, the posterior probability of the models are evaluated for prediction of reservoir performance. It is demonstrated that by bringing latest developments in computer science such as ant colony, differential evolution and multiobjective optimization, we can improve the history matching and uncertainty quantification frameworks. This thesis provides insights into performance of these algorithms in history matching and prediction and develops an understanding of their tuning parameters. The research also brings a comparative study of these methods with a benchmark technique called Neighbourhood Algorithms. This comparison reveals the superiority of the proposed methodologies in various areas such as computational efficiency and match quality

Nature-inspired Methods for Stochastic, Robust and Dynamic Optimization

Nature-inspired algorithms have a great popularity in the current scientific community, being the focused scope of many research contributions in the literature year by year. The rationale behind the acquired momentum by this broad family of methods lies on their outstanding performance evinced in hundreds of research fields and problem instances. This book gravitates on the development of nature-inspired methods and their application to stochastic, dynamic and robust optimization. Topics covered by this book include the design and development of evolutionary algorithms, bio-inspired metaheuristics, or memetic methods, with empirical, innovative findings when used in different subfields of mathematical optimization, such as stochastic, dynamic, multimodal and robust optimization, as well as noisy optimization and dynamic and constraint satisfaction problems

A literature review on the application of evolutionary computing to credit scoring

The last years have seen the development of many credit scoring models for assessing the creditworthiness of loan applicants. Traditional credit scoring methodology has involved the use of statistical and mathematical programming techniques such as discriminant analysis, linear and logistic regression, linear and quadratic programming, or decision trees. However, the importance of credit grant decisions for financial institutions has caused growing interest in using a variety of computational intelligence techniques. This paper concentrates on evolutionary computing, which is viewed as one of the most promising paradigms of computational intelligence. Taking into account the synergistic relationship between the communities of Economics and Computer Science, the aim of this paper is to summarize the most recent developments in the application of evolutionary algorithms to credit scoring by means of a thorough review of scientific articles published during the period 2000–2012.This work has partially been supported by the Spanish Ministry of Education and Science under grant TIN2009-14205 and the Generalitat Valenciana under grant PROMETEO/2010/028

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)

Introductory Overview: Optimization using Evolutionary Algorithms and other Metaheuristics

Environmental models are used extensively to evaluate the effectiveness of a range of design, planning, operational, management and policy options. However, the number of options that can be evaluated manually is generally limited, making it difficult to identify the most suitable options to consider in decision-making processes. By linking environmental models with evolutionary and other metaheuristic optimization algorithms, the decision options that make best use of scarce resources, achieve the best environmental outcomes for a given budget or provide the best trade-offs between competing objectives can be identified. This Introductory Overview presents reasons for embedding formal optimization approaches in environmental decision-making processes, details how environmental problems are formulated as optimization problems and outlines how single- and multi-objective optimization approaches find good solutions to environmental problems. Practical guidance and potential challenges are also provided.</p

Internet of Things in urban waste collection

Nowadays, the waste collection management has an important role in urban areas. This paper faces this issue and proposes the application of a metaheuristic for the optimization of a weekly schedule and routing of the waste collection activities in an urban area. Differently to several contributions in literature, fixed periodic routes are not imposed. The results significantly improve the performance of the company involved, both in terms of resources used and costs saving

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

Particle Swarm Optimization

Particle swarm optimization (PSO) is a population based stochastic optimization technique influenced by the social behavior of bird flocking or fish schooling.PSO shares many similarities with evolutionary computation techniques such as Genetic Algorithms (GA). The system is initialized with a population of random solutions and searches for optima by updating generations. However, unlike GA, PSO has no evolution operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly through the problem space by following the current optimum particles. This book represents the contributions of the top researchers in this field and will serve as a valuable tool for professionals in this interdisciplinary field