Power allocation strategies across N orthogonal channels for single-relay networks at both source and relay

We consider a wireless relay network with one source, one relay and one destination, where communications between nodes are preformed over N orthogonal channels. This, for example, is the case when orthogonal frequency division multiplexing is employed for data communications. Since the power available at the source and relay is limited, we study optimal power allocation strategies at the source and relay in order to maximize the overall source-destination capacity. Depending on the availability of the channel state information at both the source and relay or only at the relay, power allocation is performed at both the source and relay or only at the relay. Considering different setups for the problem, various optimization problems are formulated and solved. Some properties of the optimal solution are also proved.

A hybrid harmony search with arithmetic crossover operation for economic dispatch

Economic dispatch (ED) problems often exhibit non-linear, non-convex characteristics due to the valve point effects. Further, various constraints and factors, such as prohibited operation zones, ramp rate limits and security constraints imposed by the generating units, and power loss in transmission make it even more challenging to obtain the global optimum using conventional mathematical methods. Meta-heuristic approaches are capable of solving non-linear, non-continuous and non-convex problems effectively as they impose no requirements on the optimization problems. However, most methods reported so far mainly focus on a specific type of ED problems, such as static or dynamic ED problems. This paper proposes a hybrid harmony search with arithmetic crossover operation, namely ACHS, for solving five different types of ED problems, including static ED with valve point effects, ED with prohibited operating zones, ED considering multiple fuel cells, combined heat and power ED, and dynamic ED. In this proposed ACHS, the global best information and arithmetic crossover are used to update the newly generated solution and speed up the convergence, which contributes to the algorithm exploitation capability. To balance the exploitation and exploration capabilities, the opposition based learning (OBL) strategy is employed to enhance the diversity of solutions. Further, four commonly used crossover operators are also investigated, and the arithmetic crossover shows its efficiency than the others when they are incorporated into HS. To make a comprehensive study on its scalability, ACHS is first tested on a group of benchmark functions with a 100 dimensions and compared with several state-of-the-art methods. Then it is used to solve seven different ED cases and compared with the results reported in literatures. All the results confirm the superiority of the ACHS for different optimization problems.

Computational methods in the fractional calculus of variations and optimal control

The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their efficiency. Direct and indirect methods in solving fractional variational problems are studied in detail. Furthermore, optimality conditions are discussed for different types of unconstrained and constrained variational problems and for fractional optimal control problems. The introduced numerical methods are employed to solve some illustrative examples.

Majorantes para a ordem de subgrafos induzidos k-regulares

Muitos dos problemas de otimização em grafos reduzem-se à determinação de um subconjunto de vértices de cardinalidade máxima que induza um subgrafo k-regular. Uma vez que a determinação da ordem de um subgrafo induzido k-regular de maior ordem é, em geral, um problema NP-difícil, são deduzidos novos majorantes, a determinar em tempo polinomial, que em muitos casos constituam boas aproximações das respetivas soluções ótimas. Introduzem-se majorantes espetrais usando uma abordagem baseada em técnicas de programação convexa e estabelecem-se condições necessárias e suficientes para que sejam atingidos. Adicionalmente, introduzem-se majorantes baseados no espetro das matrizes de adjacência, laplaciana e laplaciana sem sinal. É ainda apresentado um algoritmo não polinomial para a determinação de umsubconjunto de vértices de umgrafo que induz umsubgrafo k-regular de ordem máxima para uma classe particular de grafos. Finalmente, faz-se um estudo computacional comparativo com vários majorantes e apresentam-se algumas conclusões.

Implementing and testing branch-and-bound algorithm for the quadratic 0-1 problem on transputers

Discrete optimization problems are very difficult to solve, even if the dimention is small. For most of them the problem of finding an ε-approximate solution is already NP-hard. The branch-and-bound algorithms are the most used algorithms for solving exactly this sort of problems.

A computational study of a parallel Branch and Bound algorithm for the quadratic 0-1 programming problem on transputers

Discrete optimization problems are very difficult to solve, even if the dimantion is small. For most of them the problem of finding an ε-approximate solution is already NP-hard.

IP/optical integration in access network infrastructures: key issues on resource provisioning

This thesis contributes to the advancement of Fiber-Wireless (FiWi) access technologies, through the development of algorithms for resource allocation and energy efficient routing. FiWi access networks use both optical and wireless/cellular technologies to provide high bandwidth and ubiquity, required by users and current high demanding services. FiWi access technologies are divided in two parts. In one of the parts, fiber is brought from the central office to near the users, while in the other part wireless routers or base stations take over and provide Internet access to users. Many technologies can be used at both the optical and wireless parts, which lead to different integration and optimization problems to be solved. In this thesis, the focus will be on FiWi access networks that use a passive optical network at the optical section and a wireless mesh network at the wireless section. In such networks, two important aspects that influence network performance are: allocation of resources and traffic routing throughout the mesh section. In this thesis, both problems are addressed. A fair bandwidth allocation algorithm is developed, which provides fairness in terms of bandwidth and in terms of experienced delays among all users. As for routing, an energy efficient routing algorithm is proposed that optimizes sleeping and productive periods throughout the wireless and optical sections. To develop the stated algorithms, game theory and networks formation theory were used. These are powerful mathematical tools that can be used to solve problems involving agents with conflicting interests. Since, usually, these tools are not common knowledge, a brief survey on game theory and network formation theory is provided to explain the concepts that are used throughout the thesis. As such, this thesis also serves as a showcase on the use of game theory and network formation theory to develop new algorithms.

A aprendizagem da noção de derivada no 11º ano

Relatório da prática de ensino supervisionada, Mestrado em Ensino da Matemática, Universidade de Lisboa, 2014

Increase of the delivered energy probability in DES using a fuzzy probabilistic modeling

The paper proposes a methodology to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The proposed methodology is based on statistical failure and repair data of distribution components and it uses a fuzzy-probabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A mixed integer nonlinear programming optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

Ant colony search algorithm for the optimal power flow problem

To maintain a power system within operation limits, a level ahead planning it is necessary to apply competitive techniques to solve the optimal power flow (OPF). OPF is a non-linear and a large combinatorial problem. The Ant Colony Search (ACS) optimization algorithm is inspired by the organized natural movement of real ants and has been successfully applied to different large combinatorial optimization problems. This paper presents an implementation of Ant Colony optimization to solve the OPF in an economic dispatch context. The proposed methodology has been developed to be used for maintenance and repairing planning with 48 to 24 hours antecipation. The main advantage of this method is its low execution time that allows the use of OPF when a large set of scenarios has to be analyzed. The paper includes a case study using the IEEE 30 bus network. The results are compared with other well-known methodologies presented in the literature.

New insights on integer-programming models for the kidney exchange problem

In recent years several countries have set up policies that allow exchange of kidneys between two or more incompatible patient–donor pairs. These policies lead to what is commonly known as kidney exchange programs. The underlying optimization problems can be formulated as integer programming models. Previously proposed models for kidney exchange programs have exponential numbers of constraints or variables, which makes them fairly difficult to solve when the problem size is large. In this work we propose two compact formulations for the problem, explain how these formulations can be adapted to address some problem variants, and provide results on the dominance of some models over others. Finally we present a systematic comparison between our models and two previously proposed ones via thorough computational analysis. Results show that compact formulations have advantages over non-compact ones when the problem size is large.

Introducing the fractional-order Darwinian PSO

One of the most well-known bio-inspired algorithms used in optimization problems is the particle swarm optimization (PSO), which basically consists on a machinelearning technique loosely inspired by birds flocking in search of food. More specifically, it consists of a number of particles that collectively move on the search space in search of the global optimum. The Darwinian particle swarm optimization (DPSO) is an evolutionary algorithm that extends the PSO using natural selection, or survival of the fittest, to enhance the ability to escape from local optima. This paper firstly presents a survey on PSO algorithms mainly focusing on the DPSO. Afterward, a method for controlling the convergence rate of the DPSO using fractional calculus (FC) concepts is proposed. The fractional-order optimization algorithm, denoted as FO-DPSO, is tested using several well-known functions, and the relationship between the fractional-order velocity and the convergence of the algorithm is observed. Moreover, experimental results show that the FO-DPSO significantly outperforms the previously presented FO-PSO.

The Salmon Algorithm - A New Population Based Search Metaheuristic

This thesis introduces the Salmon Algorithm, a search meta-heuristic which can be used for a variety of combinatorial optimization problems. This algorithm is loosely based on the path finding behaviour of salmon swimming upstream to spawn. There are a number of tunable parameters in the algorithm, so experiments were conducted to find the optimum parameter settings for different search spaces. The algorithm was tested on one instance of the Traveling Salesman Problem and found to have superior performance to an Ant Colony Algorithm and a Genetic Algorithm. It was then tested on three coding theory problems - optimal edit codes, optimal Hamming distance codes, and optimal covering codes. The algorithm produced improvements on the best known values for five of six of the test cases using edit codes. It matched the best known results on four out of seven of the Hamming codes as well as three out of three of the covering codes. The results suggest the Salmon Algorithm is competitive with established guided random search techniques, and may be superior in some search spaces.

« Resolution Search » et problèmes d’optimisation discrète

Thèse réalisée en cotutelle avec l'Université d'Avignon.

Approches générales de résolution pour les problèmes multi-attributs de tournées de véhicules et confection d'horaires

Thèse réalisée en cotutelle entre l'Université de Montréal et l'Université de Technologie de Troyes