Parameterized Complexity Analysis of Randomized Search Heuristics

This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running time of algorithms solving combinatorial problems in finer detail than traditional approaches from classical complexity theory. We outline the main results and proof techniques for a collection of randomized search heuristics tasked to solve NP-hard combinatorial optimization problems such as finding a minimum vertex cover in a graph, finding a maximum leaf spanning tree in a graph, and the traveling salesperson problem.Comment: This is a preliminary version of a chapter in the book "Theory of Evolutionary Computation: Recent Developments in Discrete Optimization", edited by Benjamin Doerr and Frank Neumann, published by Springe

Scattering by a semi-infinite lattice and the excitation of Bloch waves

The interaction of a time-harmonic plane wave with a semi-infinite lattice of identical circular cylinders is considered. No assumptions about the radius of the cylinders, or their scattering properties, are made. Multipole expansions and Graf’s addition theorem are used to reduce the boundary value problem to an infinite linear system of equations. Applying the z transform and disregarding interaction effects due to certain strongly damped modes then leads to a matrix Wiener–Hopf equation with rational elements. This is solved by a straightforward method that does not require matrix factorisation. Implementation of the method requires that the zeros of the matrix determinant be located numerically, and once this is achieved, all far field quantities can be calculated. Numerical results that show the proportion of energy reflected back from the edge are presented for several different lattice geometries. 1

Analytical techniques for acoustic scattering by arrays of cylinders

The problem of two-dimensional acoustic scattering of an incident plane wave by a semi-infinite lattice is solved. The problem is first considered for sound-soft cylinders whose size is small compared to the wavelength of the incident field. In this case the formulation leads to a scalar Wiener--Hopf equation, and this in turn is solved via the discrete Wiener--Hopf technique. We then deal with a more complex case which arises either by imposing Neumann boundary condition on the cylinders' surface or by increasing their radii. This gives rise to a matrix Wiener--Hopf equation, and we present a method of solution that does not require the explicit factorisation of the kernel. In both situations, a complete description of the far field is given and a conservation of energy condition is obtained. For certain sets of parameters (`pass bands'), a portion of the incident energy propagates through the lattice in the form of a Bloch wave. For other parameters (`stop bands' or `band gaps'), no such transmission is possible, and all of the incident field energy is reflected away from the lattice

Linear Generalized Nash Equilibrium Problems

In der vorliegenden Arbeit werden verallgemeinerte Nash Spiele (LGNEPs) unter Linearitätsannahmen eingeführt und untersucht. Durch Ausnutzung der speziellen Struktur lassen sich theoretische und algorithmische Resultate erzielen, die weit über die Ergebnisse für allgemeine LGNEPs hinausgehen

Design and Control of Power Converters 2019

In this book, 20 papers focused on different fields of power electronics are gathered. Approximately half of the papers are focused on different control issues and techniques, ranging from the computer-aided design of digital compensators to more specific approaches such as fuzzy or sliding control techniques. The rest of the papers are focused on the design of novel topologies. The fields in which these controls and topologies are applied are varied: MMCs, photovoltaic systems, supercapacitors and traction systems, LEDs, wireless power transfer, etc

High gain non-isolated DC-DC converter topologies for energy conversion systems

PhD ThesisEmerging applications driven by low voltage level power sources, such as photovoltaics, batteries and fuel cells require static power converters for appropriate energy conversion and conditioning to supply the requirements of the load system. Increasingly, for applications such as grid connected inverters, uninterruptible power supplies (UPS), and electric vehicles (EV), the performance of a high efficiency high static gain power converter is of critical importance to the overall system. Theoretically, the conventional boost and buck-boost converters are the simplest non-isolated topologies for voltage step-up. However, these converters typically operate under extreme duty ratio, and severe output diode reverse recovery related losses to achieve high voltage gain. This thesis presents derivation, analysis and design issues of advanced high step-up topologies with coupled inductor and voltage gain extension cell. The proposed innovative solution can achieve significant performance improvement compared to the recently proposed state of the art topologies. Two unique topologies employing coupled inductor and voltage gain extension cell are proposed. Power converters utilising coupled inductors traditionally require a clamp circuit to limit the switch voltage excursion. Firstly, a simple low-cost, high step-up converters employing active and passive clamp scheme is proposed. Performance comparison of the clamps circuits shows that the active clamp solution can achieve higher efficiency over the passive solution. Secondly, the primary detriment of increasing the power level of a coupled inductor based converters is high current ripple due to coupled inductor operation. It is normal to interleaved DC-DC converters to share the input current, minimize the current ripple and increase the power density. This thesis presents an input parallel output series converter integrating coupled inductors and switched capacitor demonstrating high static gain. Steady state analysis of the converter is presented to determine the power flow equations. Dynamic analysis is performed to design a closed loop controller to regulate the output voltage of the interleaved converter. The design procedure of the high step-up converters is explained, simulation and experimental results of the laboratory prototypes are presented. The experimental results obtained via a 250 W single phase converter and that of a 500 W interleaved converter prototypes; validate both the theory and operational characteristics of each power converter.Petroleum Technology Development Fund (PTDF) Nigeri