Sum of Three Cubes via Optimisation

By first solving the equation $x^3+y^3+z^3=k$ with fixed $k$ for $z$ and then considering the distance to the nearest integer function of the result, we turn the sum of three cubes problem into an optimisation one. We then apply three stochastic optimisation algorithms to this function in the case with $k=2$, where there are many known solutions. The goal is to test the effectiveness of the method in searching for integer solutions. The algorithms are a modification of particle swarm optimisation and two implementations of simulated annealing. We want to compare their effectiveness as measured by the running times of the algorithms. To this end, we model the time data by assuming two underlying probability distributions -- exponential and log-normal, and calculate some numerical characteristics for them. Finally, we evaluate the statistical distinguishability of our models with respect to the geodesic distance in the manifold with the corresponding Fisher information metric.Comment: 21 pages without the appendices. Any comments will be greatly appreciated

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

The germinal centre artificial immune system

This thesis deals with the development and evaluation of the Germinal centre artificial immune system (GC-AIS) which is a novel artificial immune system based on advancements in the understanding of the germinal centre reaction of the immune system. The key research questions addressed in this thesis are: can an artificial immune system (AIS) be designed by taking inspiration from recent developments in immunology to tackle multi-objective optimisation problems? How can we incorporate desirable features of the immune system like diversity, parallelism and memory into this proposed AIS? How does the proposed AIS compare with other state of the art techniques in the field of multi-objective optimisation problems? How can we incorporate the learning component of the immune system into the algorithm and investigate the usefulness of memory in dynamic scenarios? The main contributions of the thesis are: • Understanding the behaviour and performance of the proposed GC-AIS on multiobjective optimisation problems and explaining its benefits and drawbacks, by comparing it with simple baseline and state of the art algorithms. • Improving the performance of GC-AIS by incorporating a popular technique from multi-objective optimisation. By overcoming its weaknesses the capability of the improved variant to compete with the state of the art algorithms is evaluated. • Answering key questions on the usefulness of incorporating memory in GC-AIS in a dynamic scenario

Industrial and Technological Applications of Power Electronics Systems

The Special Issue "Industrial and Technological Applications of Power Electronics Systems" focuses on: - new strategies of control for electric machines, including sensorless control and fault diagnosis; - existing and emerging industrial applications of GaN and SiC-based converters; - modern methods for electromagnetic compatibility. The book covers topics such as control systems, fault diagnosis, converters, inverters, and electromagnetic interference in power electronics systems. The Special Issue includes 19 scientific papers by industry experts and worldwide professors in the area of electrical engineering