Metaheuristics applied to the optimization of continuous functions

Masteroppgave i informasjons- og kommunikasjonsteknologi IKT590 2013 – Universitetet i Agder, GrimstadOptimization is a field of mathematics which studies and develops mathematical methods with the aim of optimizing a wide range of problems. In physics these methods are central. Essentially all the dynamical equations in physics can be expressed as a series of optimization problems in terms of action integrals. Optimization can better be explained as finding the optima, also known as extremes, of a mathematical object. Such object may be a continuous function, as the case of this thesis. The approaches for solving optimization problems are generally divided into two categories, deterministic optimization and stochastic optimization. The main difference is that the deterministic approach applies calculus and the stochastic approach applies a search technique. For solving complex optimization problems, the stochastic approach has long proven to be most efficient. This thesis focuses on improving the two stochastic search methods: Simulated Annealing and the Genetic Algorithm. This is performed by implementing two newly developed methods. The first method is the Tangent-based Evaluation method, which is better suited to detect abnormalities in continuous functions than the common one-point evaluation method. The other method is the Analytic Swap method for generation of solutions. Solution generation is an important part of any stochastic algorithm. Usually the new solutions generated by a random function, but the Analytic Swap method combines randomness with analytics to generate better solutions