Αλγόριθμοι υπολογιστικής νοημοσύνης για αριθμητική βελτιστοποίηση

Abstract

The recent developments in science and technology make imperative the need for efficient and e_ective optimization algorithms that can address the problems that appear in applications, fast and with low computational cost. Up.to.date a plethora of optimization algorithms, designed to solve problems that could not be addressed by classical algorithms, have been proposed. Nature and the processes that take place in it constituted a source of inspiration for many modern algorithms. For example, the operations of evolutionary algorithms are heavily based on procedures that simulate the DNA procedures of living organisms that result in the development of species, according to the theory of Darwin. The class of swarm intelligence algorithms consists of methods that are closely related to the evolutionary algorithms. Their operation is based on the simulation of social dynamics as well as on the interactions of members of societies among them and with their environment. These methods have grown rapidly the last years and they have been successfully applied on many real world problems. Particle Swarm Optimization (PSO) is a swarm intelligence algorithm. It is a stochastic optimization method that exploits populations (swarms) of search points (particles) to probe the search space. Its operation is based on the information exchange among the particles as well as on their memory. From the mathematical point of view, PSO explores the search space through the stochastic movement of the particles and the generation of di_erence vectors. Di_erential Evolution (DE) is an optimization algorithm that was developed almost concurrently with PSO and works in a very similar manner, although it does not share the same source of inspiration. The main goals of this thesis were (a) the investigation of the performance of algorithms such as PSO and DE on di_erent numerical optimization benchmark problems and real world applications, (b) the development of modi_cations and improvements of the algorithms that increase their performance, and (c) the development of a Uni_ed PSO algorithm that harnesses its main variants to a uni_ed scheme. Uni_ed PSO combines the exploration and exploitation properties of PSO variants. A theoretical analysis of the new scheme was also provided. In order to achieve our goals, we employed established computational methods, such as methods for the detection of many optimizers, di_erent stochastic algorithms, as well as hybrid optimization schemes. The thesis contributed toward the direction of revealing the abilities of PSO and DE in tackling di_cult problems as well as toward the development, theoretical analysis and application of new methods.