A study on the limitations of evolutionary computation and other bio-inspired approaches for integer factorization

Integer Factorization is a vital number theoretic problem frequently finding application in public-key cryptography like RSA encryption systems, and other areas like Fourier transform algorithm. The problem is computationally intractable because it is a one-way mathematical function. Due to its computational infeasibility, it is extremely hard to find the prime factors of a semi prime number generated from two randomly chosen similar sized prime numbers. There has been a recently growing interest in the community with regards to evolutionary computation and other alternative approaches to solving this problem as an optimization task. However, the results still seem to be very rudimentary in nature and there\u27s much work to be done. This paper emphasizes on such approaches and presents a critic study in details. The paper puts forth criticism and ideas in this aspect

Asymmetrical three-phase fault evaluation in a distribution network using the genetic algorithm and the particle swarm optimisation

Abstract: Modern electric power systems are made up of three main sub-systems: generation; transmission; and distribution. The most common faults in distribution sub-systems are asymmetrical three-phase short circuit faults due to the fact that asymmetrical three-phase faults can be: line-to-line faults; two lines-to-earth faults; and single line-to-earth faults. This increases their probability of occurrence, unlike symmetrical three-phase faults which can only occur when all the three phases have been simultaneously shorted. Standard IEC 60909 and IEC 61363 provide all the basic information that is used for the detection of short circuit faults. However, the two standards use numerous estimates in their faults evaluation procedures. They estimate voltage factors (c), impedance correction factors (k), resistance to reactance ratios (R/X), resistance to impedance ratios (R/Z) and various other scaling factors for rotating machines. These IEC estimates are not evenly distributed throughout the 550kV and as such, they do not sufficiently cater for every nominal voltage. When the need arises, the user has to estimate these values accordingly. This research presents a genetic algorithm (GA) and a particle swarm optimisation (PSO) for the detection of asymmetrical three-phase short circuit faults within electric distribution networks of power systems with nominal voltages less than 550kV. GA and PSO are nature-inspired optimisation techniques. Although PSO has quick convergence, it suffers from partial optimism and premature stagnation. Some innovative coding adjustments were made in the creation of initial positions and particle distribution within the swarm. The GA struggles with: survival rates of individuals; stalling during optimisation; and proper gene replacements. Coding adjustments were also made to GA with regards to: strategic gene replacements; crossover when combining the properties of parents; and the arrangement of scores and expectation. Pattern search and Fmincon algorithms were also added to both algorithms as minimisation functions that commence after the evolutionary algorithms (EAs) terminate. The EAs were initially tested on the Rastrigin and Rosenbrock functions to ensure their efficiencies. During fault detection, the developed EAs were used to stochastically determine some of the most crucial estimates (R/X and R/Z ratios). The proposed methodology would compute these values on a case-to-case basis for every optimisation case with regards to the parameters and unique specifications of the power system. The EAs were tested on a nominal voltage that is properly catered for by Standard IEC. They obtained ratios, impedances and currents that were within an approximate range to the IEC values for that nominal voltage. This further implies that EAs can be reliably used to: stochastically determine these ratios; compute impedances; and detect fault currents for all the nominal voltages including those that are not sufficiently catered for by Standard IEC. Since R/X and R/Z ratios play a key role in determining the upstream and fault point impedances, the proposed methodology can be used to compute much more precise fault magnitudes at various network levels thereby setting up and repairing power systems sufficiently.M.Ing. (Electrical and Electronic Engineering Science