The Influence of Different Coding Schemes on the Computational Complexity of Genetic Algorithms in Function Optimization

. Function optimization is a typical application domain for genetic algorithms (GAs). Traditionally, GAs work on bit strings of fixed total length l. Significant research has been done on designing and analyzing different coding schemes, of which Gray coding is one of the most used forms. Surprisingly little attention has been devoted to directly encoding the parameters by floating-point values provided by the programming language. This form of coding has been in favor in evolution strategy. This paper discusses several coding schemes and derives the resulting complexity when optimizing functions with n independent continuous parameters. It turns out that the direct use of real-valued parameters has certain advantages. First of all, it speeds up convergence by a factor of up to l q\Gamma1 , where q denotes the number of bits per parameter. Furthermore, the use of real-valued parameters allows for more flexibility in designing the mutation operator and eases many implementation issues..

Optimisation for product and process improvement :investigation of Taguchi tools and genetic algorithms

PhD ThesisDespite criticisms of its methodology, the Taguchi philosophy for quality improvement is generally applauded. Though originally intended to primarily achieve its results "off line", during the product design phase and before manufacturing, it has frequently also been deployed to solve problems "on line". Taguchi identifies the crucial design phases as "system design" and "parameter design", and his statistically-based tools are directed at the latter. The general objective of this investigation is to study two contrasting approaches to product and process optimisation, ie Genetic Algorithms, which may be appropriate to both "system design" and "parameter design" phases, with Taguchi and related statistical tools which may be appropriate to the "parameter design" phase. The literature review concentrates on the up and downsides of Taguchi Methods, focusing on the philosophy and methodologies. Its statistical content, particularly related to the use of Signal-To-Noise ratios and saturated fractional factorial designs, have widely reported deficiencies. In order to evaluate and, if necessary, overcome these deficiencies, a combination of Taguchi and non- Taguchi tools are brought into an experimentation strategy to determine robust methodologies that contribute to enhanced product performance. The approach is motivated from a design for quality standpoint and is directed principally at improving performance. The approach is illustrated using three case studies in surface finish from metal cutting and simulation systems optimisation. These case studies involve a variety of experiments different in nature, from real physical experiments to computer-based ones, and tackling a wide range of different problems such as: surface finish in milling and turning machining (metal cutting), optimum travel time and traffic junction control (transport traffic simulator) and out-of-balanceforce problem (optimisation of simple Genetic Algorithms). The study of Taguchi tools is an extension of previous work by Taher (1995). Some of his investigations are extended, principally the reliability of Taguchi saturated fractional factorial arrays, the need for factor/level analysis, criticisms of the Taguchi Signal-to-Noise ratios and the use of sequential experimentation. In addition to these, attention is focussed on the use of repetitions within the Taguchi methodology, the use of transformations or Generalised linear Models and the possibility of using robust statistics. The adoption of a sequential experimentation approach leads to a successful use of predefined Taguchi arrays influenced by user knowledge of confounding and interaction effects on main factors. From a global viewpoint, Factor/Level analysis is highly recommended. It is also determined that the reliability of results is highly affected by the use of Signal-to-Noise ratios, and alternative dispersion control tools are strongly advised. Taguchi's robust design methodologies are of value but require integration with other design and quality assurance methodologies, such as Concurrent Engineering and Quality Function Deployment. The optimisation of a simple Genetic Algorithm (for the out-of-balanceforce problem) is used as one test case for the investigation of Taguchi tools. However, this investigation is itself of interest for the general use of genetic algorithms as it addresses issues such as appropriate population size and choices for crossover and mutation modes and probabilities. Many previous investigations of these have only been of the "one factor at a time" type.Venezuelan Government