This thesis investigates various combinations of Constraint Satisfaction Strategies with Genetic Algorithms (GA) for Solving Examination timetabling Problems (ETTPs). Since Timetabling Problems (TTPs) in their simplest form can be mapped onto GraphColouring Problems (GCP), strategies for solving these problems are also included in the research. The main GA-related issues addressed in this thesis involve the fitness function, the crossover operator and the representation. The primary contributions this investigation presents can be summarised as follows: (1) in relation to the fitness function, the Hardness Theory (HT) which intends to measure how hard it is to solve a Constraint Satisfaction Problem (CSP) has been applied with the aim of improving the quality of solutions produced by the GA with the standard penalty function which has been criticised for exhibiting a series of defects. The key idea is that the fitness value for each individual in the population at a given generation, is the measure of difficulty of solving the remaining unsolved problem, consisting of the events yet to be scheduled and the edges that connect them. Despite the fact

Abstract. Theoretically and empirically it is clear that a genetic algorithm with crossover will outperform a genetic algorithm without crossover in some fitness landscapes, and vice versa in other landscapes. Despite an extensive literature on the subject, and recent proofs of a principled distinction in the abilities of crossover and non-crossover algorithms for a particular theoretical landscape, building general intuitions about when and why crossover performs well when it does is a different matter. In particular, the proposal that crossover might enable the assembly of good building-blocks has been difficult to verify despite many attempts at idealized building-block landscapes. Here we show the first example of a two-module problem that shows a principled advantage for crossover. This allows us to understand building-block assembly under crossover quite straightforwardly and build intuition about more general landscape classes favoring crossover or disfavoring it. 1

Genetic algorithms are adaptive methods based on natural evolution which may be used for search and optimization problems. They process a population of search space solutions with three operations: selection, crossover and mutation. Under their initial formulation, the search space solutions are coded using the binary alphabet, however other coding types have been taken into account for the representation issue, such as real coding. It seems particularly natural when tackling optimization problems of parameters with variables in continuous domains. A great problem in the use of genetic algorithms is premature convergence, a premature stagnation of the search caused by the lack of population diversity. The mutation operator is the one responsible for the generation of diversity and therefore may be considered to be an important element in solving this problem. For the case of working under real coding, a solution involves the control, throughout the run, of the strength in which real ge...

The choice of genetic operators is one way in which genetic algorithms can be tailored to specific optimization problems. For bit represented problems, the choice of crossover operator, or the choice not to use a crossover operator, can dramatically affect search performance.

This paper describes the development of an object-oriented parallel programming environment for genetic algorithms. This work, carried out as part of the ESPRIT III initiative PAPAGENA, intends to promote, develop and demonstrate the effectiveness of genetic algorithm (GA) and parallel genetic algorithm (PGA) techniques in a variety of real-world application domains. Central to this task is the development of a generalpurpose programming environment for both parallel and sequential genetic algorithms. GAME (Genetic Algorithm Manipulation Environment) will offer extensive tools for the design, configuration and monitoring of GA applications. This paper gives an overview of the design philosophy behind GAME, indicating the types of service and facilities the finished product will offer. Intrinsic to the design is the provision of an extensive multilevelled GA-specific library, offering GA and PGA applications, algorithms and operators. This will allow application developers the facilities to rapidly customise, configure and test novel GA and PGA designs. To sketch the types of application to be housed in GAME, a description of the applications currently under development within this project is also included. These range from finance through economic modelling to protein structure prediction. Key design requirements for GAME are versatility, together with flexibility. For this reason GAME has been designed to run within both Sun OS and PC DOS operating system, with or without parallel support. 1 Introduction

. Exploration and exploitation are the two cornerstones of problem solving by search. Evolutionary Algorithms (EAs) are search algorithms that explore the search space by the genetic search operators, while exploitation is done by selection. During the history of EAs different operators have emerged, mimicing asexual and sexual reproduction in Nature. Here we give an overview of the variety of these operators, review results discussing the (dis)advantages of asexual and sexual mechanisms and touch on a new phenomenon: multi-parent reproduction. 1 Introduction Generate-and-test search algorithms obtain their power from two sources: exploration and exploitation. Exploration means the discovery of new regions in the search space, exploitation amounts to using collected information in order to direct further search to promising regions. Evolutionary Algorithms (EAs) are stochastic generate-and-test search algorithms having a number of particular properties. The standard pseudo-code for an...

This article describes an investigation and its results on a new crossover operator for solving the Timetabling Problem with Genetic Algorithms. Since a Timetabling Problem can be represented as a graph, and then manipulated as a Graph-Colouring Problem, the central feature behind the approach presented here considers the presence of solved cliques in the mating parents. A clique is a maximally connected subgraph, that is, any node in it is joined by an edge with any other node of the subgraph. Although nding the clique in a graph is not an easy problem, in fact, it is an NP-complete type, real timetabling problems usually include cliques whose sizes, in relation to the total size of the problem, are still manageable. Results after experimentation with several test les show that the approach and its variations is advantageous under certain circumstances. The reasons why this is happening are explained, and also the ways that, despite of the results, this research can lead to answer o...

In this paper, a new gene based adaptive mutation scheme is proposed for genetic algorithms (GAs), where the information on gene based fitness statistics and on gene based allele distribution statistics are correlated to explicitly adapt the mutation probability for each gene locus over time. A convergence control mechanism is combined with the proposed mutation scheme to maintain sufficient diversity in the population. Experiments are carried out to compare the proposed mutation scheme to traditional mutation and two advanced adaptive mutation schemes on a set of optimization problems. The experimental results show that the proposed mutation scheme efficiently improves GA’s performance.

Abstract. This paper presents a parameter-less optimization framework that uses the extended compact genetic algorithm (ECGA) and iterated local search (ILS), but is not restricted to these algorithms. The presented optimization algorithm (ILS+ECGA) comes as an extension of the parameter-less genetic algorithm (GA), where the parameters of a selecto-recombinative GA are eliminated. The approach that we propose is tested on several well known problems. In the absence of domain knowledge, it is shown that ILS+ECGA is a robust and easy-to-use optimization method. 1

Genetic algorithms are adaptive systems biologically motivated which have been used to solve different problems. Since Holland's proposals back in 1975, two main genetic operators, crossover and mutation, have been explored with success. Nonetheless, nature presents many other mechanisms of genetic recombination, based on phenomena like gene insertion, duplication or movement. The aim of this paper is to study one of these mechanisms: transposition. Transposition is a context-sensitive operator that promotes gene movement intra or inter chromosomes. This work presents an empirical study of the genetic algorithm performance, being the traditional crossover operator replaced by transposition. Such empirical study, based on an extensive set of test functions, shows that, under certain circumstances, transposition allows the GA to achieve higher quality solutions.