Genetic algorithms for multiple-choice problems

This thesis investigates the use of problem-specific knowledge to enhance a genetic algorithm approach to multiple-choice optimisation problems. It shows that such information can significantly enhance performance, but that the choice of information and the way it is included are important factors for success. Two multiple-choice problems are considered. The first is constructing a feasible nurse roster that considers as many requests as possible. In the second problem, shops are allocated to locations in a mall subject to constraints and maximising the overall income. Genetic algorithms are chosen for their well-known robustness and ability to solve large and complex discrete optimisation problems. However, a survey of the literature reveals room for further research into generic ways to include constraints into a genetic algorithm framework. Hence, the main theme of this work is to balance feasibility and cost of solutions. In particular, co-operative co-evolution with hierarchical sub-populations, problem structure exploiting repair schemes and indirect genetic algorithms with self-adjusting decoder functions are identified as promising approaches. The research starts by applying standard genetic algorithms to the problems and explaining the failure of such approaches due to epistasis. To overcome this, problem-specific information is added in a variety of ways, some of which are designed to increase the number of feasible solutions found whilst others are intended to improve the quality of such solutions. As well as a theoretical discussion as to the underlying reasons for using each operator, extensive computational experiments are carried out on a variety of data. These show that the indirect approach relies less on problem structure and hence is easier to implement and superior in solution quality. The most successful variant of our algorithm has a more than 99% chance of finding a feasible solution which is either optimal or within a few percent of optimality

Complexity reduction using expansive coding

Abstract. This paper describes a new technique for reducing the com-plexity of algorithms, such as those used in digital signal processing ~ using a genetic algorithm (GA). The method, referred to as expansive coding, is a representation methodology which makes complicated combinato-rim optimisation tasks easier to solve for a. GA. Using this technique, the representation, operators and fitness function used by the GA be-come more complicated, but the search space becomes less epistatic, and therefore easier for the GA to tackle. This reduction in epistasis (inter-action between parameters) is essential if the difficult task of complexity reduction is to be successfully achieved. Expansive coding spreads the task's complexity more evenly among the operators, fitness function and search space. We demonstrate how this technique can be applied to two cases of reduction of complexity of algorithms: a multiplier for quater-nion numbers, and a Walsh transform computation. We suggest why the technique is more successful on the former task than the latter.