This thesis investigates the application of Genetic AIgorithms (GAs) to multiple criteria problems in engineering design and operation. The GA is an evolutionary computing technique which applies Darwinian principIes such as survival of the fittest, mating and mutation to a population of individuals to evolve good solutions to a broad range of problems. GAs are normally used as single criterion optimisers. However, a Multiple Criteria Genetic AIgorithrn (MCGA) has been developed in this thesis which allows simultaneous maximisation and minimisation across several criteria. The MCGA is explained, enhanced and modified throughout the thesis as new requirements are introduced. At each stage the enhancements are tested on basic test functions to assess their performance. New concepts such as a Pareto Population, Adaptive Niche Sizing and Neural Network Preferencing are introduced. A broad range of applications have been tackled using the MCGA, all of which are combinatorial in nature. Combinatorial problems are primarily concerned with ordering or positioning of elements, the order determining the properties and attributes of fue solution. As such, standard GA operators cannot be used and novel methods have to be employed. The applications are drawn from various engineering fields. An electronic component placement problem is tackled initially with the goal of decreasing processing time as a single criterion combinatorial example. A general method of rearranging design activities so as to maximise parallelisation and reduce lead times is then performed using the MCGA. A complex scheduling model is devised and the MCGA is used to optimise various operating scenarios. Finally, the arrangement of containers in a containership is tackled.