Optimisation of layout for a problem in roofing with sheets

The most common type of roofing material used in residential construction in Australia is alloy-coated steel sheets. Because of the complicated shape of the average roof it is usual to waste between five and ten percent of the material as offcut scraps, and each year tens of millions of dollars worth of roofing material is thrown away. The selection and arrangement of the metal strips to minimise this wastage is currently an art rather than a science, and is subject to a number of interesting constraints imposed by physics, logistics and human psychology. We describe here the use of a genetic algorithm to minimise the wastage subject to all these constraints, and compare and contrast the different approaches considered