A bi-objective approach to sequencing cutting patterns

In our cooperation with a Portuguese paper producer, Respicio et al. (2002), we identified two major sequencing objectives: (1) the minimisation of the maximum number of open stacks and (2) the minimisation of the average order spread. The space around the cutting saw is narrow. As the number of produced items increase, packing mistakes arise. Objective (1) concerns the minimisation of these mistakes, in the worst case. Objective (2) regards the efficiency of the flow of work, on the average case. However the production schedulers were not able to set a preference between these two criteria. They state that “to choose a pattern sequence they need to analyse and compare the best sequences”. We propose a bi-objective sequencing problem considering these two objectives. Linhares and Yanasse (2002) clearly show that optimising these objectives leads to potentially different solutions. To our knowledge, approaches available in the literature have only dealt with single objective problems. Single objective optimisation approaches are myopic regarding other objectives and may loose Pareto optimal solutions. Approximating the Pareto optimal set allows for a more effective exploration of the solution space. We test a pure multi-objective evolutionary algorithm and a hybrid version, including local search procedures.