Rough milling optimisation for parts with sculptured surfaces using genetic algorithms in a Stackelberg game

In rough milling of sculptured surface parts, decisions on process parameters concern feedrate, spindle speed, cutting speed, width of cut, raster pattern angle and number of machining slices of variable thickness. In this paper three rough milling objectives are considered: minimum machining time, maximum removed material and maximum uniformity of the remaining volume at the end of roughing. Owing to the complexity of the modelled problem and the large number of parameters, typical genetic algorithms cannot achieve global optima without defining case-dependent constraints. Therefore, to achieve generality, a hierarchical game similar to a Stackelberg game is implemented in which a typical Genetic Algorithm functions as the leader and micro-Genetic Algorithms as followers. In this game, one of the leader’s parameters is responsible for creating a follower’s population and for triggering the optimisation. After properly weighing the three objectives, the follower performs single-objective optimization in steps and feeds the leader back with the objective values as they appear prior to weighing. Micro-Genetic Algorithm (follower) chromosome consists of the distribution of machining slice thickness, while the typical Genetic Algorithm (leader) consists of the milling parameters. The methodology is tested on sculptured surface parts with different properties, and a representative case is presented here.