Application of stochastic optimisation algorithms (metaheuristics) to the placement of non-convex objects in the plane

The placement of convex objects in the plane, especially rectangular objects, has been studied extensively in the literature and its applications to very large scale integration designs, the steel industry (stock cutting). The placement of non-convex objects and its application in many design and textile industries, especially the textile industry, has been less studied, Mathematical Approaches determining an adequate solution of such problems include linear programming and the newest genetic algorithms. In this paper we consider a particular industrial problem, the design of printing sheets for decorative porcelain. These objects permit inclusions and other geometric situations which do not appear in the case of convex objects. In this paper we prove results related to this problem for different algorithms: a heuristic algorithm, simulated annealing algorithm and a genetic algorithm.