Simulated Annealing Applied to the Simultaneous Placement of Multiple Polygons

This work deals with the problem of minimizing the waste of space of a placement of a set of two-dimensional objects inside a two-dimensional container. We address this problem with a heuristic approach based on simulated annealing, which is a probabilistic heuristic inspired on the physico-chemical processes that take place during the recrystalisation of a metal. We avoid the traditional “external penalisation” approach by applying the Minkowski sum algorithm from computational geometry to determinate collision-free regions inside the container to place an item. This gives a more universal character to the proposed algorithm, as external penalisation relies on arbitrary parameters that affect greatly the performance of the optimisation algorithm. Our algorithm is suited to non-convex items and non-convex containers, and it can be easily adapted to related problems, such as minimizing the dimensions of the container.

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