Efficient local search heuristics for packing irregular shapes in two-dimensional heterogeneous bins

In this paper we proposed a local search heuristic and a genetic algorithm to solve the two-dimensional irregular multiple bin-size bin packing problem. The problem consists of placing a set of pieces represented as 2D polygons in rectangular bins with different dimensions such that the total area of bins used is minimized. Most packing algorithms available in the literature for 2D irregular bin packing considersingle size bins only. However, for many industries the material can be supplied in a number of standard size sheets, for example, metal, foam, plastic and timber sheets. For this problem, the cut plans must decide the set of standard size stock sheets as well as which pieces to cut from each bin and how to arrange them in order to minimise waste material. Moreover, the literature constrains the orientation of pieces to a single or finite set of angles. This is often an artificial constraint that makes the solution space easier to navigate. In this paper we do not restrict the orientation of the pieces. We show that the local search heuristic and the genetic algorithm can address all of these decisions and obtain goodsolutions, with the local search performing better. We also discuss the effect of different groups of stock sheet sizes