Optimizing the placement of irregular shapes 2D Nesting

The problems of placement include a wide range of problems, namely the problems of cutting and packing and the problems of layout, which have cultivated a very high attention by numerous industries (textile, wood, ship-building ...). In our work we address the problem of placing 2D shapes in a well-defined rectangular surface so-called Nesting. Many previous works approached this problem for regular shapes such as rectangle, triangle, square, circle. In our study we focused on the optimization of placement of irregular shapes named by 2-dimensional irregular bin packing problems (2DIBPP), the particularity of irregular shapes compared to other regular types is the inability to calculate their surfaces by an exact mathematical equation. In this regard, we give interest to the mathematical modeling of this type of placement problem and develop a heuristic algorithm able to solve this NP- Hard problem while respecting a set of non-overlapping constraints, the ability to pivot, and the confinement precise shapes in the bin.