A tutorial in irregular shape packing problems

Cutting and packing problems have been a core area of research for many decades. Irregular shape packing is one of the most recent variants to be widely researched and its history extends over 40 years. The evolution of solution approaches to this problem can be attributed to increased computer power and advances in geometric techniques as well as more sophisticated and insightful algorithm design. In this paper we will focus on the latter. Our aim is not to give a chronological account or an exhaustive review, but to draw on the literature to describe and evaluate the core approaches. Irregular packing is combinatorial and as a result solution methods are heuristic, save a few notable exceptions. We will explore different ways of representing the problem and mechanisms for moving between solutions. We will also propose where we see the future challenges for researchers in this area.