Tabu Search with Consistent Neighbourhood for Strip Packing

This paper introduces a new tabu search algorithm for a strip packing problem. It integrates several key features: A consistent neighborhood, a fitness function including problem knowledge, and a diversification based on the history of the search. The neighborhood only considers valid, sometimes partial, packings. The fitness function incorporates measures related to the empty spaces. Diversification relies on a set of historically “frozen” objects. Experimental results are shown on a set of well-known hard instances and compared with previously reported tabu search algorithms as well as the best performing algorithms

A SURVEY ON HEURISTICS FOR THE TWO-DIMENSIONAL RECTANGULAR STRIP PACKING PROBLEM

ABSTRACT Two-dimensional rectangular strip packing problems belong to the broader class of Cutting and Packing (C&P) problems, in which small items are required to be cut from or packed on a larger object, so that the waste (unused regions of the large object) is minimized. C&P problems differ from other combinatorial optimization problems by the intrinsic geometric constraints: items may not overlap and have to be fully contained in the large object. This survey approaches the specific C&P problem in which all items are rectangles, therefore fully characterized by a width and a height, and the large object is a strip, i.e. a rectangle with a fixed width but an infinite height, being the problem's goal to place all rectangles on the strip so that the height is minimized. These problems have been intensively and extensively tackled in the literature and this paper will focus on heuristic resolution methods. Both the seminal and the most recent approaches (from the last decade) will be reviewed, in a rather tutorial flavor, and classified according to their type: constructive heuristics, improvement heuristics with search over sequences and improvement heuristics with search over layouts. Building on this review, research gaps are identified and the most interesting research directions pointed out

2D-Packing with an Application to Stowage in Roll-On Roll-Off Liner Shipping

Roll-on/Roll-off (RoRo) ships represent the primary source for transporting vehicles and other types of rolling material over long distances. In this paper we focus on operational decisions related to stowage of cargoes for a RoRo ship voyage visiting a given set of loading and unloading ports. By focusing on stowage on one deck on board the ship, this can be viewed as a special version of a 2-dimensional packing problem with a number of additional considerations, such as one wants to place vehicles that belong to the same shipment close to each other to ease the loading and unloading. Another important aspect of this problem is shifting, which means temporarily moving some vehicles to make an entry/exit route for the vehicles that are to be loaded/unloaded at the given port. We present several versions of a new mixed integer programming (MIP) formulation for the problem. Computational results show that the model provides good solutions on small sized problem instances.acceptedVersio