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. Diversifi...

This paper introduces a new tabu search algorithm for a twodimensional (2D) Strip Packing Problem (2D-SPP). It integrates several key features: A direct representation of the problem, a satisfaction-based solving scheme, two different complementary neighborhoods, a diversification mechanism and a particular tabu structure. The representation allows inexpensive basic operations. The solving sche...

From 13.03. to 16.03.2007, the Dagstuhl Seminar 07112 Cutting, Packing, Layout and Space Allocation was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of semi...

Given a container of fixed width, infinite height and a set of rectangular block, the 2D-strip packing problem consists of orthogonally placing all the rectangles such that the height is minimized. The position is subject to confinement of no overlapping of blocks. The problem is a complex NP-hard combinatorial optimization, thus a heuristic based on genetic algorithm is proposed to solve it. I...

We propose two mixed-integer linear programming based approaches for the 2-D orthogonal strip packing problem. Using the knowledge of the alternative forms of time representation in scheduling formulations, we show how to efficiently combine three different concepts into the xand ydimensions. One model features a discrete representation of the x-axis (strip width) and a continuous representatio...

In this paper, an orthogonal strip packing problem with rotation of items and without the guillotine packing constraint is considered. A fast heuristic algorithm for the large-scale problems is presented. This heuristic algorithm is mainly based on heuristic strategies inspired by the wall-building rule of bricklayers in daily life. The heuristics is simple and the setting of parameter is not r...

Multi-dimensional multi-container packing problems appear within many settings of theoretical and practical interest, including Knapsack, Strip Packing, Container Loading, and Scheduling problems. These various problem settings display different objective functions and constraints, which may explain the lack of efficient heuristics able to jointly address them. In this paper we introduce GASP G...

PURPOSE To measure the variation in human cone photoreceptor packing density across the retina, both within an individual and between individuals with different refractive errors. METHODS A high-resolution adaptive optics scanning laser ophthalmoscope was used to image the cones of 11 human eyes. Five subjects with emmetropia and six subjects with myopia were tested (+0.50 to -7.50 D). For ea...