This paper addresses a constrained two-dimensional (2D), non-guillotine restricted, packing problem, where a xed set of small rectangles has to be placed into a larger stock rectangle so as to maximize the value of the rectangles packed. The algorithm we propose hybridizes a novel placement procedure with a genetic algorithm based on random keys. We propose also a new tness function to drive th...

T two-dimensional bin-packing problem is the problem of orthogonally packing a given set of rectangles into a minimum number of two-dimensional rectangular bins. The problem is -hard and very difficult to solve in practice as no good mixed integer programming (MIP) formulation has been found for the packing problem. We propose an algorithm based on the well-known Dantzig-Wolfe decomposition whe...

The problem of planning the layout of containers on board supply vessels can be reformulated as the problem of packing a given set of rectangles into a larger rectangle, subject to constraints. A method combining the use of guillotine cuts with forward checking is proposed, and compared to standard forward checking on finite domains. The initial results show that the method has potential for im...

We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company’s primary objective is to minimise total processing time at the su...