A SAT-based Method for Solving the Two-dimensional Strip Packing Problem

A SAT-based Method for Solving the Two-dimensional Strip Packing Problem

We propose a satisfiability testing (SAT) based exact approach for solving the two-dimensional strip packing problem (2SPP). In this problem, we are given a set of rectangles and one large rectangle called a strip. The goal of the problem is to pack all rectangles without overlap, into the strip by minimizing the overall height of the packing. We show the method solves a 2SPP by translating it ...

A Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

A genetic algorithm for the two-dimensional strip-packing problem

The paper presents a genetic algorithm (GA) for the two-dimensional strip-packing problem (SPP) with rectangular shaped pieces. Both the non-guillotinable SPP and the guillotinable SPP can be tackled. The genetic algorithm has been derived from a GA that was proposed earlier for solving the container-loading problem (CLP) with a single container to be loaded. The characteristic features of the ...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Parallelisation of the Two-dimensional Guillotine Strip Packing/Cutting Problem