Determining an upper bound for a class of rectangular packing problems

1985 ◽  
Vol 12 (2) ◽  
pp. 201-205 ◽  
Author(s):  
Kathryn A. Dowsland
Keyword(s):  
Upper Bound ◽  
Packing Problems ◽  
Rectangular Packing

LINEAR PROGRAMMING CUTTING PROBLEMS

1993 ◽  
Vol 03 (04) ◽  
pp. 463-476 ◽  
Author(s):  
E.A. MUKHACHIOVA ◽  
V.A. ZALGALLER
Keyword(s):  
Cutting Stock ◽  
Compromise Solution ◽  
Packing Problems ◽  
Numerical Examples ◽  
Choice Procedure ◽  
Special Software ◽  
Rectangular Packing ◽  
Planning Problems ◽  
Cutting Problems ◽  
Guillotine Cutting

Different optimal cutting problems are considered in this paper. Among them are cutting forming problems (closed packing problems) and problems of cutting totality planning with intensities of their application. For solving these planning problems, linear or integer programming is used. Furthermore, different cutting technological and organizational situations are considered. Different optimal criteria and a compromise solution choice procedure are presented. All the statements are illustrated by numerical examples from a guillotine cutting area. The possibility of linear cutting approximation for a non-guillotine (closed packing) cutting stock problem is shown. Rectangular packing algorithms based on this approximation can be built. These algorithms form the basis of special software. Their characteristics are presented in the conclusion of the paper.

The Particle Swarm Optimization Algorithm for Solving Rectangular Packing Problem

2011 ◽  
Vol 186 ◽  
pp. 479-483 ◽  
Author(s):  
Yang Qi ◽  
Jin Min Wang
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Particle Swarm Optimization Algorithm ◽  
Heuristic Algorithms ◽  
Particle Swarm ◽  
Experimental Result ◽  
Swarm Optimization ◽  
Local Optima ◽  
Packing Problems ◽  
Rectangular Packing

Based on extensive researches on various heuristic algorithms, the particle swarm optimization algorithm was developed to solve the rectangular packing problems. The algorithm optimizes the parameter of dynamic attractive factors by updating the position and the velocity of the particles, and applies perturbation strategy to solve the matter that it is easy to stick at local optima. The experimental result shows that the algorithm can get a better packing result by less time.

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