The Improved Multi-Objective Programming Module and Optimization Algorithm of the Three-Dimensional Layout Optimization Problem

This paper studies the three-dimensional layout optimization problem for packing cylindrical objects into the cylindrical space. A multi-objective optimization model with performance constraints is presented. Here we introduce an improved multi-objective programming algorithm for the layout optimization model. Computational results are presented which suggest that this algorithm performs well. Moreover,we introduce a measure function to determine whether two graph elements are overlaping, touching or nonoverlapping in any way.