Channel routing problem is an important, time consuming and difficult problem in VLSI layout design. In this
paper, we consider the two-terminal channel routing problem in a new routing model, called knock-knee diagonal
model, where the grid consists of right and left tracks displayed at +45° and –45°. An optimum algorithm is
presented, which obtains d + 1 as an upper bound to the channel width, where d is the channel density.
Machining allowance distribution and related parameter optimization of machining processes have been well-discussed. However, for energy saving purposes, the optimization priorities of different machining phases should be different. There are often significant incoherencies between the existing research and real applications. This paper presents an improved method to optimize machining allowance distribution and parameters comprehensively, considering energy-saving strategy and other multi-objectives of different phases. The empirical parametric models of different machining phases were established, with the allowance distribution problem properly addressed. Based on previous analysis work of algorithm performance, non-dominated sorting genetic algorithm II and multi-objective evolutionary algorithm based on decomposition were chosen to obtain Pareto solutions. Algorithm performances were compared based on the efficiency of finding the Pareto fronts. Two case studies of a cylindrical turning and a face milling were carried out. Results demonstrate that the proposed method is effective in trading-off and finding precise application scopes of machining allowances and parameters used in real production. Cutting tool life and surface roughness can be greatly improved for turning. Energy consumption of rough milling can be greatly reduced to around 20% of traditional methods. The optimum algorithm of each case is also recognized. The proposed method can be easily extended to other machining scenarios and can be used as guidance of process planning for meeting various engineering demands.
An Optimum Channel Routing Algorithm in the
Knock-knee Diagonal Model
