Macro-cell and module placement by genetic adaptive search with bitmap-represented chromosome

Abstract

The genetic algorithm has been applied to the VLSI module placement problem. This algorithm is an iterative, evolutional approach. A placement configutation is represented by a set of primitive features such as location and orientation, and the features are arranged in the form of a two-dimensional bitmap chromosome. The representation is flexible, and can handle arbitrarily shaped cells, and pads, and is applicable to the placement of macro cells, and gate arrays. Three new versions of genetic operators, namely, crossover, inversion and mutation, are used to explore the solution space. Crossover creates new configurations by combining attributes from a pair of existing configurations. This feature passing scheme constitutes the primary difference between our genetic approach and the other traditional searching techniques. Inversion enables more uniform inheritance of features from one generation to the next, and mutation prevents the algorithm from getting trapped at local optima. We have pointed out that the bitmap representation enables the algorithm to divide the entire solution space into a set of feature-equivalent classes, or schemata where each class contains a set of solutions with common physical attributes. We show that the genetic algorithm adaptively biases the search based on the past observed fitness of the schemata. We also demonstrated the power of the genetic algorithm experimentally for macro cell placement, and obtained satisfactory results.