VLSI cell placement problem is known to be NP complete. A wide repertoire of heuristic algorithms exists in the literature for efficiently arranging the logic cells on a VLSI chip. The objective of this paper is to present a comprehensive survey of the various cell placement techniques, with emphasis on standard ce11and macro placement. Five major algorithms for placement are discussed: simulated annealing, force-directed placement, rein-cut placement, placement by numerical optimization, and evolution-based placement. The first two classes of algorithms owe their origin to physical laws, the third and fourth are analytical techniques, and the fifth class of algorithms is derived from biological phenomena. In each category, the basic algorithm is explained with appropriate examples. Also discussed are the different implementations done by researchers.

Absfrucf-This paper describes the implementation of the Genetic Algorithm for Standard-cell Placement (GASP). Unlike the other placement algorithms that apply transformations o n the physical layout, the genetic algorithm applies transformations on the chromosomal representation of the physical layout. The algorithm works on a set o f configurations constituting a constant size population. The transformations are performed through crossover operators that generate a new configuration assimilating the characteristics o f a pair of configurations existing in the current population (similar to biological reproduction). M u t a t i o n and inversion operators are also used to increase the diversity of the population, and avoid premature convergence at local optima. Due to the simultaneous optimization of a large population of configurations, there is a logical concurrency in the search of the solution space which makes the genetic algorithm an extremely efficient optimizer. Three efficient crossover techniques have been compared, and the algorithm parameters, namely mutation rate, crossover rate, and inversion rate have been optimized f o r the cell placement problem by using a meta-genetic process. The resulting algorithm was tested against T i m b e r w o l f 3.3 o n five industrial circuits consisting of 100-800 cells. The results indicate that a placement comparable in quality can be obtained in about the same execution time as T i m b e r w o l f , but the genetic algorithm needs to explore 20-50 times less configurations compared to T i m b e r w o l f , which illustrates the efficiency o f the search process. Manuscript received April 4. 1989. This work was supported by URI-Program of' the U.S. Army undcr Grant DAAL 03-87-K-0007 and by the Research Initiation Award of the National Science Foundation under Grent MIP-8808978. Thi\ paper was recommended by Associate Editor R. H. J. M. Otren. The authors are with the Department 01 Electrical Engineering and Computer Science, Univcrsity 01 Michigan. A n n Arbor, MI 48 109. IEEE Log Number 8934103.

The genetic algorithm has been applied to the VLSI module placement problem. This algorithm is an iterative, evolutional approach. A placement configuration 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.

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