Designing genetic algorithms for the state assignment problem

Finding the best state assignment for implementing a synchronous sequential circuit is important for reducing silicon area or chip count in many digital designs. This state assignment problem (SAP) belongs to a broader class of combinatorial optimization problems than the well studied traveling salesman problem, which can be formulated as a special case of SAP. The search for a good solution is considerably involved for the SAP due to a large number of equivalent solutions, and no effective heuristic has been found so far to cater to all types of circuits. In this paper, a matrix representation is used as the genotype for a genetic algorithm (GA) approach to this problem. A novel selection mechanism is introduced, and suitable genetic operators for crossover and mutation, are constructed. The properties of each of these elements of the GA are discussed and an analysis of parameters that influence the algorithm is given. A canonical form for a solution is defined to significantly reduce the search space and number of local minima. Experiments with several examples show that the GA approach yields results that are often comparable to, or better than those obtained using established heuristics that embody extensive domain knowledge