Fuzzy simulated evolution algorithm for very large scale integrated cell placement

Placement is a major step encountered during the design of very large scale integrated circuits. It is a generalization of the quadratic assignment problem with numerous constraints, several objectives, and a very noisy solution space. Besides the NP-hard nature of this problem, many circuit parameters such as area, interconnect delays, wire requirements, etc. can only be imprecisely estimated before completing the remaining design automation steps and committing the circuit to silicon. Further, the best placement is usually one that combines several desirable physical characteristics. There has not been a consensus on how to accommodate all these (conflicting) requirements in the search for near optimal feasible solutions. In this paper, we present a fuzzy simulated evolution (FSE) algorithm to tackle this problem. Identification of near optimal solutions is achieved through a novel goal-directed fuzzy search approach. This approach can be followed by other iterative (meta-) heuristics to find desirable solutions to optimization problems with noisy search space and possibly more than one objective. This approach is dominance preserving, i.e. if a solution A dominates another solution B with respect to all objective criteria, then A will surely have a higher membership in the fuzzy set of good solutions than solution B. Further, the approach scales well with larger problem instances and/or a larger number of objective criteria. Also, the operators of all stages of simulated evolution have been implemented using fuzzy logic to exploit the nature of fuzzy information of the problem domain. Experiments with benchmark tests demonstrate a noticeable improvement in solution quality.