Combinatorial optimization in VLSI physical design




Walsh, Peter Anthony

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Simulated Annealing is a general purpose combinatorial optimization technique which has been applied to many problems in VLSI design. In essence, simulated annealing is Monte Carlo iterative improvement with the ability to conditionally accept uphill moves. The notion of a cooling schedule is common to all simulated annealing implementations. A cooling schedule can be thought of as simulated annealing's control mechanisms. Experiential work has been done on estimating the cost of an optimal solution to some combinatorial optimization problem instances. Such an estimate can be used to determine termination criteria for general purpose optimization techniques such as iterative improvement or simulated annealing. We have extended this idea and designed a complete simulated annealing general cooling schedule based on the cost of an optimal solution to a problem instance. We call the resultant schedule an extended goal-directed general cooling schedule. One of the major problems with simulated annealing is its long computation times. This problem can be addressed by first using a fast heuristic to find a good initial configuration and then applying simulated annealing. This approach is called Simulated Sintering. To exploit the potential of simulated sintering one needs an appropriate general cooling schedule. The extended goal-directed cooling schedule is equally applicable to simulated annealing and simulated sintering. To date, no one cooling schedule has proven suitable for all optimization problem instances. In our view, no such cooling schedule exits. Consequently, we have attempted to identify the type of problem best suited to optimization by simulated annealing and simulated sintering using the extended goal-directed schedule. We have applied the extended goal-directed schedule to standard-cell placement and floorplanning problems using both simulated annealing and simulated sintering. Within this context, we have compared the performance of the extended goal-directed schedule to other published schedules. Our results indicate that in terms of layout quality, the extended goal-directed schedule performs as well or better than the other schedules. In this dissertation, we have developed a new general cooling schedule. Our evaluation of the extended goal-directed schedule suggests that it is a useful research contribution in the area of simulated annealing algorithms.



Combinatorial optimization, Simulated annealing (Mathematics)