Annealing placement by thermodynamic combinatorial optimization

Abstract

Placement is key issue of integrated circuit physical design. There exist some techniques inspired in thermodynamics coping with this problem as Simulated Annealing. In this article, we present a combinatorial optimization method directly derived from both Thermodynamics and Information Theory. In TCO (Thermodynamic Combinatorial Optimization), two kinds of processes are considered: microstate and macrostate transformations. Applying the Shannon's definition of entropy to reversible microstate transformations, a probability of acceptance based on Fermi--Dirac statistics is derived. On the other hand, applying thermodynamic laws to macrostate transformations, an efficient annealing schedule is provided. TCO has been compared with a custom Simulated Annealing (SA) tool on a set of benchmark circuits for the FPGA (Field Programmable Gate Arrays) placement problem. TCO has provided the high-quality results of SA, while inheriting the adaptive properties of Natural Optimization (NO).