Energy-Efficient Mapping for 3D NoC using Logistic Function Based Adaptive Genetic Algorithms

The problem of mapping application tasks is one of key issues in 3D Network on chip (3D NoC) design. A novel Logistic function based adaptive genetic algorithm (LFAGA) is proposed for energy-aware mapping of homogeneous 3D NoC. We formulate the mapping problem and show the Standard genetic algorithm (SGA). The LFAGA is presented in detail with the goal of obtaining higher convergence speed while preventing the premature convergence. Experimental results indicate that the proposed LFAGA is more efficient than previously proposed Chaos-genetic mapping algorithm (CGMAP). In the experiments, a randomly generated task graph of size 27 is mapped to a 3D NoC of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3× 3× 3,t</tex> he convergence speed of LFAGA is 2.55 times faster than CGMAP in the best condition. When the task size increases to 64 and the 3D NoC size extends to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4× 4× 4</tex>, LFAGA is 2.31 times faster compared to CGMAP. For the NoC sizes in the range from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3× 3× 2</tex> to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4× 4× 4</tex>, solutions obtained by the LFAGA are consistently better than the CGMAP. For example, in the experiment of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4× 4× 4</tex>, the improvement of final result reaches 30.0% in term of energy consumption. For a real application of size <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3× 4× 2</tex>, 18.6% of energy saving can be achieved and the convergence speed is 1.58 times faster than that of the CGMAP.