GGAPack experimental setups

Initial experiments have been set up for investigating GGAPack results. Since the GA outputs are stochastic, the GGAPack was executed for one hundred times, and the results are collected for statistical analysis. The targeted FPGA architecture was the same as used in Section 5.5 for VPack and

Start Evaluate population Randomly initialise population, individual #: N Crossover Mutation Survived individuals individual #: N/2 New population individual #: N MO selection + Evaluate population MO selection Terminate? End Iteration Evolution Find the best

individual, and translate

to a netlist

Yes

No

Figure 6.7: The flow of GGAPack: The population is initialised randomly – each BLE is in a CLB with a random CLB index. Individuals are as-

signed multiple fitnesses by multiple fitness functions. MO selection uses the non-dominated sort and crowding distance (NSGA-2 method) to form new population. GGAPack, the GA, iterates for a fixed number of generations then stops. The best individual is filtered and translated as a netlist.

RVPack, where the CLB has I = 18, N = 8, one clock and the BLE contains 4-input LUT and a reconfigurable FF, and the experiments are based on the MCNC-20 benchmarks (Yang, 1991). For the initial experiments, GGAPack outputs, solution-quality-related results, are directly compared to other circuit clustering algorithms, which are the CLB numbers and CLB interconnect numbers. The detailed testing flow is shown in Figure 6.8. As the pattern match is a duplicated process, each GGAPack program starts from the pattern matched netlist – the BLEs. These tests are still carried out on the same high performance computing cluster, referred to Section 5.5, where execution time of each program is the cluster-processor-occupying time.

Before loading GGAPack to the computing cluster, a number of GA pa- rameters have to be chosen in order to produce useful results: First, according to the optimal CLB number of the MCNC-20 benchmark, the generation number is estimated. This is accomplished using the largest benchmark “clma”. The “clma” has 8,383 BLEs, when clustering this benchmark into a 8-BLE CLB, the optimal CLB number is 1,048 (8,383 over 8). In GGAPack,

Start

Pattern Match the Netlist Synthesised

MCNC-20

GGAPack GGAPack GGAPack GGAPack

End

...

Figure 6.8: GGAPack executing and testing flow. Before forwarding the synthesised MCNC-20 netlist (LUTs + FFs) to GGAPack, a duplicated process, the pattern match, can be first performed, so that the GGAPack deals with the BLEs directly.

mutation is the primary operation to create the CLBs, and in each generation two CLBs are eliminated. If this operation is carried out on all CLBs (the initial individual has one BLE per CLB), this will mean that the smallest mutation number is at least 4,192 (8,383 over 2). However, that is an ideal situation as the mutation does not happen to every effective CLB. In practice, the random-CLB-eliminating mutation can also occur to well clustered CLBs. In order to move all BLEs in an optimal CLB number, or a near optimal CLB number, the generation number is set to ten times the minimum re- quirement – the smallest mutation number. To simplify the problem, the GA generation number of each benchmark is rounded to 40,000, and this can also ensure smaller benchmarks have enough generations to evolve. Figure A.2 in Appendices shows GGAPack GA convergence under different generations. Test indicates that 40,000 generations are enough.

Second, the crossover rate of GA is adjusted. To get an efficient crossover rate, the crossover rate has been tested under a range, which is from 0.2 to 0.8 based on the GA empirical settings that are introduced in Chapter 4. The testing shows that if the rate is set to 0.6, as shown in Figure 6.9

Figure 6.9: Box plot of CLB numbers vs. different crossover rates of GGAPack executions. The test is based on “clma” – the largest benchmark in MCNC- 20. For each crossover rate, GGAPack executes for 100 times, final CLB number means that each GGAPack executes for 40,000 generations. When the crossover rate is 0.6, the GA result variation is small, and CLB number is small as well.

– testing GGAPack performance of different crossover rates based on the largest benchmark “clma”, the GA can achieve small number of CLBs in a short time, and its results also have small variations. The figure only shows the testing results of “clma”, however, the crossover rate is not linked to a particular benchmark; even when the benchmark is changed, the GA is still efficient. For the population size, to speed up the GA, it is set to 10, as, in GGAPack, experiments show that the population size does not significantly affect the quality of GA results, where this can be proofed by the graph of GA convergence vs. different population size as shown in Figure A.3 in Appendices.

The GA parameters for GGAPack are summarised as follows:

1) Population size: 10. 2) Crossover rate: 0.6

0   200   400   600   800   1000   1200   1400  

alu4   apex2   apex4   bigkey   clma   des   diffeq   dsip   ellip9c   ex1010  

CLB  N umb er     MCNC-­‐20  Benchmarks   GGAPack  Worst   GGAPack  Best   VPack   RVPack   0   100   200   300   400   500   600   700   800   900  

ex5p   frisc   misex3   pdc   s298   s38417   s38584.1   seq   spla   tseng  

CLB  N umb er     MCNC-­‐20  Benchmarks   GGAPack  Worst   GGAPack  Best   VPack   RVPack  

Figure 6.10: GGAPack clustered CLB number for MCNC-20 benchmarks compared to VPack and RVPack, lower is better. Data boxplot and detailed data are provided in Appendices in Figure A.12 and Table A.10.

4) Generation number: 40,000