4.1. Benchmark instances

We evaluated the performance of the multilevel evolutionary algorithm (MLVMA) against its single variant (MA) using a set of instances taken from SATLIB. (http://www.informatik.tudarmstadt.de/AI/SATLIB). Table 1 shows the instances used in the experiment. IBM SPSS Statistics version 19 was used for statistical analysis. Due to the randomization nature of the algorithms, each problem instance was run 100 times with a cutoff parameter (max time) set to 15 min. The 100 runs were adopted because pilot runs had shown the size of the difference to be so large that 100 runs were enough for an acceptable statistical power (power > :95); this is in accordance with the suggestions given in a recent report on statistical testing of randomized algorithms [20].

The tests were carried out on a DELL machine with 800 MHz CPU and 2 GB of memory. The code was written in C and compiled with the GNU C compiler version 4.6. The list of parameters used in the experiments are as follows:


Table 1. Benchmark set of the SAT competition Beijing.

