The Interactive Effects of Operators and Parameters to GA Performance Under Different Problem Sizes

The complex effect of genetic algorithm's (GA) operators and parameters to its performance has been studied extensively by researchers in the past but none studied their interactive effects while the GA is under different problem sizes. In this paper, We present the use of experimental model (1)~to investigate whether the genetic operators and their parameters interact to affect the offline performance of GA, (2)~to find what combination of genetic operators and parameter settings will provide the optimum performance for GA, and (3)~to investigate whether these operator-parameter combination is dependent on the problem size. We designed a GA to optimize a family of traveling salesman problems (TSP), with their optimal solutions known for convenient benchmarking. Our GA was set to use different algorithms in simulating selection ($\Omegas$), different algorithms ($\Omegac$) and parameters ($pc$) in simulating crossover, and different parameters ($pm$) in simulating mutation. We used several $n$-city TSPs ($n={5, 7, 10, 100, 1000}$) to represent the different problem sizes (i.e., size of the resulting search space as represented by GA schemata). Using analysis of variance of 3-factor factorial experiments, we found out that GA performance is affected by $\Omega_s$ at small problem size (5-city TSP) where the algorithm Partially Matched Crossover significantly outperforms Cycle Crossover at $95\%$ confidence level.