  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 ($\Omega_s$), different algorithms ($\Omega_c$) and
parameters ($p_c$) in simulating crossover, and different parameters ($p_m$) 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.
