Effects of discrete design-variable precision on real-coded Genetic Algorithm

In this paper, we describe how discretizing design variables on real-coded genetic algorithms (RCGAs) can influence the convergence and the diversity of Pareto optimal solutions. We use Non-dominated Sorting Genetic Algorithm II (NSGA-II) as an RCGA based on Pareto dominance, changing the number of significant digits after the decimal point for each design variable. Test problems and engineering problems are investigated. Computational results show that the use of a smaller number of significant figures instead of larger ones achieves better convergence that a larger number in many cases. In the DTLZ3 test problem, low applied precision avoids dominance-resistant solutions (DRSs) and improves both the generational distance (GD) and the inverted generational distance (IGD). On the other hand, in the DTLZ4 test problem, low digit precision improves GD, whereas it worsens IGD. This indicates that a minimum digit precision is required to maintain the diversity of Pareto optimal solutions in some problems. When we use RCGAs, it is critical to set the number of significant digits after the decimal point to realistically represent actual engineering problems.