In this paper, we propose a new adaptive discretization method of design variables on real-coded genetic algorithms(RCGAs) for improving convergence performance while maintaining diversity.The convergence can be accelerated by setting the appropriate number of discrete classes in RCGAs. However, it is difficult to decide it in advance in most of the practical optimization problems.In addition, the diversity may be lost if the number of discrete classes is too small.In order to overcome these difficulties, we use a simple index which is based on the standard deviation to adaptively determine the number of discrete classes in each design variable.Since the proposed method merely rounds the value of the design variable after applying genetic operators such as crossover and mutation, it can be applied to various RCGAs.Here, we use NSGA-II as an RCGA and investigate the performance efficiency of convergence and diversity by using nineteen benchmark problems, including engineering problems.The convergence and diversity performance are evaluated using GD and IGD, respectively.The results of the numerical experiments show that the proposed method can obtain good convergence while maintaining diversity.

View full abstract

One of the most powerful approximation solution methods for the traveling salesman problem (TSP) is a genetic algorithm using edge assembly crossover (GA-EAX), which has found best-known tours to several 100 thousand points scale TSP instances. However, due to the nature of multi-point search, in many cases GAs take more computation time than local search-based algorithms, and it is difficult to fully exercise the capability of GA-EAX for very large TSP instances having more than 1 million points within a reasonable computation time. In this research, we introduce a MPI parallel implementation of GA-EAX. However, in a naive master slave method, the communication costs between the processes are too high to obtain the effect of parallelization sufficiently. So, we introduce a method to reduce the amount of communication between processes to avoid this problem. We also introduce a MPI/thread hybrid parallel implementation of GA-EAX where each MPI process is executed using multiple threads. Experimental results show that the hybrid parallel model achieved up to 29.4 times speedup using 16 PCs, each with 4 cores.

View full abstract