K-Means Clustering and Chaos Genetic Algorithm for Nonlinear Optimization

To reduce the computational amount and improve estimation accuracy for nonlinear optimizations, a new algorithm, K-means clustering with Chaos Genetic Algorithm (KCGA) is proposed, in which initial population are generated by chaos mapping and refined by competition. Within each iteration of this approach, in addition to the evolution of genetic algorithm (GA), the K-means Clustering algorithm is applied to achieve faster convergence and lead to a quick evolution of the population.

The main purpose of the paper is to demonstrate how the GA optimizer can be improved by incorporating a hybridization strategy. Experimental studies revealed that the hybrid KCGA approach can produce much more accurate estimates of the true optimum points than the other two optimization procedures, the chaos genetic algorithm (CGA) and GA. Further, the proposed hybrid KCGA approach exhibits superior convergence characteristics when compared to other algorithms in this paper separately. On the whole, the new approach is demonstrated to be extremely effective and efficient at locating optimal solutions and verified by an empirical example from construction.