A new unconstrained global optimization method based on clustering and parabolic approximation

The clustering technique and parabolic approximation are used in this method.

A new unconstrained global optimization method based on clustering and parabolic approximation
(GOBC-PA) is proposed. Although the proposed method is basically similar to other
evolutionary and stochastic methods, it represents a significant advancement of global optimization
technology for four important reasons. First, it is orders of magnitude faster than existing optimization
methods for global optimization of unconstrained problems. Second, it has significantly better repeatability,
numerical stability, and robustness than current methods in dealing with high dimensionally
and many local minima functions. Third, it can easily and faster find the local minimums using the
parabolic approximation instead of gradient descent or crossover operations. Fourth, it can easily
adapted to any theoretical or industrial systems which are using the heuristic methods as an intelligent
system. In this study, we assume that the best cluster center gives the
position of the possible global optimum. The usage of clustering and curve fitting techniques brings
multi-start and local search properties to the proposed method. The experimental studies show that
the proposed methodology is simple, faster and, it demonstrates a superior performance
when compared with some state of the art methods.
Paper: Pence, I., Cesmeli, M. S., Senel, F. A., & Cetisli, B. (2016). A New Unconstrained Global Optimization Method based on Clustering and Parabolic Approximation. Expert Systems with Applications, 55, 493-507.