Continuous optimization by hierarchical gaussian mixture with clustering embedded resource allocation

Continuous optimization problems, which are highly related to real-world problems, are difficult since they are multimodal and rugged. In this paper, we introduce a new algorithm called Global and Local Adaptation with Clustering Embedded Resource Allocation (GLACERA) to solve problems with relaxed conditions. We believe that continuous optimization problems are solvable as long as the local optima can serve as clues for finding the global optimum. To solve the problems more efficiently, a new clustering technique is proposed to help identify potential local optima. Then, a new multi-armed bandit technique, aiming to reach global optimum with greater probability, is presented to allocate resources for each local optimum. Finally, a new formula is proposed for balancing exploration and exploitation according to remaining number of function evaluations. We compare GLACERA with four milestone algorithms that are commonly used for continuous optimization, and show that it can solve a new class of functions while others failed, while remain competitive in solving benchmark problems of IEEE CEC2005 and IEEE CEC2013.