Hybrid optimization using DIRECT, GA, and SQP for global exploration

This paper presents a new hybrid optimization approach, which combines multiple optimization algorithms. To develop an efficient hybrid optimization algorithm, it is necessary to determine how the optimization process is performed. This paper focuses on the balance between local and broad searches, and multiple optimization methods are controlled to derive both the optimum point and the information of the landscape. By this approach, we can describe the global landscape after derivation of optimization. To achieve the proposed optimization strategy, three distinguished optimization algorithms are introduced: DIRECT (Dividing RECTangles), GAs (Genetic Algorithms), and SQP (Sequential Quadratic Programming). To integrate these three algorithms, each algorithm, especially DIRECT, was modified and developed. The performance of the proposed hybrid algorithm was examined through numerical experiments. From these experiments, not only the optimum point but also the information of the landscape was determined. The information of the landscape verified the reliability of optimization results.