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

Abstract

Abstract-As there are many good optimization algorithms each with its own characteristics, it is very difficult to choose the best method for optimization problems. Thus, it is important to select and apply the appropriate algorithms according to the complexities of the problem. However, it is difficult to solve very complicated problems with only a single algorithm, and a hybrid optimization approach, which combines multiple optimization algorithms, is necessary. 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. Multiple optimization methods are controlled to derive both the optimum point and the information of the landscape. 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. This paper describes a new hybrid method using these three algorithms. 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.

A Hybrid Approach for Solving Constrained Multi-Objective Mixed-Discrete Nonlinear Programming Engineering Problems

“…Hybridization of an EA or GA with a gradient-based local search algorithm is not new. There are numerous references demonstrating how hybridization may improve the quality of the search for both single objective and multi-objective problem formulations; these include, but are not limited to, those appearing in [3,[19][20][21][22][23][24][25][26][27][28][29][30][31][32]. The local search can be considered as the local learning that takes place in an individual throughout its lifespan.…”

Optimization of a Three-Phase Tetrahedral High Voltage Transformer used in the Power Supply of Microwave

“…OPTIMIZATION OF THE TETRAHEDRAL TRANSFORMER USED IN THE POWER SUPPLY The optimization stage is based on the model developed on Matlab/Simulink of the three-phase HV power supply with three-magnetron per phase. This model will allow us to study with respect to the reference transformer case (non-optimized transformer) the sensitivity of each geometrical parameter to the nominal operation of the power supply [11][12][13]. This study will give us an idea of how we can simultaneously vary all the parameters in order to meet the following criteria:…”