A hybrid approach to constrained global optimization

•We proposed a novel stochastic search method, called Greedy Diffusion Search (GDS). It holds the ability to escape from local minima for multi modal problems.•Combining GDS with limited memory BFGS, we propose a hybrid global optimization method to solve constrained optimization problems.•To evaluate the effectiveness of the proposed algorithm, some benchmark problems as well as some examples from the literature are tested. The outcomes are highly satisfactory.

In this paper, we propose a novel hybrid global optimization method to solve constrained optimization problems. An exact penalty function is first applied to approximate the original constrained optimization problem by a sequence of optimization problems with bound constraints. To solve each of these box constrained optimization problems, two hybrid methods are introduced, where two different strategies are used to combine limited memory BFGS (L-BFGS) with Greedy Diffusion Search (GDS). The convergence issue of the two hybrid methods is addressed. To evaluate the effectiveness of the proposed algorithm, 18 box constrained and 4 general constrained problems from the literature are tested. Numerical results obtained show that our proposed hybrid algorithm is more effective in obtaining more accurate solutions than those compared to.

Graphical abstractThe contribution of this paper is to develop a new stochastic search strategy which is specific for hybrid global optimization. Numerical experiments show that this method achieves better performance those many compared existing algorithms. Figure optionsDownload full-size imageDownload as PowerPoint slide