Test Problems for Parallel Algorithms of Constrained Global Optimization

In this paper, we propose basic and improved algorithms based on polynomial B-spline form for constrained global optimization of multivariate polynomial functions. The proposed algorithms are based on a branch-and-bound framework. In improved algorithm we introduce several new ingredients, such as B-spline box consistency and B-spline hull consistency algorithm to prune the search regions and make the search more efficient. The performance of the basic and improved algorithm is tested and compared on set of test problems. The results of the tests show the superiority of the improved algorithm over the basic algorithm in terms of the chosen performance metrics. We compare optimal value of global minimum obtained using the proposed algorithms with CENSO, GloptiPoly and several state-of-the-art NLP solvers, on set of $11$ test problems. The results of the tests show the superiority of the proposed algorithm and CENSO solver (open source solver for global optimization of B-spline constrained problem) in that it always captures the global minimum to the user-specified accuracy.

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Multi-strategy gravitational search algorithm for constrained global optimization in coordinative operation of multiple hydropower reservoirs and solar photovoltaic power plants

Applied Soft Computing ◽

10.1016/j.asoc.2021.107315 ◽

2021 ◽

Vol 107 ◽

pp. 107315

Author(s):

Wen-jing Niu ◽

Zhong-kai Feng ◽

Shuai Liu

Keyword(s):

Global Optimization ◽

Power Plants ◽

Search Algorithm ◽

Gravitational Search Algorithm ◽

Solar Photovoltaic ◽

Constrained Global Optimization ◽

Photovoltaic Power ◽

Gravitational Search ◽

Hydropower Reservoirs

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A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions

Mathematics ◽

10.3390/math9020149 ◽

2021 ◽

Vol 9 (2) ◽

pp. 149

Author(s):

Yaohui Li ◽

Jingfang Shen ◽

Ziliang Cai ◽

Yizhong Wu ◽

Shuting Wang

Keyword(s):

Global Optimization ◽

Pareto Frontier ◽

Kriging Model ◽

Optimization Method ◽

Function Evaluation ◽

Sampling Point ◽

Constrained Global Optimization ◽

Multi Objective ◽

Sample Data ◽

Sampling Points

The kriging optimization method that can only obtain one sampling point per cycle has encountered a bottleneck in practical engineering applications. How to find a suitable optimization method to generate multiple sampling points at a time while improving the accuracy of convergence and reducing the number of expensive evaluations has been a wide concern. For this reason, a kriging-assisted multi-objective constrained global optimization (KMCGO) method has been proposed. The sample data obtained from the expensive function evaluation is first used to construct or update the kriging model in each cycle. Then, kriging-based estimated target, RMSE (root mean square error), and feasibility probability are used to form three objectives, which are optimized to generate the Pareto frontier set through multi-objective optimization. Finally, the sample data from the Pareto frontier set is further screened to obtain more promising and valuable sampling points. The test results of five benchmark functions, four design problems, and a fuel economy simulation optimization prove the effectiveness of the proposed algorithm.

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