Approximate optimization method for constraints dynamic relaxation of black box model

In the complex engineering design problems represented by aircraft design, in order to improve the design performance, reduce the development cost and shorten the design cycle, it is usually necessary to optimize the product performance, cost and other design indexes. At the same time, in order to improve the credibility of simulation results, high time-consumption simulation models are more and more widely used in actual engineering design, while the improvement of model simulation accuracy leads to an exponential increase in simulation time, resulting in an increase in computational cost and a decrease in optimization efficiency. Therefore, surrogate-based optimization methods are introduced to achieve the goal of reducing design, analysis and computational consumption. In practical engineering problems, it is necessary to combine with constraint handling methods to obtain the optimal feasible solution that satisfies the constraints. After the introduction of constraints, complex factors such as the type of constraints, the number of different constraints, the size of the feasible domain, the number of valid constraints, etc. can lead to problems such as reduced efficiency of the optimization algorithm and difficulty in searching for the globally optimal solution. Therefore it is necessary to conduct research for constraint handling methods.

The feasibility rule method is easy to implement and does not require tedious parameter tuning, but ignores the ability of high-quality infeasible solutions to explore the boundary of the feasible domain. Especially for the surrogate models optimization problem, it is difficult to get a more accurate solution at the early stage of optimization, and the high-quality infeasible solutions near the feasible domain can improve the accuracy of the models on the constraint boundaries and enhance the algorithm's ability to explore the boundary of the feasible domain. Therefore, the idea of ε-constraint holding is proposed, where the feasible domain is enlarged at the early stage of optimization, and as the algorithm iterates, the feasible domain shrinks until it coincides with the real feasible domain. As the infeasible solutions with smaller constraint conflicts are added to the sample set constructed by the surrogate models in the pre-optimization stage, the accuracy of the constraint boundary surrogate models is improved, which can better support the algorithm to explore the boundary of the feasible domain.

When performing the test algorithms, more than 25 independent runs are performed for each of the algorithms to ensure the stability of the results. The optimization results are compared with the Chaotic grey wolf optimization method, The extended balanced ranking method and Modified global best artificial bee colony method published in recent years. The proposed CDRAO (constraints dynamic relaxation approximate optimization) algorithm is a constrained optimization algorithm with superior performance and possesses the potential for complex engineering constrained optimization applications. The CDRAO method is used to optimize the solid rocket motor charge design, the optimization objective is the stability of the combustion surface during the combustion process of the pillars, and the constraints are the mass of the pillars of the motor, and the results also verify the effectiveness of the algorithm.

In order to address the problem of optimal design of high time-consuming models, the adaptive sampling phase of surrogate models is investigated. Considering various types of constraints on the objective function, a multi-constraint adaptive sampling method is proposed, and the proposed method is verified by mathematical and engineering examples.