Researchs On Optimization Algorithms Based On Generalized Response Surface Of Complex Black-box Model

When designing the complex mechanical system, engineers now often need to establish the computer simulation models of mechanical system, and then adjust the relevant parameters of system based on simulation models to make the performance of the mechanical system reach a better level. This kind of computer-simulation model based optimized design is typical simulation optimization problem, which is characterized by the relationship between objectives, constraints and design variables not explicitly expressed. In iteration, the computational analysis simulation model would be performed to calculate the value of objective function or constraints. The computational simulation model is a kind of black-box function to the oprimization problem. Due to the increasing complexity of modern mechanical systems, the precision of computer-aided analysis model is also getting higher and higher, so the computation time required for the simulation models are also getting longer and longer. Although the computing power of computer has dramatically improved compared to the previous, but the time required by the entire optimization process in solving complex, high-fidelity simulation model parameter optimization problem is still too long, so that the engineers can not directly use traditional optimization methods. To reduce the computational cost, the response surface model based optimization theory has been developed, and has been widely used in engineering personnel aerospace, shipbuilding marine engineering, mechanical engineering, vehicle engineering, chemical engineering, biological and other areas in the past 20 years. This kind of optimization method usually establishs approximate mathematocal representation of the original complex black-box model, and reasonable distributes the computing resources, take use of approximate mathematical calculations ("cheap valuation") as much as possible instead of using model simulation("expensive valuation") in the optimization process, in order to reduce the overall optimization process computational overhead.Response surface model (RSM) is the approximate description of input variables and output response for simulation model. The construction process of RSM is firstly adopting experiment design method to obtain a series of sampling data, and then performing computational simulation on these sample points to achive the corresponding response value, finally establishing the approximate function between input-output. The RSM based optimization is performing scan-iteration based on the RSM we obtained. In one hand, the method should analysis the area around the best point of current RSM. In other hand, the method should explore the unknown region in the design space. So how to rational allocate the computational overhead to determine the search process iterates is the key point of RSM based optimization. For complex black-box model optimization problem, this paper performs a series of studies based response surface model to solve unconstrained optimization problems, constrained optimization problems, mixed integer optimization problems as well as multi-objective optimization problems. The main contents can be summarized as follows:(1) Analyze the characteristics of several commonly used response surface model and propose AMGO (Adaptive Metamodel -based Global Optimization) algorithm. The proposed method take uses of hybrid response surface model in the optimization process to approximate simulation model in order to combine the features of multiple response surface model features and enhance stability of the approximation model.In the AMGO algorithm, a new iteration point selection strategy is adopted to banlance the local search ability and global search ability of algorithm, which makes the iteration points located around the optimum of current RSM and also around the unexplored region. The AMGO method is compared by three representative metamodel based optimization algorithms by numerical tests, and then applied into the inner rotor pump optimization design problem, which effectively enhance the flow characteristics of the rotor pump.(2) Propose response surface model based constrained optimization method (RCGO) for black-box function constrained optimization problem. The proposed method constructs RBF metamodel for black-box objective function and each black-box constraint function rather than simplely deal with the constraint functions by penalty function method. The algorithm is divided into two stages:the first stage is to search an initial feasible solution using existing data when all the initial sampling points are not feasible; the second stage is to search better design point on the basis of existing feasible point. The algorithm does not require the engineer to provide an initial feasible point in the algorithm initially, and can use gradient information of response surface model for black-box objective and constraint functions to perform constraint correct to obtain more feasible point under lower computational overhead.(3) Analyze the advantages of response surface model based optimization method in solving mixed integer optimization problems involving simulation models, then extend the DIRECT method and combine it with RSM method to develop METADIR (METAmodel and DIRect) algorithm. When the iterative search, the proposed method firstly takes use of DIRECT method to constantly subdivide the design space and identify the sub-region that may contain the optimal value. When iterative points gather into a sub-region to some extent, we terminate the search progress of DIRECT and turn to the next stage. In the second phase, a local metamodel is constructed in this potential optimal sub-region, and then an auxiliary optimization problem extended from AMGO is established based on the local metamodel to obtain the iterative points, which are then applied to update the metamodel adaptively.(4) Detailly discuss the prediction error and uncertainty estimates of Kriging metamodel on unsampled point, and combine the Kriging metamodel with particle swarm algorithm to solve the multi-objective optimization problem involving black-box functions. The huge computational overhead is the main challenge in the application of community based optimization methods, such as multi-objective particle swarm optimization and multi-objective genetic algorithm, to deal with the multi-objective optimization involving costly simulations. This paper proposes a Kriging metamodel assisted multi-objective particle swarm optimization method to solve this kind of expensively black-box multi-objective optimization problems. On the basis of crowding distance based multi-objective particle swarm optimization algorithm, the new proposed method constructs Kriging metamodel for each expensive objective function adaptively, and then the non-dominated solutions of the metamodels are utilized to guide the update of particle population. To reduce the computational cost, the generalized expected improvements of each particle predicted by metamodels are presented to determine which particles need to perform actual function evaluations.(5) Take use of Maltab engine technology and MEX application interface to realize the integration of multi-disciplinary platform MDesigner and Matlab, and provide a basic platform for multidisciplinary optimization design. Based on Matlab engine technology and MEX application program interface, the MDesigner platform can directly call the response surface optimization algorithms under Matlab environment. Finally, the optimal design of gear box shows the entire process of response surface optimization under MDesigner platform, which demonstrates the versatility of platform and effectiveness of the approach.Finally, we summarize the study in this paper and make an outlook about the next work and future study. The research hotspot and trends about response surface model based optimization are also discussed.