Research On Adding Point Criterion In Adaptive Surrogate Model

The surrogate model replaces the complex primitive function to reduce the computational load is a common means in optimization problems.Compared with the static surrogate model,the adaptive surrogate model has obvious advantages,and the key technology of the adaptive surrogate model is the rule of adding points.Based on the research of relevant scholars at home and abroad and Kriging surrogate model,this paper studies the point adding rule,parallel point adding strategy and swarm intelligence algorithm technology in surrogate model.The main research content includes:(1)A four stage method,which can effectively balance global search and local search,has been proposed.In the adaptive surrogate model,how to use fewer sampling points to achieve higher efficiency is the key to the point adding criterion.The addition criterion should not only ensure that the iterative process does not fall into a local optimal solution,but also ensure the accuracy of the optimal solution.However,in optimization problems,these two objectives have a contradiction between global search and local search in the addition strategy.To address this contradiction,this paper proposes an addition method that divides the entire iteration process into four stages.In the four stage method,the first stage fits the original function as a whole,the second stage judges the region where the global optimal solution is located,the third stage quickly improves the accuracy of the optimal solution,and the fourth stage slowly improves the accuracy of the optimal solution.The first and second stages avoid the iterative process getting stuck in local optimization by reducing the uncertainty near multiple best samples in the sample points;In the third and fourth stages,the accuracy of the optimal solution is improved by whether to use the information of the surrogate model,so as to ensure that the accuracy of the global optimal solution is improved as much as possible without falling into the local optimal solution.The final example shows that the four stage method has better ability to avoid falling into local optima and better optimal solution accuracy.(2)The four stage method and MSG criterion have been extended,and three parallel addition strategies have been proposed.In the single point addition criterion,even if simulation resources are sufficient,the next addition based on information must wait for the results of the previous simulation.The addition efficiency is relatively low,so the parallel addition strategy has been developed.After summarizing the common conversion methods from single point addition to parallel addition,this article expands the four stage method to parallel addition.At the same time,an improved MSG criterion IMSGT-Ⅰ criterion in parallel environment is proposed based on the addition purpose of the MSG criterion,and an improved MSG criterion IMSGT Ⅱ criterion in parallel environment is proposed based on the addition method of the MSG criterion.Finally,the three point adding methods mentioned above are compared with the q-EI criterion for example testing.The q-EI criterion uses intelligent algorithms to obtain numerical solutions,and the comparison of examples proves that each of the three methods proposed in this paper has its advantages.(3)The particle swarm optimization algorithm is improved,and the IPSOFO optimization algorithm that is more suitable for the surrogate model is proposed.Whether the sample points found in the surrogate model according to the point adding criteria are accurate enough will directly affect whether the efficiency of the point adding criteria is fully exerted.Because the surrogate model is easy to obtain the predicted value,this technology is mainly solved by swarm intelligence algorithm.After summarizing the common improvement strategies of particle swarm optimization algorithm,this paper introduces the idea of four stage method into particle swarm optimization algorithm and improves the particle swarm optimization algorithm,proposes FSPSO algorithm,and then improves the FSPSO algorithm to make it more suitable for surrogate model,proposes IPSOFO algorithm.Finally,some numerical examples were used to compare it with common population intelligence algorithms,proving that the improved particle swarm optimization algorithm in this paper has higher efficiency and accuracy in optimization.