Direct Method For Interval Multi-Objective Optimization And Its Engineering Application

In practical engineering multi-objective optimization problems,there may be uncertain parameters in the geometric characteristics,material characteristics,boundary conditions,etc.of the engineering structure,so the optimization problem that needs to be solved may be an uncertainty optimization problem.The main methods for solving uncertain optimization problems are stochastic programming,fuzzy programming and interval optimization methods.Among them,the interval optimization method only needs to know the upper and lower boundaries of the uncertainty parameters to solve the problem,so it has been widely used in engineering.When using the interval optimization method to solve the uncertainty problem,the interval optimization problem is usually converted first by interval programming,and then the converted problem is solved by the existing optimization algorithms.For uncertain multi-objective optimization problems,it is necessary to use the midpoint,radius or a combination of midpoint and radius of the objective functions intervals as the approximate values of the optimization objectives.The problem solved in this way is a converted problem,and its solutions efficiency and accuracy are limited by the effectiveness of the interval conversion model used.There is also a method that does not need to transform the original problem,using the multi-objective evolutionary algorithm as the framework,redefining the interval non-dominated relationship to compare different solutions,and solving the problem directly.This type of method has not yet considered the problem of uncertain parameters in the constraint functions,which limits the application of this type of method in practical engineering problemsIn view of the above problems,this paper studies the direct method for interval multi-objective optimization based on micro-genetic algorithm to efficiently solve uncertain multi-objective optimization problems,and realizes its application in practical engineering problems.First,under the framework of micro-multi-objective genetic algorithm,the original non-dominated sorting and individual crowding distance are sorted by interval numbers,and the interval non-dominated sorting and individual general crowding distance are extended to achieve individual comparison and selection.A direct method for interval multi-objective optimization based on micro-genetic algorithm is obtained,and its solution efficiency is verified by the test functions;Then,the designer's known information on the problem is added to the optimization process through the set preference indicators,and the research is based on set preference interval multi-objective optimization direct method,the solution performance of this method is also verified by the test functions;Then,the two algorithms studied are applied to the multi-objective optimization of the ten-bar truss structure and the collision resistance of the composite tube multi-objective optimization problem and multi-objective optimization problem of automobile body structure crashworthiness,its ability to solve practical engineering problems is verified;Finally,in order to make the researched multi-objective optimization direct method more convenient to apply to practical engineering problems,this paper based on the researched algorithm,an interval multi-objective optimization design algorithm software package was developed.The software is easy to operate,and engineers only need to enter the parameters of the question to get the results.