Method for optimizing multi-objective coordination problem in progressive combination manner

Abstract

The invention discloses a method for optimizing a multi-objective coordination problem in a progressive combination manner. The method specifically comprises the following steps of (1) target decomposition, decomposing the multi-objective coordination problem layer by layer, forming a hierarchical structure for optimizing the problem, and converting the operation of solving the original problem into the operation of solving the lagrangian function relaxation problem by utilization of a lagrangian relaxation method, wherein penalty parameters in a lagrangian relaxation penalty function are updated in the second step; (2) updating the penalty parameters by utilization of an iterative method; (3) checking convergence, stopping and outputting an optimal solution when the number of iterations exceeds a set threshold value or the minimum value obtained in two successive functions is smaller than a given number, otherwise returning to the second step, updating the penalty parameters, and calculating and checking the convergence by utilization of the updated penalty parameters.

Description

technical field [0001] The invention relates to the technical field of electromechanical system design, and discloses a progressive combination optimization method for multi-objective coordination problems. Background technique [0002] At present, there are many problems in engineering problems, such as multi-objective collaborative optimization, and combined optimization problems of mixed variables and their couplings, such as the optimization and solution of complex antenna feeder systems, which belong to this type of problems. Common methods for solving such problems include Smart law and planning law, etc. However, the intelligent method is inefficient, and it is difficult to deal with continuous and combinatorial optimization optimization problems of different nature; while the planning method will produce local optimization, which is only suitable for solving the case of few variables, and it is difficult to deal with global optimization and multivariable problems, so...

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Problems solved by technology

However, the intelligent method is inefficient, and it is difficult to deal with continuous and combinatorial optimization optimization problems of different nature; while the planning method will produce local optimization, which is only suitable for solving the case of few variables, and it is difficult to deal with global optimization and multivariable problems, so there is no suitable solution for this problem. Appropriate methods for complex engineering problems

[0003] The standard collaborative optimization method uses distributed design ideas to reduce the complexity of system design, which has certain effects, but it is easy to fall into local optimum, making it difficult to obtain the optimal solution; in response to this problem, scholars have proposed introducing various improvements measure

There are mainly two kinds of improved numerical method and artificial intelligence method. The collaborative algorithm improved by numerical method can effectively search the local area around the initial design point; for the problem that the design space has the characteristics of continuous and single peak, the improved algorithm can Fast search along the fastest descending direction is also easy to enter the local optimum due to the high requirements on the initial point; while the artificial intelligence method has the advantages of good adaptability and global search, but the efficiency is extremely low

Another disadvantage of the standard collaborative optimization method is that it is only applicable to the solution of two-level problems at the system level and subject level, that is, it is a two-level optimization method, and the decomposition of the problem is very strict, and the analysis model after the decomposition must be at the same level , if the decomposition is unreasonable, the convergence is difficult to guarantee

There is still no very good way to improve this problem

However, complex engineering systems are usually multi-level, so it is difficult for collaborative optimization algorithms to guarantee their definite convergence

[0004] The Lagrange multiplier method is very convenient for solving convex function problems, but it is easy to fail for non-convex problems, and it is difficult to solve large nonlinear optimization problems

The augmented Lange multiplier method has improved it, but it is still only suitable for solving convex programming problems with linear constraints, and it is difficult to determine the penalty function

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