Lagrange function based least-squares multi-objective optimization method

A multi-objective optimization and least squares technology, applied in complex mathematical operations, biological neural network models, etc.

Inactive Publication Date: 2012-09-12
高俊文 +1
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0005] However, due to the large number of inversion operations in the a...

Method used

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  • Lagrange function based least-squares multi-objective optimization method
  • Lagrange function based least-squares multi-objective optimization method
  • Lagrange function based least-squares multi-objective optimization method

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Embodiment

[0053] This embodiment studies the essence of solving multi-objective optimization parameters is to regard the weight coefficient in the evaluation function as a variable parameter, and then proposes a neural network based on the Lagrange function, using the calculation of the optimal weight coefficient under the condition of the least squares criterion , give appropriate parameters according to actual needs, and obtain a satisfactory and stable effective solution.

[0054] Existing model optimization methods for multi-objective optimization:

[0055] In objective optimization, record m vector objective functions as

[0056] f(x)=(f 1 (x), f 2 (x),...,f m (x)) (1)

[0057] The constraint set is denoted as

[0058] D={x: x ∈ R n , g i (x)≥0, i=1, 2, ..., p; h j (x)=1, j=1, 2, ..., q} (2)

[0059] Then the formulation of the problem is to solve

[0060] min x ∈ D f ...

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Abstract

The invention discloses a Lagrange function based least-squares multi-objective optimization method which includes the steps of step 1, converting multi-objective programming into single-objective programming; step 2, fitting established models to obtain a fitting error; step 3, obtaining an optimal solution model; step 4, interposing a weighted factor beta into a target function Q(n); step 5, obtaining an extended function; step 6, removing non-negative weights from the optimal solution model; and step 7, calculating an optimal weighting coefficient by least-squares criterion. By the method, a system can evolve to the equilibrium state no matter how the initial state of the system is, a neural network can converge a variable into a unique global optimal solution no matter how an initial value of an optimized variable is.

Description

technical field [0001] The invention relates to the field of objective optimization calculation, in particular to a least-squares criterion multi-objective optimization method based on Lagrange function. Background technique [0002] When solving practical problems, in order to achieve satisfactory results, people always choose the best solution from many alternative solutions according to a certain standard. When there is only one target in the considered problem as the criterion for judging the pros and cons, this is the usual single solution. However, in order to better solve practical problems, it is more and more necessary to consider the optimization problem of multiple objectives at the same time, that is, the multi-objective optimization problem. The key to solving the multi-objective optimization problem lies in the determination of the objective weights. Multi-objective optimization methods can be widely used in optimization computing, pattern recognition, array s...

Claims

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Application Information

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IPC IPC(8): G06F17/10G06N3/02
Inventor 高俊文刘建成
Owner 高俊文
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