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Nonlinear interval uncertainty optimization method based on affine algorithm

A technology of uncertainty and optimization method, applied in the fields of genetic laws, genetic models, complex mathematical operations, etc., can solve problems such as low processing efficiency, inappropriate multi-objective multi-constraint complex optimization, etc., to achieve the effect of improving computational efficiency

Pending Publication Date: 2019-09-27
NANJING UNIV OF SCI & TECH
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Problems solved by technology

However, for each set of design variables generated by the external optimizer, the internal optimizer has to perform two deterministic optimization processes, which has extremely low processing efficiency and is not suitable for complex optimization problems with multiple objectives and constraints.

Method used

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  • Nonlinear interval uncertainty optimization method based on affine algorithm
  • Nonlinear interval uncertainty optimization method based on affine algorithm
  • Nonlinear interval uncertainty optimization method based on affine algorithm

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Embodiment

[0033] In order to verify the scheme of the present invention, the following nonlinear interval uncertainty optimization example is solved.

[0034] The optimization problem of this example is:

[0035]

[0036] Step 1: Order

[0037] Step 2: Calculate the affine type of the objective function and constraints:

[0038] Compute the affine quantities in the objective function:

[0039]

[0040] Because ε 1 ,ε 3 ∈[-1,1], so ε 1 2 ,ε 3 2 ∈[0,1], so the Δu in the above formula 1 2 ε 1 2 with Δu 3 2 ε 3 2 rewritten as:

[0041]

[0042] where ε 1 * ,ε 3 * ∈[-1,1] is a new noise symbol.

[0043] Then the objective function f(X,U) can be rewritten as:

[0044]

[0045] The interval in which the objective function can be obtained is:

[0046]

[0047] Compute the affine quantities in constraints:

[0048]

[0049] Because ε 2 ∈[-1,1], so ε 2 2 ∈[0,1], so the Δu in the above formula 2 2 ε 2 2 rewritten as:

[0050]

[0051] where ε ...

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Abstract

The invention discloses a nonlinear interval uncertainty optimization method based on an affine algorithm. The nonlinear interval uncertainty optimization method comprises the following steps: converting an interval uncertainty quantity into an affine type uncertainty quantity; processing the nonlinear objective function and constraint by using an affine algorithm to obtain an interval of the objective function and constraint at a design variable; converting the non-linear interval uncertainty optimization problem into a single-layer deterministic optimization problem; and adopting a genetic algorithm to solve the optimization problem. According to the method, the nonlinear interval uncertainty optimization problem can be converted into a single-layer certainty optimization problem, and the solving efficiency is improved.

Description

technical field [0001] The invention relates to the field of uncertainty optimization, in particular to an affine algorithm-based nonlinear interval uncertainty optimization method. Background technique [0002] The interval programming method has been widely used in uncertain optimization because it only needs upper and lower bounds of uncertain parameters and does not need other information. At present, two-layer nested optimization methods are often used for interval uncertain optimization problems, in which the outer layer optimization is used to optimize the design vector, and the inner layer optimization is used to calculate the interval of uncertain objective functions and constraints. For example, in the paper "Anonlinear interval number programming method for uncertainty optimization problems.European Journal of Operational Research", Jiang Chao et al. proposed a two-layer nested interval optimization method based on the interval sequence and interval possibility mo...

Claims

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Application Information

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IPC IPC(8): G06F17/17G06N3/12
CPCG06F17/17G06N3/126
Inventor 徐凤杰杨国来范雨萌李雷
Owner NANJING UNIV OF SCI & TECH
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