Batch reactor optimal control method based on single population and pre-crossed differential evolution algorithm

A differential evolution algorithm and optimal control technology, applied in the direction of adaptive control, general control system, control/regulation system, etc., can solve the problems of slow convergence speed, complex operation, poor search ability, etc., to achieve fast convergence speed, easy operation Simple, the effect of improving the convergence speed

Inactive Publication Date: 2009-06-24
ZHEJIANG UNIV OF TECH
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Problems solved by technology

[0014] In order to overcome the disadvantages of complex operation, slow convergence speed, and poor search ability of the existing optimal control method for batch reactors, the present invention p

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  • Batch reactor optimal control method based on single population and pre-crossed differential evolution algorithm
  • Batch reactor optimal control method based on single population and pre-crossed differential evolution algorithm
  • Batch reactor optimal control method based on single population and pre-crossed differential evolution algorithm

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example 1

[0049] Example 1: The dynamic optimization problem of a batch reactor belongs to the category of continuous optimization problems in the chemical industry. This type of problem is characterized by a set of differential equations with multiple local optimal solutions and global optimal solutions. Solving this type of problem is challenging sex.

[0050] Consider the following reaction process:

[0051] dx 1 dt = - ( k 1 + k 2 + k 3 ) x 1

[0052] dx 2 dt = k 1 x 1 - k ...

example 2

[0064] Example 2: The optimization algorithm proposed by the present invention is applied to the following batch reactor optimal control problem, and the reaction process is A → k 1 B → k 2 C , Described by the following system of differential equations:

[0065] dx 1 dt = - k 1 x 1 2

[0066] dx 2 dt = k 1 x 1 2 - k 2 x 2

[0067] where x 1 with x 2 Respectively reactan...

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Abstract

An optimal control method for a batch reactor of a differential evolution algorithm based on a single population and pre-crossover comprises the following steps: 1), an evolutional generation g is caused to be equal to 1, and an individual number i is caused to be equal to 1, and a parameter is initialized; 2), the population is initialized; 3) the highest fitness and the lowest individual fitness in S1 are respectively fmax and fmin; if |fmax minus fmin| is smaller than or equal to an eps, then the algorithm is stopped, and a final result is output; if not, g is caused to be equal to g plus 1, and i is caused to be equal to 1; whether an evolutional generation is maximized or not is judged; and if yes, the algorithm is stopped and a change curve of the yield of a target product is output, and if not, the algorithm is continued; 4) a pre-crossover operation is conducted; 5) i is caused to be equal to i plus 1; if i is equal to a pop, step 3) is returned, and if not, step 4) is returned; and 6), three individuals are selected from S1 at random to conduct an mutation crossover operation, and an acquired experimental individual is yi; if f(yi) is smaller than f(xi), yi is used for replacing xi; and if f(yi) is larger than f(xi) and f(yi) is smaller than f (xi'), yi is used to replace xi', and step 5) is returned. The optimal control method has the advantages of simple operation, high convergence rate and high searching ability.

Description

technical field [0001] The invention relates to an industrial optimization technology, in particular to an optimal control method for a batch reactor. Background technique [0002] Differential Evolution (DE) is a new evolutionary calculation method, which was first proposed by Storn et al. in 1995. At that time, it was conceived to solve the Chebyshev polynomial problem. Later, it was found that DE is also an effective solution to complex optimization problems. technology. DE has a very special relationship with artificial life, especially evolutionary algorithm. Like genetic algorithm and particle swarm algorithm, it is an optimization algorithm based on swarm intelligence theory. The swarm intelligence generated by the cooperation and competition among individuals in the group guides the optimization search . Compared with the evolutionary algorithm, DE retains the population-based global search strategy, adopts real number coding, simple mutation operation based on dif...

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Application Information

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IPC IPC(8): G05B13/04
Inventor 俞立黄骅陈秋霞
Owner ZHEJIANG UNIV OF TECH
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