CN106372270A - Life cycle group search optimization algorithm-based optimization design method for pressure container - Google Patents

Abstract

The invention relates to a life cycle group search optimization algorithm-based optimization design method for a pressure container. The method comprises the following steps of initializing parameters; assessing a fitness value; updating data; performing iteration: if a preset stop condition is not met, returning to the step of assessing the fitness value; and if the iterative stop condition is met, stopping calculation and finally outputting a result. The design method of the invention is easy to realize, has the advantages of relatively good global search capability, high convergence speed, high optimization precision and the like, and has a very effective optimization effect for the problem on the weight of the pressure container.

Description

Pressure container optimization design method based on life cycle group search optimization algorithm

Technical Field

The invention relates to a pressure container optimization design method based on a life cycle group search optimization algorithm, belongs to the field of chemical machinery, and also relates to the field of group intelligent algorithms.

Background

The pressure container is an important component of chemical equipment, and plays a great key role in developing and perfecting chemical raw materials and products. The pressure vessel mainly comprises a thin-wall pressure vessel, a pressure storage tank, an external pressure vessel, a multilayer pressure vessel, a high-pressure vessel, an ultrahigh-pressure vessel and the like. During the production and use of the pressure container, especially when flammable, explosive or corrosive materials are placed in the pressure container, the pressure container is quite dangerous, and the safety problem of the pressure container needs to be paid great attention. On the other hand, the manufacture of pressure vessels consumes a large amount of metal material. Thus, the design and optimization of pressure vessels is of increasing interest.

Aiming at the complex optimization problem of pressure vessel optimization design, if the traditional mathematical programming method is adopted to solve the problem, ideal results cannot be achieved in the two aspects of the solving precision and the solving efficiency of the model. In recent years, the intelligent optimization algorithm based on biological heuristic calculation, which widely simulates biological behaviors, has attracted extensive attention of scholars, obtains better results when being used for solving the problems, and shows the unique advantages of the intelligent optimization algorithm based on biological heuristic calculation in solving the complex optimization problem. However, the optimization of the genetic algorithm and the ant colony algorithm proposed earlier is high in complexity, poor in robustness and high in randomness of obtained results; although the particle swarm optimization is high in optimization speed, the particle swarm optimization is easy to fall into local optimization, and particularly the solving precision of a high-dimensional optimization problem is not high; classical bacterial foraging algorithms focus on the description and simulation of bacterial behavior. When the existing algorithms solve relatively complex optimization problems, the optimization performance of the existing algorithms cannot meet the requirements of satisfactory precision and stability. In order to better solve the problems, by using the biological life cycle theory for reference, the life cycle group search optimization algorithm based on the population normal distribution is invented, the algorithm realizes the self-adaptive search, and has the advantages of strong global search capability, high convergence speed, high optimization precision and the like.

Disclosure of Invention

Aiming at the defects in the prior art, the invention provides the pressure container optimization design method based on the life cycle group search optimization algorithm by using the biological life cycle theory for reference, realizes self-adaptive search, and has the advantages of strong global search capability, high convergence speed, high optimization precision and the like.

The technical scheme adopted by the invention for realizing the purpose is as follows: a pressure container optimization design method based on a life cycle group search optimization algorithm comprises the following steps:

initializing parameters;

evaluating the fitness value;

updating data;

iteration: if the preset termination condition is not reached, returning to the step of evaluating the fitness value; and if the iteration termination condition is reached, stopping the calculation, and finally outputting the result.

The parameter initialization comprises: initializing the population scale; initializing upper and lower limits of a search space, maximum iteration times and convergence precision; initializing foraging mode selection probability, cross probability and mutation probability; initializing a chaotic variable, a normal distribution mean and a normal distribution standard deviation.

The calculation method for evaluating the fitness value comprises the following steps:

and updating the global extremum: the optimal individual p in the initial population_gSetting the initial extreme value as a global initial extreme value;

according to the design standard of the pressure container: under the same environment, the fitness evaluation standard of the population is established by taking the criterion that the smaller the weight of the pressure container is, the more the population is.

The data update comprises the following steps:

executing growth and development operation: the optimal individual in the group executes the chaotic chemotaxis operation, and other individuals select the probability to execute the assimilation operation or the transposition operation according to the foraging mode;

and (3) executing reproduction operation: pairing individuals in the group in sequence in pairs, and executing single-point cross operation;

and (3) executing death operation: linearly arranging the individuals in the group according to the adaptive value, adjusting the adaptive value, and selecting the individuals by adopting a roulette method;

performing mutation operation: the individuals in the group perform a direction mutation operation;

and updating the global extremum: and calculating the fitness of all individuals in the current group, and setting the optimal individual in the current group.

The invention has the following advantages and beneficial effects: the design is easy to realize, the method has the advantages of strong global search capability, high convergence rate, high optimization precision and the like, and has a very effective optimization effect on the weight problem of the pressure vessel.

Drawings

FIG. 1 is a flow chart of the execution of a lifecycle group search optimization algorithm;

FIG. 2 is a view of the pressure vessel;

FIG. 3 is a graph comparing the convergence curves of pressure vessel designs.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and examples.

The common engineering hemispherical head pressure vessel has a simple design, as shown in fig. 1, and is widely applied to industries such as petroleum and chemistry. On the premise of meeting the requirements of strength and the like, the weight of the pressure container is taken as an objective function. The problem has 4 constraints and 4 optimization variables.

An objective function: $f\left(X\right)=0.6224X_1{X}_3{X}_4+1.7781X_2{X}_3^2+3.1661X_1^2{X}_4+19.84X_1^2{X}_3$

constraint conditions are as follows: g₁(X)＝0.0193X₃-X₁≤0

g₂(X)＝0.00954X₃-X₂≤0

$g_3\left(X\right)=1,296,000-{\mathrm{\πX}}_3^2{X}_4-4/3{\mathrm{\πX}}_3^3\≤0$

g₄(X)＝X₄-240≤0

Wherein, X₁And X₂Respectively comprises a seal head (Th) and a cylinder wall thickness (Ts), and X is more than or equal to 0.0625₁，X₂≤6.1875；X₃Is the radius (R, X) of the bottom surface of the cylinder body and the end socket₄The length (L) of the cylinder is more than or equal to 10 and less than or equal to X₃，X₄Less than or equal to 200. Of 4 variables, X₁And X₂Is a uniform discrete variable, X, with an interval of 0.0625₃And X₄Is a continuous variable.

Aiming at the defects that the traditional mathematical programming method is exposed when solving the large-scale and multidimensional complex optimization problem of pressure vessel optimization design and the optimization performance of the traditional intelligent optimization algorithm can not meet the requirements of satisfactory precision and stability, the invention provides the pressure vessel optimization design method of the intelligent optimization algorithm based on the population normal distribution by using the biological life cycle theory.

The invention is used for designing the minimum weight of the pressure container on the premise of meeting the requirements of strength and the like, and comprises the following steps:

1) parameter initialization

Design X according to pressure vessel design criteria₁And X₂Respectively comprises a seal head (Th) and a cylinder wall thickness (Ts), and X is more than or equal to 0.0625₁，X₂≤6.1875；X₃Is the radius (R, X) of the bottom surface of the cylinder body and the end socket₄The length (L) of the cylinder is more than or equal to 10 and less than or equal to X₃，X₄Less than or equal to 200. Of 4 variables, X₁And X₂Is a uniform discrete variable, X, with an interval of 0.0625₃And X₄Is a continuous variable. Then, determining the initial population scale according to the decision variable range, and generally selecting 50-100, generating an initial population with the population size of and satisfying the normal distribution; initializing upper and lower limits of a search space, maximum iteration times and convergence precision; initializing foraging mode selection probability, cross probability and mutation probability; initializing a chaotic variable, a normal distribution mean and a normal distribution standard deviation. Some of the parameters involved in the algorithm may be determined by a pressure vessel weight objective function.

2) Evaluating fitness value

The common engineering hemispherical head pressure vessel has a simple design, as shown in fig. 1, and is widely applied to industries such as petroleum and chemistry. On the premise of meeting the requirements of strength and the like, the weight of the pressure container is taken as an objective function. The problem has 4 constraints and 4 optimization variables.

An objective function: $f\left(X\right)=0.6224X_1{X}_3{X}_4+1.7781X_2{X}_3^2+3.1661X_1^2{X}_4+19.84X_1^2{X}_3$

constraint conditions are as follows: g₁(X)＝0.0193X₃-X₁≤0

g₂(X)＝0.00954X₃-X₂≤0

$g_3\left(X\right)=1,296,000-{\mathrm{\πX}}_3^2{X}_4-4/3{\mathrm{\πX}}_3^3\≤0$

g₄(X)＝X₄-240≤0

Wherein, X₁And X₂Respectively comprises a seal head (Th) and a cylinder wall thickness (Ts), and X is more than or equal to 0.0625₁，X₂≤6.1875；X₃Is the radius (R, X) of the bottom surface of the cylinder body and the end socket₄The length (L) of the cylinder is more than or equal to 10 and less than or equal to X₃，X₄Less than or equal to 200. Of 4 variables, X₁And X₂Is a uniform discrete variable, X, with an interval of 0.0625₃And X₄Is a continuous variable.

Aiming at the design optimization problem of the pressure container with the constraint, the constraint condition can be converted into a fitness value by using a method of an adaptive penalty function. Criteria are then formulated that define a weight that is less or more optimal. And updating the global extremum. And setting the optimal individuals in the initial population as global initial extreme values.

3) Data update

Executing growth and development operation: the optimal individual in the group executes the chaotic chemotaxis operation, and other individuals select the probability to execute the assimilation operation or the transposition operation according to the foraging mode; and (3) executing reproduction operation: pairing individuals in the group in sequence in pairs, and executing single-point cross operation; and (3) executing death operation: linearly arranging the individuals in the group according to the adaptive value, adjusting the adaptive value, and selecting the individuals by adopting a roulette method; performing mutation operation: the individuals in the group perform a direction mutation operation; and updating the global extreme value, calculating the fitness of all individuals in the current group, and setting the optimal individuals in the current group.

4) Iteration

And if the preset termination condition is not reached, returning to the step 2), if the iteration termination condition is reached, stopping the calculation, and finally outputting the result.

The algorithm implementation steps are shown in fig. 2.

The step 1) specifically comprises the following steps:

1.1) determining the initial population scale n, generally selecting 50-100 initial populations, and generating the initial population with the population scale of normal distribution; with a variable dimension of 4, decision variable X₁And X₂Is a uniform discrete variable, X, with an interval of 0.0625₃And X₄Is a continuous variable.

1.2) initializing search space Upper and lower bounds B_upAnd B_loMaximum number of iterations T_maxConvergence accuracy ξ, initial foraging mode selection probability P_fCross probability P_cAnd the mutation probability P_m(ii) a Initializing a chaotic variable Sc, a normal distribution mean mu and a normal distribution standard deviation sigma.

The step 2) specifically comprises the following steps:

2.1) updating the global extremum. The optimal individual p in the initial population_gSet to the global initial extremum.

2.2) according to the design standard of the pressure container, under the same environment, the smaller the weight of the pressure container, the more the fitness evaluation standard of the population is established as a criterion.

The step 3) specifically comprises the following steps:

3.1) growth and development

The optimal individual in the population performs chaotic chemotaxis operations. The chemotaxis rule adopts a chaotic search mode based on the current position to try to find a position which is better than the current position in a global scope and move. The Logistic equation is a typical chaotic system:

S_n+1＝uS_n(1-S_n),n＝0,1,2,...

wherein u is a control parameter, when u is 4, S is more than or equal to 0₀When the dynamic characteristic of the system is less than or equal to 1, the dynamic characteristic of the system is completely different, and the initial information of the system is completely lost and is in a chaotic state. From an arbitrary initial value S₀∈[0,1]A determined chaotic sequence S can be iterated₁，S₂，S₃…. This output is effectively equivalent to a random output between 0 and 1. The output of the system has ergodicity between 0 and 1, and any state of the system can not repeatedly appear.

And introducing a chaotic variable generated by Logistic mapping into an optimized variable by adopting an optimal individual foraging strategy in the group by adopting a carrier wave-like method, simultaneously converting a traversal range of chaotic motion into a domain of the optimized variable, and then searching by utilizing the chaotic variable. The method comprises the following implementation steps:

step 1: the current optimization variable is marked as X₀Its performance function value f (X)₀)。

Step 2: generating n chaotic variables (X) using Logistic mapping₁,X₂,…,X_n)

X_i+1＝4X_i(1-X_i),i＝0,1,2,...,n-1

And step 3: and converting the traversal range of the chaotic motion into the domain of the optimization variable.

X_i＝B_lo+(B_up-B_lo)X_i,i＝1,2,...,n

Wherein, B_upAnd B_loAre the upper and lower bounds of the search space.

And 4, step 4: and calculating the performance function values of the n chaotic variables. (f (X)₁),f(X₂),…,f(X_n))

And 5: if f (X) is present_i) Is superior to f (X)₀) Then, then

$X_0\⇐X_i,f\left(X_0\right)\⇐f\left(X_i\right)$

And other individuals select to execute assimilation operation or transposition operation according to the foraging mode selection probability.

The foraging paths of the individuals in the group adopting the social foraging mode are assimilated by the optimal individuals and are searched along with the optimal individuals in the group.

$X_i^{k+1}=X_i^k+rand\left(\right)(X_p^k-X_i^k)$

The above equation represents the position of the ith individual at the kth iterationTracking the current optimal individual within the groupSearching is carried out; r is₁∈RⁿAre random numbers uniformly distributed between (0, 1).

Except the optimal individuals in the group, the foraging execution method of the individuals adopting the independent foraging mode adopts a transposition rule, and the individuals search in the energy range of the individuals.

${\mathrm{ub}}_i^k=\frac{X_p^k}{X_i^k}\·\mathrm{\Δ}$

${\mathrm{lb}}_i^k=-{\mathrm{ub}}_i^k$

Wherein,is an individualStep of transpositionLength; r is₂∈RⁿAre random numbers uniformly distributed between (0, 1);andindividual i searches for the maximum range in the k generation; Δ is the entire search space range.

3.2) propagation

And pairing the individuals in the group in sequence in pairs, and executing single-point crossing operation.

$X_i^{k+1}\[m:p\]=X_j^k\[m:p\]$

$X_j^{k+1}\[m:p\]=X_i^k\[m:p\]$

Where m and p represent the indices of the beginning and end of the gene segment, respectively.

3.3) death

The selection rule firstly adopts a linear sorting method to adjust the individual adaptive values in the group, carries out descending sorting on the adjusted objective function values, and then adopts a roulette selection strategy to execute individual selection operation.

$f^{*}\left(x_i\right)=2-sp+2\×(sp-1)\×\frac{p\left(x_i\right)-1}{S-1}$

Wherein f is^*(x_i) (i ═ 1,2, … S) is the fitness of the adjusted individual; s is the number of individuals in the population; sp is a selected pressure difference, sp-2; p (x)_i) Is the fitness value f (x) of the individual i_i) The ranking position in the population.

3.4) variation

Individuals in the group perform a directional mutation operation. In the n-dimensional search space, each individual X_i∈Rⁿ，X_i＝(x_i1,x_i2,…,x_in) Is a value x representing a direction of movement of j (1, 2, …, n) in each dimension_ijThen the step size of the movement of the individual in this direction is indicated. Directional variability refers to random changes in the step size of an individual's movements in their selected direction.

$X_i^{k+1}\left(j\right)=rand\left(\right)(B_{up}-B_{lo})+B_{lo}$

3.5) updating the global extremum

Calculating the fitness f (X) of all individuals in the current group, and setting the optimal individual in the current group as X_g。

The step 4) specifically comprises the following steps:

4.1) judging whether to terminate: according to a preset iteration termination condition, generally presetting convergence precision or reaching the maximum function evaluation times; if the termination condition is met, terminating the iteration; otherwise, the steps are continuously repeated until the termination condition is met;

4.2) finishing the optimization, and outputting the final optimization result of each variable parameter and the final optimization value of the weight of the pressure container, as shown in figure 3.

Claims (4)

1. A pressure container optimization design method based on a life cycle group search optimization algorithm is characterized by comprising the following steps:

initializing parameters;

evaluating the fitness value;

updating data;

iteration: if the preset termination condition is not reached, returning to the step of evaluating the fitness value; and if the iteration termination condition is reached, stopping the calculation, and finally outputting the result.

2. The method of claim 1, wherein the initializing parameters comprises: initializing the population scale; initializing upper and lower limits of a search space, maximum iteration times and convergence precision; initializing foraging mode selection probability, cross probability and mutation probability; initializing a chaotic variable, a normal distribution mean and a normal distribution standard deviation.

3. The pressure vessel optimization design method based on the life cycle group search optimization algorithm as claimed in claim 1, wherein the calculation method for the evaluation fitness value is as follows:

and updating the global extremum: the optimal individual p in the initial population_gSetting the initial extreme value as a global initial extreme value;

according to the design standard of the pressure container: under the same environment, the fitness evaluation standard of the population is established by taking the criterion that the smaller the weight of the pressure container is, the more the population is.

4. The method for optimally designing a pressure vessel based on the life cycle group search optimization algorithm as claimed in claim 1, wherein the data updating comprises the following steps:

executing growth and development operation: the optimal individual in the group executes the chaotic chemotaxis operation, and other individuals select the probability to execute the assimilation operation or the transposition operation according to the foraging mode;

and (3) executing reproduction operation: pairing individuals in the group in sequence in pairs, and executing single-point cross operation;

and (3) executing death operation: linearly arranging the individuals in the group according to the adaptive value, adjusting the adaptive value, and selecting the individuals by adopting a roulette method;

performing mutation operation: the individuals in the group perform a direction mutation operation;

and updating the global extremum: and calculating the fitness of all individuals in the current group, and setting the optimal individual in the current group.