CN101872374A - Method for optimizing beer production formula - Google Patents

Method for optimizing beer production formula Download PDF

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CN101872374A
CN101872374A CN 201010180631 CN201010180631A CN101872374A CN 101872374 A CN101872374 A CN 101872374A CN 201010180631 CN201010180631 CN 201010180631 CN 201010180631 A CN201010180631 A CN 201010180631A CN 101872374 A CN101872374 A CN 101872374A
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CN101872374B (en
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葛铭
郑松
魏江
郑小青
李春富
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Hangzhou Kuntian Automation System Co ltd
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Hangzhou Dianzi University
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Abstract

The invention relates to a method for optimizing a beer production formula. A conventional production formula is determined by a method which combines human experience and tests. The method comprises the following steps of: obtaining main raw materials in a beer formula; establishing a comprehensive production performance index estimation model according to the parameters of the raw materials, wherein main considered comprehensive performance indexes comprise saccharifying power, wort total nitrogen, wort alpha amino nitrogen, wort beta glucan and the thickness of a distilled grain layer of a filter tank; and optimizing a beer formula model by using a variable-metric ant colony optimization method and finally obtaining a production formula with the lowest cost. The method of the invention has the advantages of openness, robustness, parallelism and global convergence.

Description

Beer production formula optimization method
Technical Field
The invention belongs to the technical field of information and control, relates to an automation technology, and particularly relates to a beer production formula optimization method.
Background
The optimization design problem of the raw material formula is an important research content in the fields of chemical industry, food, materials and the like. In order to obtain a formula which has excellent performance and can meet the use requirement, the use amount proportion relation of various raw materials is determined by testing, optimizing, identifying and reasonably selecting the raw materials according to the performance requirement and the process condition of a product. In recent years, research on application of formula optimization design is active, and for such a complex multi-target formula system, a test design method is mostly adopted at present. The formulation design of beer enterprises is no exception, and in order to make the style of the beer consistent, the malt enters the factory, the approximate calculation of raw material components is carried out through analysis, the batching scheme is determined, and then the batching production test scheme is finally determined through small saccharification inspection and verification. And finally, the product ingredients are ordered through production verification and modification.
In the production process of beer, the formula of the beer raw materials determines important indexes of the product such as flavor, quality, cost and the like. At present, the production formula of beer production enterprises is still determined by manual experience and a test method, and although the basic requirements of the process can be met, the index parameters such as the total cost of raw materials, taste and the like are easy to be high. Therefore, the optimization of the beer formula has important significance for improving the production efficiency of enterprises and reducing the product cost. The optimization of the beer formula is a formula optimization problem containing multiple extreme points. So far, the formulation optimization problem mostly adopts common traditional mathematical optimization methods, such as a simplex method, a conjugate gradient method, a geometric mean analysis method, an orthogonal design method and the like. Since these optimization methods lack robustness of global optimal search and most of the conventional optimizations require gradient information, it is difficult to solve such an optimization problem with a complex mathematical form.
Disclosure of Invention
The invention aims to provide a formula optimization method with strong global optimization capability aiming at some problems in beer formula optimization.
The technical scheme of the invention is to convert a continuous formula optimization problem into a discrete combined optimization problem, then adopt a bionic ant colony algorithm and adopt a variable-scale method to improve the algorithm optimization performance, shorten the calculation time and finally establish a beer production formula optimization method.
The method comprises the following specific steps:
step 1, obtaining parameters such as the yield, alpha amino nitrogen, saccharifying power, total soluble nitrogen, beta glucan, unit price and the like of main raw materials (including barley malt, special malt, wheat malt, auxiliary raw materials and the like) in a beer formula, wherein the data can be obtained by suppliers or statistics in the production process;
and 2, establishing a comprehensive production performance index estimation model according to the parameters of the raw materials, wherein the main comprehensive performance indexes considered are malt saccharification capacity, wort total nitrogen, wort alpha-amino nitrogen, wort beta-glucan and the thickness of a filter tank grain layer.
Malt saccharification ability
Under normal saccharification operation (30-45 min at 65-68 ℃), each kilogram of mixed raw materials should contain 1500-2000 WK of saccharification force. The upper limit value can shorten the refining time and obtain the wort with higher fermentation degree; the lower limit value of saccharification time is long, and the fermentation degree is low. If the weight is less than 1500WK, the saccharification operation is influenced, the utilization rate of raw materials is influenced, and the composition of wort is influenced. And the total soluble nitrogen of the malt can be estimated according to the following formula:
Figure GSA00000134752600021
in the formula, Ti、XiRespectively representing the saccharifying power intensity and mass fraction of the component i, wherein i is more than or equal to 1 and less than or equal to n;
② total nitrogen of wort
The total soluble nitrogen level of a typical beer wort is:
900-1200 mg/L whole malt wort
Adding 700-850 mg/L of concentrated alcohol beer wort as auxiliary material
550-700 mg/L of light beer wort added with auxiliary materials
Also, the total soluble nitrogen of wort can be estimated as follows:
Figure GSA00000134752600022
in the formula,
Figure GSA00000134752600023
is the total nitrogen mass concentration of component i; A. v is the total mass of raw materials required by a batch and the required wort yield, and the unit is kilogram and liter respectively; gamma, gamma,
Figure GSA00000134752600024
The protein decomposition strength and the boiling nitrogen precipitation rate are respectively.
③ wort alpha amino nitrogen
The alpha amino nitrogen of the wort is related to the flavor substances of the beer, namely high-grade alcohol and diacetyl, and the control of the concentration of the alpha amino nitrogen of the wort is particularly important for controlling the flavor of the beer. Generally, the alpha amino nitrogen of the wort is preferably controlled within the range of 160-180 mg/L. And the alpha amino nitrogen content of the wort can be estimated by the following formula:
in the formula,
Figure GSA00000134752600026
is the mass concentration of alpha amino nitrogen of component i, and kappa is the amino nitrogen coefficient.
Fourthly, the wheat juice beta glucan
The beer containing a proper amount of beta glucan is one of the substances for keeping the mellow feeling of the beer, but if the beta glucan is too much, the decomposition of the beta glucan in the malt is insufficient, and a series of related problems are brought about in the beer brewing process. Therefore, the content of beta glucan in the malting process is lower than 250 mg/L. And the wort beta glucan content can be estimated by the following formula:
Figure GSA00000134752600031
in the formula,is the beta glucan mass concentration of the component i, and nu is the glucan coefficient.
Fifth thickness of the groove layer of the filter tank
During mashing, the insoluble spent grain contained in the mash will form a layer of grains. The thickness of the grains is too thick, the filtration speed of the wort is slow, and the filtration time is prolonged; the thickness of the layer is too thin, which, although increasing the filtration rate, reduces the clarity of the wort. The thickness of the grain layer in the production is generally controlled to be 30-50 cm. And the thickness of the tank can be estimated by the following formula:
Figure GSA00000134752600033
wherein D is the diameter of the filter tank equipment,
Figure GSA00000134752600034
the yield of component i is the cell yield.
And 3, optimizing the beer formula model by using a variable-scale ant colony optimization method, and finally solving the production formula with the lowest cost. The method comprises the following specific steps:
firstly, initializing parameters, dividing each component into N equal parts by mass percentage, and performing discrete interval of each component
Figure GSA00000134752600035
Wherein,
Figure GSA00000134752600036
the upper and lower limits of the mass percentage of the components.
If max (h)1,h2,...,hn) Stopping the algorithm when the epsilon is less than or equal to epsilon, and outputting the current optimal scheme, wherein epsilon represents the ending condition; otherwise, turning to the step 3;
(r, i) is the ith node on the r component, and the numerical value is marked as Xr,i(ii) a (r +1, j) is the jth node on the r +1 component; [ (r, i), (r +1), j)]Is a connecting line from the node (r, i) to the node (r +1, j), the probability that the ant k transfers from the position (r, i) to the position (r +1, j) at the time t during the movement of the ant group with the number m of ants in the ant group is
<math><mrow><msubsup><mi>p</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>k</mi></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msub><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><msub><mi>M</mi><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msub></munderover><msub><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mrow></math>
In the formula: mr+1Is the allowable value range of the r +1 component, and ensures that the sum of the proportions of all varieties is not more than 100 percent. If the r +1 th variety is not the last undetermined variety, Mr+1A value range of
Figure GSA00000134752600038
But for the last breed, Mr+1Can only take values of
Figure GSA00000134752600039
τ[(r,i),(r+1,j)](t) at time t at [ (r, i), (r +1), j]The intensity of pheromone concentration remained on the connecting line is equal to that on each path under the initial condition, i.e. tau[(r,i),(r+1,j)](0) C constant.
Ant k (k 1, 2.. m) is randomly selected according to the probability on each path. In the process of creating the solution, after ants visit the nodes, the pheromones on the paths traveled by the ants are updated by adopting a local pheromone updating rule
<math><mrow><msubsup><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>new</mi></msubsup><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>&rho;</mi><mo>)</mo></mrow><msubsup><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>old</mi></msubsup><mo>+</mo><mi>&rho;</mi><mo>&CenterDot;</mo><mi>&Delta;&tau;</mi></mrow></math>
Where ρ is an information amount attenuation parameter, (0 < ρ < 1), let
Figure GSA00000134752600042
Q is a constant, JnnThe formula cost of the ant obtaining scheme is shown. Each ant is recurred in this way and finally generates a respective formulation.
Fourthly, eliminating the infeasible schemes which do not meet the production indexes by using the index model, calculating formula cost J of the feasible schemes according to the following formula, comparing the formula cost J with the best scheme, and recording the scheme as the best scheme if the formula cost J is less than the formula cost in the best scheme;
Figure GSA00000134752600043
wherein M isiIs the unit price of the starting component i.
Fifthly, when all ants construct a formula scheme, the pheromone is globally updated according to the following formula to obtain the concentration intensity of the pheromone
Figure GSA00000134752600044
Figure GSA00000134752600045
In the formula: j. the design is a squaremin gbThe lowest value of the objective function obtained at the start of the iteration.
Sixthly, updating iteration times t ← t + 1; if t is more than or equal to tmaxTurning to the step 3; otherwise, find the best scheme at present, update xr0、wrWherein w isr=2·hrAnd correcting the upper and lower search limits x according to the following formularupper、xrlowerGo to step 1, where xr0Is the best quality percentage of the r component in the best scheme.
<math><mfenced open='{' close=''><mtable><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><mn>1</mn><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><mn>1</mn><mo>&LeftArrow;</mo><msub><mi>w</mi><mi>r</mi></msub></mtd><mtd><mi>if</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>></mo><mn>1</mn></mtd></mtr><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac></mtd><mtd><mi>if</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>&le;</mo><mn>1</mn><mi>and</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>w</mi><mi>r</mi></msub><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><mn>0</mn></mtd><mtd><mi>if</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>&le;</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math>
Compared with the prior art, the invention has the following beneficial effects: the method has the characteristics of openness, robustness, parallelism, global convergence, no special requirement on the mathematical form of the problem and the like.
Drawings
FIG. 1 is a schematic diagram of the discrete intervals of the components in the process of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
The method comprises the following steps:
step 1, obtaining parameters such as the yield, alpha amino nitrogen, saccharifying power, total soluble nitrogen, beta glucan, unit price and the like of main raw materials (including barley malt, special malt, wheat malt, auxiliary raw materials and the like) in a beer formula, wherein the data can be obtained by suppliers or statistics in the production process;
and 2, establishing a comprehensive production performance index estimation model according to the parameters of the raw materials, wherein the main comprehensive performance indexes considered are malt saccharification capacity, wort total nitrogen, wort alpha-amino nitrogen, wort beta-glucan and the thickness of a filter tank grain layer.
Malt saccharification ability
Under normal saccharification operation (30-45 min at 65-68 ℃), each kilogram of mixed raw materials should contain 1500-2000 WK of saccharification force. The upper limit value can shorten the refining time and obtain the wort with higher fermentation degree; the lower limit value of saccharification time is long, and the fermentation degree is low. If the weight is less than 1500WK, the saccharification operation is influenced, the utilization rate of raw materials is influenced, and the composition of wort is influenced. And the total soluble nitrogen of the malt can be estimated according to the following formula:
in the formula, Ti、XiRespectively representing the saccharifying power intensity and mass fraction of the component i, wherein i is more than or equal to 1 and less than or equal to n;
② total nitrogen of wort
The total soluble nitrogen level of a typical beer wort is:
900-1200 mg/L whole malt wort
Adding 700-850 mg/L of concentrated alcohol beer wort as auxiliary material
550-700 mg/L of light beer wort added with auxiliary materials
Also, the total soluble nitrogen of wort can be estimated as follows:
Figure GSA00000134752600052
in the formula,
Figure GSA00000134752600053
is the total nitrogen mass concentration of component i; A. v is the total mass of raw materials required by a batch and the required wort yield, and the unit is kilogram and liter respectively; gamma, gamma,
Figure GSA00000134752600054
The protein decomposition strength and the boiling nitrogen precipitation rate are respectively.
③ wort alpha amino nitrogen
The alpha amino nitrogen of the wort is related to the flavor substances of the beer, namely high-grade alcohol and diacetyl, and the control of the concentration of the alpha amino nitrogen of the wort is particularly important for controlling the flavor of the beer. Generally, the alpha amino nitrogen of the wort is preferably controlled within the range of 160-180 mg/L. And the alpha amino nitrogen content of the wort can be estimated by the following formula:
Figure GSA00000134752600055
in the formula,
Figure GSA00000134752600056
is the mass concentration of alpha amino nitrogen of component i, and kappa is the amino nitrogen coefficient.
Fourthly, the wheat juice beta glucan
The beer containing a proper amount of beta glucan is one of the substances for keeping the mellow feeling of the beer, but if the beta glucan is too much, the decomposition of the beta glucan in the malt is insufficient, and a series of related problems are brought about in the beer brewing process. Therefore, the content of beta glucan in the malting process is lower than 250 mg/L. And the wort beta glucan content can be estimated by the following formula:
in the formula,is the beta glucan mass concentration of the component i, and nu is the glucan coefficient.
Fifth thickness of the groove layer of the filter tank
During mashing, the insoluble spent grain contained in the mash will form a layer of grains. The thickness of the grains is too thick, the filtration speed of the wort is slow, and the filtration time is prolonged; the thickness of the layer is too thin, which, although increasing the filtration rate, reduces the clarity of the wort. The thickness of the grain layer in the production is generally controlled to be 30-50 cm. And the thickness of the tank can be estimated by the following formula:
Figure GSA00000134752600063
wherein D is the diameter of the filter tank equipment,
Figure GSA00000134752600064
the yield of component i is the cell yield.
And 3, optimizing the beer formula model by using a variable-scale ant colony optimization method, and finally solving the production formula with the lowest cost. The method comprises the following specific steps:
firstly, initializing parameters, dividing each component into N equal parts by mass percentage, and performing discrete interval of each component
Figure GSA00000134752600065
Wherein,the upper and lower limits of the mass percentage of the components.
As shown in fig. 1, each vertical stripe represents a material and is discretized into N equal parts, and the discretized nodes represent the mass fraction of the component. After discrete processing, the formula optimization problem is changed into a problem of finding an optimal path. Ants start from a start point, gradually pass through nodes on each variety, and finally reach an end point, so that one circulation is completed, and a complete formula is formed.
If max (h)1,h2,...,hn) Stopping the algorithm when the epsilon is less than or equal to epsilon, and outputting the current optimal scheme, wherein epsilon represents the ending condition; otherwise, turning to the step 3;
(r, i) is the ith node on the r component, and the numerical value is marked as Xr,i(ii) a (r +1, j) is the jth node on the r +1 component; [ (r, i), (r +1), j)]Is a connecting line from the node (r, i) to the node (r +1, j), the probability that the ant k transfers from the position (r, i) to the position (r +1, j) at the time t during the movement of the ant group with the number m of ants in the ant group is
<math><mrow><msubsup><mi>p</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>k</mi></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msub><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><msub><mi>M</mi><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msub></munderover><msub><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mrow></math>
In the formula: mr+1Is the allowable value range of the r +1 component, and ensures that the sum of the proportions of all varieties is not more than 100 percent. If the r +1 th variety is not the last undetermined variety, Mr+1A value range of
Figure GSA00000134752600072
But for the last breed, Mr+1Can only take values of
Figure GSA00000134752600073
At time t in [ (r, i), (r +1), j]The intensity of pheromone concentration remained on the connecting line is equal to that on each path under the initial condition, i.e. tau[(r,i),(r+1,j)](0) C constant.
Ant k (k 1, 2.. m) is randomly selected according to the probability on each path. In the process of creating the solution, after ants visit the nodes, the pheromones on the paths traveled by the ants are updated by adopting a local pheromone updating rule
<math><mrow><msubsup><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>new</mi></msubsup><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>&rho;</mi><mo>)</mo></mrow><msubsup><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>old</mi></msubsup><mo>+</mo><mi>&rho;</mi><mo>&CenterDot;</mo><mi>&Delta;&tau;</mi></mrow></math>
Where ρ is an information amount attenuation parameter, (0 < ρ < 1), let
Figure GSA00000134752600075
Q is a constant, JnnShowing the formula cost of the ant obtaining scheme. Each ant is recurred in this way and finally generates a respective formulation.
Fourthly, eliminating the infeasible schemes which do not meet the production indexes by using the index model, calculating formula cost J of the feasible schemes according to the following formula, comparing the formula cost J with the best scheme, and recording the scheme as the best scheme if the formula cost J is less than the formula cost in the best scheme;
Figure GSA00000134752600076
wherein M isiIs the unit price of the starting component i.
Fifthly, when all ants construct a formula scheme, the pheromone is globally updated according to the following formula to obtain the concentration intensity of the pheromone
In the formula: j. the design is a squaremin gbThe lowest value of the objective function obtained at the start of the iteration.
Sixthly, updating iteration times t ← t + 1; if t is more than or equal to tmaxTurning to the step 3; otherwise, find the best scheme at present, update xr0、wrWherein w isr=2·hrAnd correcting the upper and lower search limits x according to the following formularupper、xrlowerGo to step 1, where xr0Is at bestThe optimal mass percentage of the component r in the scheme.
<math><mfenced open='{' close=''><mtable><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><mn>1</mn><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><mn>1</mn><mo>&LeftArrow;</mo><msub><mi>w</mi><mi>r</mi></msub></mtd><mtd><mi>if</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>></mo><mn>1</mn></mtd></mtr><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac></mtd><mtd><mi>if</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>&le;</mo><mn>1</mn><mi>and</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>w</mi><mi>r</mi></msub><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><mn>0</mn></mtd><mtd><mi>if</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>&le;</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math>

Claims (1)

1. A beer production formula optimization method is characterized by comprising the following steps:
step 1, obtaining the yield, alpha amino nitrogen, saccharifying power, total soluble nitrogen, beta glucan and unit price of main raw materials in a beer formula;
step 2, establishing a malt saccharification force, wort total nitrogen, wort alpha-amino nitrogen, wort beta-glucan and filter tank grain layer thickness comprehensive production performance index estimation model;
Figure FSA00000134752500011
in the formula, Ti、xiRespectively representing the saccharifying power intensity and mass fraction of the component i, wherein i is more than or equal to 1 and less than or equal to n;
Figure FSA00000134752500012
in the formula,
Figure FSA00000134752500013
is the total nitrogen mass concentration of component i; A. v is the total mass of raw materials required by a batch and the required wort yield, and the unit is kilogram and liter respectively; gamma, gamma,The protein decomposition strength and the boiling nitrogen precipitation rate are respectively measured;
Figure FSA00000134752500015
in the formula,
Figure FSA00000134752500016
is the mass concentration of alpha amino nitrogen of the component i, and kappa is the amino nitrogen coefficient;
Figure FSA00000134752500017
in the formula,
Figure FSA00000134752500018
is the beta glucan mass concentration of component i, and v is the glucan coefficient;
Figure FSA00000134752500019
wherein D is the diameter of the filter tank equipment,
Figure FSA000001347525000110
the yield of component i is the yield of component i;
and 3, optimizing the beer formula model by using a variable-scale ant colony optimization method, and finally solving the production formula with the lowest cost, wherein the specific steps are as follows:
firstly, initializing parameters, dividing each component into N equal parts by mass percentage, and performing discrete interval of each componentWherein,
Figure FSA000001347525000112
respectively representing the upper limit and the lower limit of the mass percentage of the components;
if max (h)1,h2,...,hn) Stopping the algorithm when the epsilon is less than or equal to epsilon, and outputting the current optimal scheme, wherein epsilon represents the ending condition; otherwise, turning to the step 3;
(r, i) is the ith node on the r component, and the numerical value is marked as Xr,i(ii) a (r +1, j) is the jth node on the r +1 component; [ (r, i), (r +1), j)]Is a connecting line from the node (r, i) to the node (r +1, j), the number of ants in the ant group is m, and the probability that the ant k is transferred from the position (r, i) to the position (r +1, j) at the moment t in the motion process is
<math><mrow><msubsup><mi>p</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>k</mi></msubsup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow><msub><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mrow><munderover><mi>&Sigma;</mi><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><msub><mi>M</mi><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msub></munderover><msub><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac></mrow></math>
In the formula: mr+1Is the allowable value range of the r +1 th component, tau[(r,i),(r+1,j)](t) at time t at [ (r, i), (r +1), j]Residual pheromone concentration intensity on the connecting line is obtained;
an ant k (k is 1, 2.. m) is randomly selected according to the probability on each path, and after the ant visits a node, the pheromone on the path where the ant walks is updated by adopting a local pheromone updating rule
<math><mrow><msubsup><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>new</mi></msubsup><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>-</mo><mi>&rho;</mi><mo>)</mo></mrow><msubsup><mi>&tau;</mi><mrow><mo>[</mo><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>i</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>]</mo></mrow><mi>old</mi></msubsup><mo>+</mo><mi>&rho;</mi><mo>&CenterDot;</mo><mi>&Delta;&tau;</mi></mrow></math>
Where ρ is an information amount attenuation parameter, (0 < ρ < 1), let
Figure FSA00000134752500023
Q is a constant, JnnRepresenting the formula cost of the ant obtaining scheme, and each ant recurs in such a way and finally generates a respective formula scheme;
fourthly, eliminating the infeasible schemes which do not meet the production index by using the index modelCalculating a formula cost J by the scheme and comparing the formula cost J with the best scheme, and if the formula cost J is less than the formula cost in the best scheme, recording the scheme as the best scheme;wherein M isiIs the unit price of the raw material component i;
fifthly, when all ants construct a formula scheme, globally updating the pheromone according to the following formula to obtain the pheromone concentration intensity tau'[(r,i),(r+1,j)]
Figure FSA00000134752500025
In the formula: j. the design is a squaremingbThe lowest objective function value obtained when the iteration is started;
sixthly, updating iteration times t ← t + 1; if t is more than or equal to tmaxTurning to the step 3; otherwise, find the best scheme at present, update xr0、wrWherein w isr=2·hrAnd correcting the upper and lower search limits x according to the following formularupper、xrlowerGo to step 1, where xr0For the best mass percentage of the r-th component in the best case,
<math><mrow><mfenced open='{' close=''><mtable><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><mn>1</mn><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><mn>1</mn><mo>-</mo><msub><mi>w</mi><mi>r</mi></msub></mtd><mtd><mi>if</mi></mtd><mtd><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>></mo><mn>1</mn></mtd></mtr><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac></mtd><mtd><mi>if</mi></mtd><mtd><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>+</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>&le;</mo><mn>1</mn><mi>and</mi><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>></mo><mn>0</mn></mtd></mtr><mtr><mtd><msubsup><mi>x</mi><mi>r</mi><mi>upper</mi></msubsup><mo>&LeftArrow;</mo><msub><mi>w</mi><mi>r</mi></msub><mo>,</mo><msubsup><mi>x</mi><mi>r</mi><mi>lower</mi></msubsup><mo>&LeftArrow;</mo><mn>0</mn></mtd><mtd><mi>if</mi></mtd><mtd><msub><mi>x</mi><mrow><mi>r</mi><mn>0</mn></mrow></msub><mo>-</mo><mfrac><msub><mi>w</mi><mi>r</mi></msub><mn>2</mn></mfrac><mo>&le;</mo><mn>0</mn></mtd></mtr></mtable></mfenced><mo>.</mo></mrow></math>
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