JPH09201167A - Design for blending of feed - Google Patents

Abstract

PROBLEM TO BE SOLVED: To flexibly deal with a case in which a restriction equation and a cost accounting equation are nonlinear or the number of restriction equations is many and the satisfaction of the whole restriction equations are very difficult in a design method for minimizing a blending cost under a restriction condition of given nutrient components of a feed for a domestic animal, a domestic fowl and a cultured fish and feed raw materials. SOLUTION: Restriction equations of nutrients and an equation for showing a formula feed are prepared and a blending ratio of each feed raw material is coded as a gene. A group (initial individual group) of an organism individual (chromosome) is prepared by random numbers at an early stage of a design. The blending ratio of each feed raw material to minimize an objective function is obtained as the optimum solution while repeteadly carrying out a genetic operator such as crossing and mutation.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to a feed composition of pigs, cows, chickens and livestock such as yellowtail and yellowtail, poultry, and farmed fish under the constraint conditions of given nutritional ingredients and feed ingredients. Relates to a design method for minimizing the compounding cost. Furthermore, in detail, based on the constraint conditions of nutritional ingredients and feed ingredients indicated in the Japanese Feeding Standard, NRC Feeding Standard, etc., the optimal formulation that minimizes the objective function such as formulation design cost based on the unit price of each feed ingredient. It relates to the design method.

[0002]

2. Description of the Related Art In the past, the feed mix design of livestock and the like was performed by hand. However, since all manual calculations rely on the knowledge and experience of the designer, mistakes are likely to occur due to the designer's self-righteousness, and the designer's perception is entirely dependent on the price. In order to avoid such mistakes by the designer's self-righteousness, supply necessary and sufficient nutrients, and design the cheapest feed, in recent years, a linear programming method (hereinafter abbreviated as LP) has been used to The method of calculating the composition has come to be used.

An LP is a mixed feed containing m kinds of nutrients (composition or nutritional value) in a predetermined amount a _i (i = 1 to m), and the raw material price is c _i (i = 1 to n).
This is a problem of obtaining the feed material mixture ratio x _i (i = 1 to n) that is realized at the lowest price using various kinds of feed materials.

When the above conditions are expressed as a mathematical expression, the following expression
X _i that satisfies the constraints of (1) and (2) and minimizes the equation (3) showing the formulation design cost based on the unit price of the feed raw material is obtained.

B ₁₁ x ₁ + b ₂₁ x ₂ + ... + b _n1 x _n ≧ a ₁ b ₁₂ x ₁ + b ₂₂ x ₂ + ... …… + b _n2 x _n ≦ a ₂ ………………………… …………………………………… (1) …………………………………………………… b _1m x ₁ + b _2m x ₂ + ……… + b _nm x _n ≧ a _m

X ₁ + x ₂ + x ₃ + ... + x _n = 100 (2)

Z = c ₁ x ₁ + c ₂ x ₂ + ... …… + c _n x _n → Min. ...... (3)

Here, b _ij is the content rate of the nutrient j contained in the feed raw material i. For the actual LP formulation calculation, the optimum solution is obtained by a simplex method or the like on a computer.

On the other hand, a plurality of linear objective functions represented by the above equation (3) are set, and the above phase competition is performed under the linear constraint condition equations (1) and (2) which are also formulated. A blending design is also attempted with the aid of multi-objective linear programming, which is a method for finding an optimal solution that minimizes a plurality of objective functions simultaneously.

[0010]

As described above, in recent years,
Design of compound feed for livestock and poultry is mainly performed by LP using a computer. On the other hand, it is known that, for example, the relationship between broiler growth and feed energy and protein content is shown by a quadratic surface. The weight gain of poultry and poultry is non-linear, and the relationship between feed price and ingredients is also non-linear. Therefore, taking a broiler as an example, the blending ratio that minimizes the blending design cost and maximizes the sales profit changes in a curve.

As described above, when the constraint condition of each nutrient in the compounded feed and the calculation condition of the compounding cost based on the unit price of each feed material are non-linear, the compounding design by LP is unsuitable, and the composition design site is not suitable. In each case, the correction based on the experience of a skilled engineer is added to the result of the compounding design by LP.

Furthermore, in recent years, when the number of feed raw materials to be mixed has increased due to the higher functionality of the compound feed, the number of constraint condition formulas inevitably increases in the compounding design by LP, which satisfies all the conditions and reduces the cost. It is difficult to obtain the optimum solution that minimizes, and similarly, the mixing ratio of feed ingredients and the content ratio of nutrients are often corrected based on the experience of a skilled engineer.

In blending design utilizing multi-objective linear programming, objective functions such as blending design cost often compete with each other, and there is generally no perfect optimal solution that minimizes all objective functions at the same time. Therefore, in order to improve the value of a certain objective function as a passive solution instead of the perfect optimal solution, a Pareto optimal solution that incorporates the concept of so-called trade-off that deteriorates the value of at least one other objective function. As a result of the blending design, there are still many points to be improved in order to use it in the actual design site.

On the background of the above-mentioned technical level regarding the design of the compound feed for livestock, poultry, cultured fish, etc., in the field of the compound design, the constraint formula and the cost calculation formula are non-linear and There was a demand for the development of a new formulation design algorithm that can flexibly deal with the case where it is extremely difficult to satisfy all the constraint conditions by designing with LP due to the large number of LPs.

[0015]

The present invention provides livestock, poultry,
In the design method to minimize the compounding cost under the constraint condition of the fed nutritional components and feed materials such as farmed fish and the like, create the constraint formula of each nutrient and the formula showing the compounding design cost, Coding the mixing ratio of feed ingredients as a gene, at the beginning of the design, a population of such organisms (chromosomes) (initial population) is created with random numbers, and genetic operators such as crossover and mutation are repeated. This is a method of obtaining the optimum mixing ratio of each feed ingredient that minimizes the objective function while multiplying.

The present invention is applicable to the case where the constraint formulas and the cost calculation formulas of the formulation are non-linear in the design of the practical compound feed, and when the number of constraint formulas is large and it is very difficult to satisfy all the constraint conditions. As a new formulation design algorithm that can be flexibly handled on computer software, GA that imitates the process of biological evolution and its function on computer software is used to realize a formulation design similar to the experience of a skilled formulation engineer. It provides a new formulation design method.

In a conventional calculation method for an optimization problem, for example, a mountain climbing method, for a so-called multimodal problem having a plurality of locally optimal solutions, an initial point artificially selected at the start of execution is generally used. Depending on, only one local optimal solution can be found.

In recent years, as a global optimization method for such a multimodal problem, a genetic algorithm (henceforth called GA) proposed by taking a hint from a biological evolution process has been attracting attention. This method is a method that does not target only one solution candidate, but targets a group of solution candidates and applies an evolution law of a living organism to the group to obtain an optimal solution.

In the GA method, the solution candidates are called individuals and are represented by randomly generated character strings. Operations such as selection, crossover, and mutation that are based on the evolutionary law of the organism are performed on such a population of individuals. Selection and crossover have the function of improving the search so as to obtain an optimal solution sooner, and mutation has a function of preventing the search point from falling into a local optimal solution.

This method has the advantages that it is much simpler to calculate than the conventional random search method, and that the method for improving the search can be expressed as common knowledge that can be conveyed to people. Furthermore, this method is effective for global search, and many application examples have already been reported.

The genetic algorithm was found in the process of modeling the process of biological evolution and performing engineering simulation to elucidate its mechanism. Currently,
In addition to research on the genetics of living organisms, it has been found that this genetic algorithm can be effectively used in other fields such as industry for problems that were difficult to solve by conventional methods.

The genetic algorithm is a search algorithm learned from the evolution of living things. GA is one of the search methods for engineeringly simulating the mechanism of biological evolution, and usually consists of three operations: selection, crossover, and mutation.
In the natural world, the principle of natural selection works, and organisms with strong genes that are suitable for the environment are selected and their offspring are left behind.

A DNA molecule having genetic information is a base molecule having a double helix structure. When a parent replicates its offspring, the DNA helix unwinds and associates with other DNA, creating a new individual. That is, a new individual is born by linking one gene with another gene. This is the crossover of genes.

First, the problem is converted into a character string corresponding to the genotype. This character string represents an individual and handles this group. A character string representing this individual is evaluated and a group having a high evaluation value is selected and left. This corresponds to selection in nature. A new character string is generated by applying an operator to this selected group.

The basic operator is a self-reproducing device having a function of copying a character string, a crossing operation for producing a new character string by partially exchanging two character strings, and a stochastic operation when copying a character string. There is a mutation that causes an error. By repeating this cycle as shown in FIG. 1, a character string having a high evaluation value according to the environment is created, and the evaluation value of the entire character string group is improved.

As can be understood from the above description, the GA
When applying to an actual problem, it is necessary to introduce an expression, operation, or heuristic suitable for the problem. Not all problems can be solved easily by simply introducing GA. The present invention solves the optimization problem of feed mix design of livestock etc. by using a genetic algorithm.

[0027]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 shows the flow of a blending design process by GA of the present invention. Hereinafter, a specific processing method will be described along the flow of processing.

1) Creation of Constraint Formula and Objective Function Similar to the case of the formulation design by LP, the constraint formula of each nutrient and the formula showing the formulation design cost are created.

2) Determination of genotype In the case of designing the composition by GA, corn, milo,
The mixing ratio of each feed material such as bran and cassava is coded as a gene as shown in FIG.

3) Occurrence of population of organisms In population design by GA, such population of organisms (chromosomes) (initial population) is randomly generated at the beginning stage of design as shown in FIG. In addition, while repeatedly applying genetic operators such as crossover and mutation, the mixture ratio of each feed ingredient that minimizes the objective function is obtained as an optimum solution. Here, m is the number of individuals in the population, and the initial value of the mixing ratio _xn of each feed ingredient is determined by a random method based on random number generation under set conditions.

4) Evaluation of Individual Fitness First, the compounding cost based on the compounding ratio of each individual is calculated by the above formula (3) as in the case of designing by LP. At this time, a ratio (hereinafter referred to as a penalty value) at which the optimum solution candidate (chromosome) violates the same constraint condition (1) as in the LP design is calculated. The penalty value is calculated by the following formula.

Penalty value = (value in which the left side of expression (1) exceeds the upper limit or the lower limit of each nutrient) / (the upper limit value-lower limit value of each nutrient) (4)

Next, the fitness of each individual is calculated by the following equation.

Fitness = 1 / (Combination cost × (Penalty value + 1)) (5)

In an actual mixture design problem, a solution that satisfies all the constraint conditions is often not obtained, and the simplex method cannot obtain an optimum solution. According to the method of the present invention, even if the constraint condition is violated, the fitness is reduced in proportion to the ratio of the violated constraint, so that the solution can be obtained. Further, even if the constraint expression is a non-linear function, the penalty value is calculated only by the ratio of breaking the constraint value, so that it can be processed on the computer program as in the case where the constraint expression is linear.

5) Judgment of the optimum solution The arrangement of each chromosome in the individual population is performed from the one with high fitness obtained in 4) to the one with low fitness, and the mixing ratio of the feed raw material coded as the gene of each chromosome. Based on, the compounding design cost is calculated for each chromosome. Based on the obtained cost, it is determined whether or not the optimum solution (combination of combination rates) that realizes the minimum combination design cost has been obtained.

6) Crossover Processing In the crossover processing unit shown in FIG. 1, a part of high fitness chromosomes is copied to low fitness chromosomes to perform apparent crossover processing. That is, one point between genes in two chromosomes is selected and the right or left part thereof is copied. In addition, the fitness of the two chromosomes is low at the time of copying (belonging to the lower 1/3 of the population when the individuals with higher fitness are arranged in order).
In some cases, it copies a part of the elite (highest fitness of the population) chromosome to each (called elite strategy). This is to accelerate the convergence to the optimal solution and preferentially treat excellent chromosomes so that the solution can be obtained at a high rate. The concept of crossover processing is shown in FIG.

7) Mutation processing Generally, a normal random number is used in a genetic algorithm, but in order to accelerate the convergence in the early stage of evolution, the method of combining uniform random numbers and normal random numbers is adopted for each, and the loci to cause mutation are identified. Along with the selection, a random number is used to determine a new blending ratio for the locus. Naturally, the blending ratio is a value within the constraint range of the blending ratio. The concept of this processing is shown in FIG. Further, the states of the crossover processing, the elite strategy, and the mutation processing, which are GA operations in the chromosome population (population) adopted in the present invention, are collectively shown in FIG.

The elite strategy of 1 in the figure is the lowest 1 of the evaluation values.
If you select a gene of / 3, cross with "elite", 2
In the case of 1-point crossover, when 2/3 of the evaluation values are selected, the mating is free, and the mutation of 3 causes mutations with various probabilities with respect to the population.

8) 100% adjustment treatment The total of the compounding ratios of the compounding ingredients of the compounding feed is adjusted to 100% as shown in the constraint equation (2). In other words, as a result of crossover and mutation processing, if expression (2) is no longer satisfied, a part of the chromosome (mixing ratio selected by random numbers)
It is forcibly changed to satisfy (2). Optimal blending design is realized by repeatedly performing the above-described processing (changing generations of individual biological population).

[0041]

EXAMPLE As an example of the present invention, the design of a practical compound feed for fattening pigs will be described. When designing the cone,
Milo, barley, bran, defatted rice bran, soybean meal,
Twenty feed ingredients such as corn gluten feed were selected, and 13 nutrients (composition / nutrition value) such as crude protein, crude fat, crude fiber, crude ash, digestible crude protein and total digestible nutrients were selected. Table 1 below summarizes the constraint conditions of the content rate of these nutrients and the mixing rate of the feed raw material and the unit price of the feed raw material per ton set.

[0042]

[Table 1]

Next, based on the content rate of nutrients contained in each feed raw material, the feed raw material mixture restriction condition, the nutrient mixture restriction condition and the raw material unit price shown in Table 1, the results are shown in the section of the prior art. We created each constraint and cost evaluation formula which is the objective function. Moreover, the composition design by LP was performed for the purpose of comparative examination with the composition design result by GA.

The mixing ratio of each feed material was determined by random numbers within the constraint conditions, and a plurality of chromosomes, that is, populations, were coded on the two-dimensional array memory of the computer. Following the above pre-processing,
The crossover, elite strategy, and mutation operations, which are the main routines of the GA for mixed feed design of the present invention, were added to the population, and the same process was repeated to perform generational alternation of the population. The mutation rate is 1 as the GA parameter for GA for formulation design
4 levels between / 4 and 1, the initial number of individuals is 300 to 15
Similarly, 4 levels were set between 00 and a design simulation was performed.

FIG. 7 shows the result of comparison with the design by LP as an example of the design simulation. As is clear from the figure, the optimum blending design by GA can obtain almost the same result as when LP is used, and the cost per ton based on the raw material unit price shown in Table 1 is about 2
Achieved 6,400 yen. On the other hand, regarding the composition and the nutritional value, the optimum solution by GA and the optimum solution by LP show almost the same composition distribution, and it was clarified from these results that the optimum blending design by GA of the practical feed is possible.

FIG. 8 also shows, as an example of a design simulation by GA, a function that should be assumed in the formula for calculating the blending design cost and the condition that the unit price per ton gradually decreases as the amount of feed raw material used increases, or Introducing non-linear terms such as interval linear conditions assuming that the unit price per ton of feed material decreases by a certain amount if a boundary is set for the amount and the amount exceeds 100 t
The result of the simulation is shown below.

In the same figure, the design results by LP are also shown for comparison. There is a large difference between the GA solution and the LP solution in the optimum compounding ratio in specific feed materials such as corn and milo. The GA solution introduces a non-linear term in the raw material unit price, so that a so-called conflict phenomenon is recognized in order to satisfy the constraint conditions of nutritional composition and nutritional value. In addition, the cost of GA solution was about 2% lower than that of LP solution.

Looking at the nutritional composition and nutritional value of the simulation results, as shown in FIG.
No significant difference was found in the solutions. From the above results, it is clear that the feed composition design incorporating the genetic algorithm of the present invention can realize the cost reduction while satisfying the constraint conditions of the nutritional composition and the nutritional value similarly to the conventional LP design. became.

[0049]

EFFECTS OF THE INVENTION According to the blending design of livestock feed which incorporates the genetic algorithm of the present invention, the following effects can be obtained. Regardless of whether the constraint formulas such as the ratio of feed ingredients and the content ratio of nutrients and the formulas for calculating costs are linear or non-linear, they can be freely set by computer software.

Further, even when a large number of feed ingredients are mixed for the purpose of enhancing the functionality of the compound feed, it is possible to realize a compound design close to the experience of a skilled compound design engineer.
Further, compared to the design by the linear programming method, the compounding cost can be reduced, and the flexibility with respect to the constraint condition is high.

[Brief description of drawings]

FIG. 1 is a flow chart of a blending design process using a genetic algorithm of the present invention.

FIG. 2 is an explanatory diagram of the concept of genetic coding.

FIG. 3 is an explanatory diagram of a concept of generation of a biological individual population.

FIG. 4 is an explanatory diagram of a concept of crossover processing.

FIG. 5 is an explanatory diagram of a concept of mutation processing.

FIG. 6 is an explanatory diagram showing a crossover process, an elite strategy, and a mutation process that are GA operations in a chromosome population (population) adopted in the present invention.

FIG. 7 is a graph showing an example of the design simulation of the present invention.

FIG. 8 is a graph showing an example of the design simulation of the present invention.

FIG. 9 is a graph showing an example of the design simulation of the present invention.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Tatsumi Furuya 5-9-43 Matsushiro Tsukuba-shi, Ibaraki Prefecture (72) Inventor Yoshiyuki Minami 53-14 Morinosato, Kukizaki-cho, Inashiki-gun Ibaraki Prefecture Fumio Tachibana Ibaraki Prefecture 1881-16 Ami, Ami-machi, Inashiki-gun

Claims (1)

[Claims] 1. In a design method for minimizing the compounding cost under the constraint condition of the nutrient components and the feed materials to which the feed such as livestock, poultry, and farmed fish is fed, the constraint formula and the compounding design of each nutrient are provided. Create a formula that shows the cost, code the mixing ratio of each feed ingredient as a gene, create an initial population with random numbers at the beginning of the design, and repeat the genetic operators such as crossover and mutation A method for designing the composition of feed, characterized in that the compounding ratio of each feed material that minimizes the function is obtained as an optimum solution.