KR20220046271A - Precision animal feed formulation using an evolutionary multi-objective approach - Google Patents

Abstract

The present invention relates to an animal feed blending method and, more specifically, to an animal feed blending method for minimizing feed cost and satisfying nutritional requirements. According to one aspect of the present invention, a feed blending method for minimizing feed cost and satisfying nutritional requirements for dairy cows satisfies an objective expression 1 (feed cost) and objective expression 2 (deviation from the prescribed nutritional requirements) represented by Minimize｜MP - M｜+ ｜Lys - N｜ + ｜Ca - O｜ + ｜P - Q｜ +｜ME - R｜ + ｜Met - S｜, with respect to dairy cows, wherein n is the number of components under consideration, w_i is the weight in kg, cost_i is the cost of feed raw materials (KRW/kg), MP is metabolic protein, Lys is lysine, Ca is calcium, P is phosphorus, ME is metabolic energy, Met is methionine, M, N, O, Q, R, and S define the requirements for MP, Lys, Ca, P, ME, and Met, respectively, and the requirements vary depending on the age and weight of a dairy cow.

Description

PRECISION ANIMAL FEED FORMULATION USING AN EVOLUTIONARY MULTI-OBJECTIVE APPROACH

The present invention relates to a method for compounding animal feed, and more particularly, to a method for compounding animal feed using an evolutionary multi-purpose approach.

In animal production, the main purpose of feed formulation is to provide balanced nutrition to support physiological functions such as growth, maintenance, reproduction and lactation, as well as energy sources for body and metabolic activities. Livestock studies have demonstrated that growth rates and milk yield depend on the availability of nutrients, including amino acids, fatty acids, minerals, glucose and other substrates. In addition, an animal's nutritional requirements change according to the animal's different life stages, as well as its role, such as seed stock, breeding, and protein source. An inadequate balance of feed nutrients results in nutritional deficiencies, related diseases, and performance problems. In Korea, the nutrients emphasized for beef cattle are DMI, MC, TDN, CP, Ca, P, and for dairy cattle, Met, Lys, Arg, Thr, Leu, Ile, Val, His, Phe, Trp, ME, Ca, P constitutes the nutritional requirements. To be profitable, feed formulation must include finding the right amount of a combination of different ingredients to meet the nutritional needs of the animal at the lowest cost.

The lowest cost feed formulation was approached as a standard optimization problem, where applications of mathematical programming such as LP, multi-step multiple-selection programming algorithms, mixed-integer programming, integer programming, and mixed-integer linear programming became the standard. The main weakness of these approaches is that they use fixed strict limits, allowing only one objective optimization at a time, and in many situations a feasible solution cannot be found. In other words, in traditional livestock feed formulations, the minimum nutritional requirements are expressed as stringent constraints that must be met. As a result, during the optimization process, any small violations related to nutritional requirements render this solution infeasible and are discarded. Imposing minimal nutritional requirements therefore results in feed formulations that, although slightly less practicable, are not always cost-effective compared to solutions that are still acceptable to the breeder. Slight easing of one or more nutritional requirements, which may not be significant at a particular growth stage, can result in significant reductions in feed costs without negatively impacting animal performance. Thus, knowledge of the essential nutritional requirements at each stage and their relationship to cost can help increase the cost-effectiveness of formulated feeds. Based on these observations, an interactive feed formulation using an evolutionary algorithm was proposed, where each nutrient requirement mitigation was achieved in the algorithm via acceptable parameters.

Feed formulations usually include several goals in addition to minimizing the cost of feed while meeting nutritional requirements. Some of the goals considered in previous studies include maximizing land use, maximizing the use of stored feed, and reducing nitrogen and phosphorus emissions. In some studies, minimization of changes in protein, methionine, and lysine as well as minimization of cost was considered. The multi-goal optimization process involves defining goals and priorities; Next involves iteratively finding solutions for linear or nonlinear functions. In other words, each goal is solved sequentially according to priority, and the previous goal(s) remains constant in the model. There may be several trade-offs between several conflicting feed formulation goals. This process results in a set of offset solutions called the Pareto-optimal solution. To advance certain goals, a solution that does not sacrifice at least one or more goals is impossible. In other previous feed formulation literature, goal programming is believed to be a very effective approach to solving multi-goal decision-making problems. However, goal programming usually requires the user to set a penalty value for each goal, and the choice of penalty severely affects the quality of the optimized offset solution, resulting in ineffective decision-making. Recently, evolutionary multi-objective optimal design methods have become popular because of their effectiveness in dealing with complex, conflicting, nonlinear goals without the need for penalties.

As mentioned above, loosening some constraints related to nutritional requirements can reduce the cost of feed formulation without seriously affecting the growth of the animal. Also in known interactive feed formulations, each nutritional requirement is assigned an acceptable parameter. Changes in acceptable parameters related to the applicable nutritional requirements will result in an acceptable or unacceptable solution for the breeder. In other words, finding the relationship between the acceptable parameters of each nutrient requirement and the cost of feed requires a time-consuming process of trial and error. Moreover, the decision-making process is complicated by the lack of adequate understanding between different nutritional requirements and feed costs.

An object of the present invention is to provide an animal feed formulation method using an evolutionary multi-purpose approach that can satisfy the cost of feed raw materials and the nutritional needs of animals.

According to one aspect of the present invention in order to solve the above-mentioned problems, in a feed formulation method that minimizes feed cost and satisfies nutritional requirements for dairy cows,

The method satisfies the following Objectives 1 and 2 for cows,

Purpose 1: Feed cost

Objective 2: Deviation from prescribed nutritional requirements

Minimize｜MP - M｜+ ｜Lys - N｜ + ｜Ca - O｜ + ｜P - Q｜ +｜ME - R｜ + ｜Met - S｜

where n is the number of ingredients under consideration, wi is the weight in kg, costi is the cost of feed ingredients (KRW/kg), MP is metabolic protein, Lys is lysine, Ca is calcium, P is phosphorus, ME is Metabolic energy, Met represents methionine, M, N, O, Q, R, S define the requirements for MP, Lys, Ca, P, ME, Met, respectively, and the requirements depend on the age and weight of the cow different

It is preferred that NSGA-II, an evolutionary multi-objective optimization algorithm, be used to optimize the multi-objective expression in the above aspect.

In addition, according to another aspect of the present invention, there is provided a feed mixing method that minimizes feed cost and satisfies nutritional requirements for beef cattle,

The method satisfies the following Objective Expressions 3 and 4 for beef cattle,

Objective 3: Feed Cost

(4)

(4)

Objective 4: Deviation from prescribed nutritional requirements

Minimize｜DMI - A｜+ ｜CP - B｜+ ｜TDN - C｜ + ｜Ca - D｜+｜P - E｜+ ｜Rhage - F｜+ ｜MC - G｜+ ｜Conc. - H｜

where n is the number of ingredients under consideration, wi is the weight in kg, costi is the cost of feed ingredients (KRW/kg), DMI is dry matter intake, CP is crude protein, TDN is total digestible nutrients, and Ca is calcium , P is phosphorus, Rhage is roughage, MC is moisture content, Conc. is rich feed, A, B, C, D, E, F, G, H are DMI, CP, TDN, Ca, P, Rhage, The requirements for Mc, Conc. are prescribed, and the requirements are different depending on the age and weight of the cattle.

It is preferred that NSGA-II, an evolutionary multi-objective optimization algorithm, be used to optimize the multi-objective expression in the above aspect.

In the present invention, deviations of different feed formulations from the specified requirements, together with the minimization of feed costs, are regarded as targets to be minimized. The two goals - a) minimization of feed costs and b) deviation from the specified requirements (Nutrient dev) are at odds with each other. Using NSGA-II, an evolutionary multi-goal optimization algorithm, concurrent optimization can be achieved. The use of evolutionary multi-purpose optimization design methods is provided as a set of one-run construct solutions (Pareto sets), without the need to pre-define penalties and priorities. The form of the Pareto Front, which is representative of the Pareto set, depends on the type and number of nutritional requirements specified for the animal and the cost of the feed ingredients. Thus, from the Pareto aggregation, the present invention can easily establish the following relationships which can help the breeder to make better decisions.

a. The relationship between feed cost and overall deviation from defined nutritional requirements

b. Relationship between feed cost and deviation from individually defined nutritional requirements

c. The relationship between each individual nutritional requirement at different feed costs

Therefore, according to the present invention, it is possible to provide an animal feed formulation method using an evolutionary multi-purpose approach that can satisfy the cost of feed raw materials and the nutritional needs of animals.

1 is a graph showing a comparison between MOP and traditional single optimization;
Fig. 2 is a diagram showing the feed formulation curve of cow case 1 - OL: optimal line; P1, P2, P3: point; OLC: best-fit cost; Nutrientdev: Deviation from prescribed nutritional requirements - ;
Fig. 3 is a diagram showing the feed formulation curve of cow case 2 - OL: optimal line; P1, P2, P3: point; OLC: best-fit cost; Nutrientdev: Deviation from prescribed nutritional requirements - ;
Fig. 4 is a diagram showing the feed formulation curve of cow case 3 - OL: optimal line; P1, P2, P3: point; OLC: best-fit cost; Nutrientdev: Deviation from prescribed nutritional requirements - ;
5A and 5B are diagrams showing the feed formulation curve of beef cattle case 1 - Each column represents the result corresponding to each of the three considered levels, and Levels 1, 2, and 3 are enriched feeds of different levels, respectively. mean, OR: optimal region; P1, P2, P3: point; ORC: optimal area cost; OP: Optimal point; Nutrientdev: Deviation from prescribed nutritional requirements - ;
6 is a diagram showing the feed formulation curve of beef feed 2 - OR: optimal region; P1, P2, P3: point; ORC: optimal area cost; OP: Optimal point; OPC: optimal point cost;Nutrientdev: deviation from prescribed nutritional requirements - ;
7 is a diagram showing the feed formulation curve of beef cattle case 3 - OR: optimal region; P1, P2, P3, P4: point; ORC: optimal area cost; OP: Optimal point; OPC: optimal point cost; Nutrientdev: Deviation from prescribed nutritional requirements - ;
8 is a diagram showing the feed formulation curve of beef cattle case 4 - OR: optimal region; P1, P2, P3, P4: point; ORC: optimal area cost; OP: Optimal point; Nutrientdev: Deviations from prescribed nutritional requirements -;
9A and 9B are views showing feed cost and nutritional value of Korean dairy cows;
10A and 10B are views showing feed cost and nutritional value of Korean beef cattle;
11 is a flowchart showing a processing flow in NSGA-II.

Advantages and features of the present invention, and methods for achieving them, will become apparent with reference to the embodiments described below in detail in conjunction with the accompanying drawings. However, the present invention is not limited to the embodiments disclosed below, but will be implemented in various different forms.

In the present specification, the present embodiment is provided to complete the disclosure of the present invention, and to fully inform those of ordinary skill in the art to which the present invention pertains to the scope of the present invention. And the invention is only defined by the scope of the claims. Accordingly, in some embodiments, well-known components, well-known operations, and well-known techniques have not been specifically described in order to avoid obscuring the present invention.

Like reference numerals refer to like elements throughout. And, the terms used (mentioned) in this specification are for the purpose of describing the embodiments and are not intended to limit the present invention. In this specification, the singular also includes the plural unless specifically stated otherwise in the phrase. In addition, elements and operations referred to as 'include (or include)' do not exclude the presence or addition of one or more other elements and operations.

Unless otherwise defined, all terms (including technical and scientific terms) used herein may be used with the meaning commonly understood by those of ordinary skill in the art to which the present invention belongs. In addition, terms defined in a commonly used dictionary are not ideally or excessively interpreted unless they are defined.

Materials used in the description of the present invention are named as shown in Table 1 below.

[Table 1] Nomenclature of terms used in the present invention

1.1 data

The raw materials of the feed, their nutritional profile, and cost information used to prepare the simulated dairy and beef feed mixing ratios were obtained from the Rural Development Administration of Korea (see FIGS. 9a and 9b and FIGS. 10a and 10b). Data on nutritional requirements of dairy cows and beef cattle were obtained from the Rural Development Administration of Korea (Tables 2 and 3), and they serve as prescribed nutritional requirements. The nutritional requirements of cows in Korea are summarized as follows: Met, Lys, Arg, Thr, Leu, Ile, Val, His, Phe, Trp, ME, Ca, P.

[Table 2] Nutritional requirements for each breeding stage of cows in Korea

The nutritional requirements of beef cattle in Korea are summarized as follows: DMI, MC, TDN, CP, Ca, P. The requirements of the various cases considered (classified according to age and weight) are shown in Table 2 and It is summarized in 3. In Table 3, Level 2 represents the diet of the normal forage requirement without the concentrated feed (Conc.).

[Table 3] Nutritional requirements for each stage of breeding beef cattle in Korea

1.2 Problem formula

In feed formulations, enforcing strict nutritional requirements usually results in a sharp increase in feed cost. On the other hand, by relaxing some constraints, it is possible to reduce the feed cost without affecting the physiological characteristics of the animal. The nutritional requirements that can be alleviated depend not only on the type and stage of development of the animal, but also on the condition of the animal. In addition, the nutritional requirements of feed formulations vary from region to region. DMI (kg) is the amount of dry matter consumed daily, and CP (%) measures the nitrogen content, including both real protein and non-protein nitrogen. The total feed digestible fiber, protein, lipid and carbohydrate component in the feed amount is called TDN and is directly related to digestible energy. Minerals are essential feed ingredients that require at least 17 species. However, the two mainly included in the computer model are Ca and P. Calcium is the most abundant mineral in the body, and about 98% is present as a structural component of bones and teeth. The remaining 2% is distributed in extracellular fluid and soft tissues and is involved in important functions such as blood coagulation, membrane permeability, muscle contraction, nerve impulse transmission, cardiac regulation, secretion of certain hormones, and activation and stabilization of various enzymes.

Consequently, modified feed formulations for dairy cows and beef cattle were presented to facilitate the mitigation of their respective nutritional requirements using acceptable parameters. The cow and beef feed formulations are presented below.

Single Purpose Formula for Cows

Single Purpose Formula for Beef Cattle

In each problem formulation, the corresponding acceptable parameter (δ) is used for demand relaxation.

In these formulations, the breeder can change the tolerance parameters of the demand to be relaxed and use evolutionary algorithms to optimize the solution. Changes in allowable parameters result in cost fluctuations. However, the relationship between the different acceptable parameters and feed cost is not clear, and finding the best feed formulation involves a time-consuming trial and error process.

In the present invention, constraints related to different nutritional requirements are added together to form an objective function, and at the same time the feed cost is also optimized. These two objectives are in conflict with each other and may be referred to as a multi-purpose formulation. Multi-purpose formulas for dairy cows and beef cattle are presented in equations (3) and (4) below.

As mentioned earlier, the problem was formulated based on inspiration from previous studies, where the acceptable parameters had to be changed to adapt to the cost and nutritional requirements of the formulator, so that every time the acceptance parameters changed, Simulation had to be done. Consequently, the constraints in the new formulation are Pareto-fronted so that nondominated solutions can be chosen as the optimal option when no objective can be improved without detrimental to one or more other objectives. was formulated for the purpose of eliminating iterative simulations. Therefore, as in the first objective of minimizing cost using Equation (3), summing the weight (wi) of the selected raw material multiplied by the cost (costi), the nutrient requirements of the cows assessed for the raw material during the screening process were calculated. The constraint M, N, O, Q, R, and S denoted are all summed up and used to find costs in all search spaces (Pareto Front). By looking at all constraints according to a Pareto front, it offers the possibility to show various combinations of nutrient content and corresponding cost.

Example 1: Cow

Purpose 1: Feed cost

(3)

(3)

Objective 2: Deviation from prescribed nutritional requirements

Minimize｜MP - M｜+ ｜Lys - N｜ + ｜Ca - O｜ + ｜P - Q｜ +｜ME - R｜ + ｜Met - S｜

For cows, n is the number of ingredients under consideration, wi is the weight in kg, and costi is the cost of feed ingredients (KRW/kg). Consequently, M, N, O, Q, R, and S define the requirements for MP, Lys, Ca, P, ME, and Met, respectively. The requirements depend on the age and weight of the cattle.

Example 2: Beef

Purpose 1: Feed cost

(4)

(4)

Objective 2: Deviation from prescribed nutritional requirements

Minimize｜DMI - A｜+ ｜CP - B｜+ ｜TDN - C｜ + ｜Ca - D｜+｜P - E｜+ ｜Rhage - F｜+ ｜MC - G｜+ ｜Conc. - H｜

where n is the number of components under consideration, wi is the weight in kg, and costi is the cost (KRW/kg).

Constraints A, B, C, D, E, F, G, and H define the requirements of DMI, CP, TDN, Ca, P, Rhage, Mc, and Conc., respectively. Requirements depend on the age and weight of the cattle.

Unlike single-purpose formulations, multi-purpose approaches do not involve any process of trial and error. Moreover, the result is a set of constituent solutions for different feed costs and nutrient requirements. The availability of a full set of offset solutions facilitates better decision making when compared to single-purpose trial-and-error approaches.

1.3 Methods used in recent studies

In a multi-objective optimal design method, due to the conflicting nature of the objectives, no single optimal solution exists, but, as shown in Fig. 1, a construct called a Pareto front (in object space) or Pareto set (in variable space). A set of solutions exists. As shown, various Pareto fronts exist, and the goal of the multi-objective algorithm is to find the optimal Pareto front. In other words, an optimal Pareto front is not a set of solutions (optimal, not a better solution for all purposes), rather than non-existent solutions that are better for all purposes. In addition, Pareto Front solutions must be well-distributed or diversified to enable better decision-making.

Multi-purpose problems can be solved in a variety of ways,

A single-purpose optimal design method that prescribes weights for each objective. Depending on the set of weights, the algorithm provides a single solution to the Pareto front. Therefore, in order to estimate the entire Pareto front, multiple runs are required through different weight combinations. However, because of the non-linear relationship between the weights and the Pareto front, it is difficult to find various well-distributed solutions. Target programming commonly adopted in feed formulation falls into this category.

a. Evolutionary multi-purpose optimization, a population-based approach, can deliver the entire Pareto front in a single run.

b. Evolutionary multi-objective optimization, a population-based approach, can provide an entire Pareto front in one run.

In terms of feed optimization, Pareto's optimal solutions refer to a set of constituent solutions (see Fig. 1), where point A is the solution that best meets nutrient requirements but incurs a high cost; Point B is the solution with the lowest cost but high deviation from nutrient requirements; Point C represents a constituent solution with a significant reduction in cost and a large deviation from nutritional requirements. The decision-making process depends on the form of the Pareto Front and therefore mainly depends on the nutritional composition and the cost and nutritional requirements of the individual ingredients. In addition, relationships between different nutritional requirements across the entire cost range can be obtained. Thus, the entire Pareto Front is available in one run, and showing the relationship between individual nutritional requirements promotes better decision-making.

In this study, the present inventors used NSGA-II, an evolutionary multi-objective optimization algorithm, to optimize the multi-objective problems presented in equations (3) and (4). In order to obtain a diverse set of Pareto-optimal solutions, NSGA-II adopts the concepts of Pareto dominance and crowding distance.

For reference, the details of NSGA-II are as follows.

Background of NSGA-II

A multipurpose evolutionary algorithm is a population-based algorithm applied to solve two competing goals. The main advantage of MOEA is that it provides a set of solutions rather than a single solution. Among all MOEAs, NSGA-II is the more popular and widely adopted algorithm that can be applied in practice. In NSGA-II, a randomly generated population of N evaluates the objective function using operations such as mutation, crossover, and environmental selection to provide a final set of offset solutions. This process is repeated until the termination criteria are met. Mutation operators (polynomial mutation, binomial crossover) are used to give better offspring to the current population, and then selection is made using non-dominant classification according to cluster distance. The ultimate goal of any MOEA is convergence and diversity. In NSGA-II, the Pareto dominance of the final cancellation solution can be obtained using procedures such as non-dominant classification and cluster distance.

Basic definitions used in NSGA-II

Progeny generation: generate identical populations of N using some mutation operators, such as mutations and crosses

Mutations and crosses: producing new solutions from a population by modifying some of the features

Environmental selection: finding the best N solution from available 2N solutions for the next generation, using some of the primary and secondary selection methods. In NSGA-II, first-order selection is made using a non-dominant solution classification method in a Pareto front. Secondary selection is made using cluster distance measurements.

Non-dominant solution (solution): A solution that dominates other solutions for at least one or all purposes is called a non-dominant solution.

Cluster Distance: For each purpose, reflects the density of an object, or the cuboid distance of an object with respect to its two closest neighbors, acting only on the two nearest neighbors located on either side. This is known as the cluster distance of the solution.

11 is a flowchart illustrating a general processing procedure of NSGA-II to help understand NSGA-II, and a detailed description thereof will be omitted.

1.4. Experiment setup and simulation

A multi-purpose feed formulation according to the invention is simulated using - a) 3 cow cases in Korea, b) 4 beef cattle cases in Korea.

a) Cows:

Case 1: Immediately after birth to 20 months of age, less than 500 kg of live weight

Case 2: From 20 to 40 months, 500-650 kg live weight

Case 3: 40-46 months, 650 kg or more live

b) Beef cattle:

Case 1: Immediately after birth to 10 months, live weight less than 260 kg

Case 2: 10-17 months, live weight 260-452 kg

Case 3: 17-25 months, live weight 452-640 kg

Case 4: Maintenance phase where farmers try to keep their animals at the lowest cost

Simulations were performed in MATLAB, and the average execution time of each simulation of the proposed algorithm was 20 seconds on a 3.7 GHz Intel Core i5 processor, 8 GB RAM, and 128 GB SSD in Windows 10 operating system. The parameters of the optimization algorithm were set as follows:

Population size: 300

Maximum number of spawns: 2000

Mutation Distribution Index (nm): 20

Crossing Distribution Index (n c): 20

Mating Probability (Pc): 1.0

Mutation Probability (Pm): 1/10

Crossing: Simulated Binary Crossing

Mutation: polynomial mutation

Combine Constraints: 0-20

2. Results of simulation

2.1.1 Cows: Case 1

The Pareto-optimal front for both purposes is presented in (A) of FIG. 2, and the amounts of different feed materials selected among the solutions at the front, P1, P2, and P3 points are presented in (B) of FIG. 2(C) to 2(H) show the relationship between feed cost and individual nutritional requirements in feed. These graphs provide insight into the extent to which individual nutritional requirements contribute to overall cost. In Fig. 2(A), P1 represents a solution in which most nutritional requirements are met at a cost of about 4000KRW. 2(C) to 2(H), the horizontal dotted line indicates the specified demand (OL) for the corresponding feed component, and the OLC indicates the cost area in which the corresponding nutritional requirement is satisfied.

In Fig. 2(A), the point P2 and the point P1 appear to have almost the same deviation from the demand, but the cost is significantly lower at 1300KRW. Also, in P2, 5 out of 6 nutritional requirements set by the Rural Development Administration of Korea are met. However, Ca deviates greatly from the requirement. In the region P1 to P2, the cost increase is mainly due to the algorithm's attempt to meet Ca requirements. However, this results in slight deviations in other nutritional requirements such as Met, P, and MP. In Fig. 2(A) , P3 indicates a point where ME, Ca, and P requirements are met, while deviations in MP, Lys, and Met requirements are also observed. The cost fluctuations in the region between P2 and P3 are mainly due to the algorithm's attempt to meet the MP demand. To satisfy MP, Met, and Lys, Ca deviates from the required amount (see FIG. 2 ).

From Figure 2, it is evident that P1 is the point at which the prescribed nutrients were reasonably met. However, moving left from P1 to P2, the overall deviation becomes approximately equal to the large deviation of Ca. Therefore, if the deviation from the prescribed Ca can be tolerated, the choice of P2 will result in a cost savings of 223% compared to P1. For cows, MP requirements depend on several factors, such as the animal's age and activity. It was reported that milk yield and milk protein ratio did not improve in Chinese Holstein dairy cows, even if the conventional diet contained the prescribed MP. Therefore, in this scenario, the focus will be on ME (see Fig. 2(C)), and the choice of P3 will result in a cost reduction of 160% compared to P2, and will have little effect on the feed quality.

From Fig. 2(B) and Figs. 10a, 10b, it is clear that because of the low cost and equivalent nutrient content, a large amount of chasing feed was selected in the algorithm at three points (P1, P2, P3). In addition, the chupa feed has a high ME content, which explains that this constraint is satisfied at these three points. In P1 and P2, the selection of molasses with a reasonable Ca content compared to other nutrients indicates an excess content of Ca at this point. The excess Ca is initially due to the selection of cheaper raw materials, usually with a higher Ca content, since the Ca content is moderate and other nutrient-rich products are usually more expensive.

2.1.2. Cows: Case 2

In case 2, the Pareto-optimal line is presented in Fig. 3(A) together with P1, P2, and P3. The different feed stocks selected at these points are shown in FIG. 3(B). 3(C) to 3(H) show the relationship between feed cost and individual nutritional components of the feed. As noted in Case 1, OL and OLC represent, respectively, the cost domains in which the prescribed and corresponding nutritional requirements are met.

In Fig. 3(A), a small deviation from feed requirement was observed between 3600KRW and 5000KRW, and it is clear that this is a significant fluctuation in cost. Between P1 and P2, Ca is inversely related to all other requirements. In other words, as the feed cost increased, the nutrient requirements such as Met, Lys, P, and MP in the feed decreased while Ca increased.

As in case 1, case 2 also recorded the satisfaction of ME at low cost (P3), showing some stability from P3 to P1. As in case 1, depending on the user's needs, different solution areas may be selected, and the associated costs may vary. In the selected raw material in Fig. 3(B), the algorithm also selected feed for chasing at these points (P1 to P3).

It also verifies the degree of satisfaction of ME at all investigated points. Compared to the higher levels of molasses selected in P1 and P2, higher amounts of whole barley were selected in P3. Compared with the relatively expensive molasses, which has only measurable levels of ME, Ca, and P, the low cost and high nutrient content of whole barley (Fig. 3(C), (F), (G)) was recorded in P3 It explains the excess nutrients (approximately defined content reported in Fig. 3 (D), (E), (G), (H) and P1 and P2). This shows that the algorithm tries to meet the first objective, cost, and then tries to balance the prescribed nutrients.

2.1.3. Cows: Case 3

4 summarizes the results of case 3. In P1, an approximation of the prescribed requirement was observed. However, while moving to the left to P2, Met ((D) in FIG. 4), Lys ((E) in FIG. 4), and MP ((H) in FIG. 4) deviated from the prescribed value, but the prescribed level of P was ( 4(G)) was satisfied. However, moving left to P3, all other nutritional requirements, except for Ca, deviate from the prescribed requirements. However, if the focus is only on ME, choosing P3 will result in a 220% reduction in cost compared to P2.

As in cases 1 and 2, large amounts of whole barley in P3 and high amounts of molasses in P1 and P2 (Fig. .

2.2.1. Beef Cattle: Case 1

For beef cattle, in different combinations in different countries, two main feed types are used, Rhage and Conc., at different stages of animal growth, with one type dominating the other. do. Beef cattle are usually fed mainly as roughage, after weaning, until the final stage in which more concentrated feeds are fed. The main role of the enriched feed is to provide the concentrated nutrition and energy in the animal feed. Worldwide, a variety of grains and grains and their by-products constitute the thick feed fed to animals. Since grains and kernels are often more expensive types of feed, substituting some with by-products such as distillery can help reduce costs. The advantage is that, from an economic and physiological point of view, it is possible to increase the digestibility of the feed (a limiting factor for high-dose feeds) with relatively small amounts of grain and grain, without sacrificing animal growth or performance. In addition, other cost-effective, concentrated forms of nutrients, such as supplements (see Figures 10a, 10b), can be used to compensate for any nutritional deficiencies as needed. Therefore, the constraint on the amount of fed enriched feed can be easily relaxed. In the present invention, as shown in Table 3, the inventors conducted experimental simulations for three different levels of concentrated feed and fixed forage. 5a and 5b show simulation results obtained from three levels (level1 to level3) of enriched feed for the first stage of Korean beef cattle.

Each column in FIGS. 5A and 5B represents a result corresponding to each of the three levels considered. The defined best-satisfied area is denoted by OR, and the optimal area cost is denoted by ORC.

Level 1 represents the nutritional and feed types of beef cattle recommended by the Rural Development Administration of Korea. At level 1, all prescribed requirements were met at P1, with the exception of forage, which was not possible at any feed cost. Moving to the left, with P2, the defined CP, TDN, P, DMI (Fig. 5a,b, level 1 (C), (D), (F), (I)) were met, and Ca (Fig. 5a, b, Level 1 (E)) and Conc. (Fig. 5a,b, level 1 (H)) deviates from the prescribed values, whereas only P3 meets the recommended Ca (Fig. 5a,b, level 1 (E)). became 5A (B) , the dominant raw material selected in P1 and P2 was corn gluten feed, whereas in P3 it was molasses. However, a higher amount of corn gluten diet was selected in P1 than in P2. This may be due to the molasses replacing the missing nutrients in P2. In addition, the selection of corn gluten feed with a lower Ca content compared to molasses at P3 resulted in an excess of Ca at P3 (Fig. 5a, level 1, (A)). Emphasizing TDN, Ca, P, Conc., and DMI (Fig. 5a,b, level 1 (D)-(H), (I)), the selection of the point P2 where they are met is at a cost of 125% from P1. Savings will be possible, where all nutrients specified except for roughage are met.

In level 2 of Figure 5a,b, the present inventors Conc. Nutrient deviation curves with moderated requirements were investigated (Fig. 5a, level 2 (A)). The results showed a trade-off between rough and enriched feed. In this case, the demand for enriched feed stipulated by the Rural Development Administration of Korea was reduced by 50%, while the roughage was fixed. In P1, with different ingredients, brewer's wort was recorded as having a higher selection (alfalfa hay, cornmeal, confectionery by-products). This explains why P1 was a better feed solution with a defined nutrient content. As explained in the previous section, in Level 2, various feed solutions with similar cost and different nutrient contents were recorded. Two solutions (P2 and P3) were selected from these domains and analyzed. For P2 and P3, brewers weighing 2.60 kg and 2.74 kg were selected, respectively, and for limestone, 5.22 kg and 5.21 kg were selected in the order of P2 and P3. However, the larger the amount of brewer's wort in P2, the lower the cost and higher nutrient content than in the P3 area. Sudan Grass and corn gluten diets were selected in P1, whereas they were not seen in the other two sites. The selection of these two components helped to meet the prescribed amounts for TDN, P, and roughage, which were not met in P2 and P3.

In level 3 of Figs. 5a and b, different Pareto fronts were obtained (Fig. 5a, level 3 (A)). In P1, all prescribed amounts of nutrients were fully met (Fig. 5a,b, level 3 (C)-(H)). However, moving left from P1 to P2, at point P2, only the prescribed amount for roughage was not met ((G) in Fig. 5B). The roughage content at the point P2 did not reach 0.02 kg. This shows that if 0.02 kg is an acceptable level, cost savings of 14% can be recorded. As in level 1, only the prescribed amount of Ca was met in P3. Level 3 results further demonstrate the trade-off between forage and forage, which requires an offsetting effect, primarily documented in feed formulation. At level 3, different amounts of cornmeal were chosen at three points (P1 to P3) because of their low cost and nutrient content compared to other by-products. Also, compared to other low-cost by-products, cornmeal contains the highest TDN content, which is the most important in beef feed formulations. Italian ryegrass and confectionery by-products were selected from P1 and P2 to balance the feeding amount. Compared with P1, the smaller selection of Italian ryegrass in P2 resulted in insufficient forage requirements stipulated in P2.

5a and b, it is observed that the nutritional requirements of the enriched feed and the forage are in conflict with each other, and in this way, it is possible to find a feed formulation that satisfies the forage while the demand for the rich feed is relaxed (from level 1 to level 3) can do. In addition, the cost of feed for which all requirements were met continued to decrease. In other words, at level 1, it was impossible to find a feed formulation that could satisfy all requirements even at a cost exceeding 4000KRW. However, at Levels 2 and 3, an algorithm has become possible to find a feed formulation that satisfies all requirements at a cost between about 2500KRW and 1450KRW. By comparing the three levels, it was found that the cost of the feed formulated in level 3 was 30% lower than that of level 2 and 65% lower than that of level 1. The feed formulation of level 2 was 50% lower than that of level 1.

2.2.1. Beef Cattle: Case 2

P1 and P2 showed a close distance to P2 in the Pareto front, and the cost was 13% lower (FIG. 6(A)). However, P2 lacked 0.3 kg in the prescribed TDN (FIG. 6(D)) content. Although the P1 solution for roughage fell short of the prescribed amount by 50%, P2 did not meet the prescribed amount by 100%. Also, the excess of P in P2 was better than the excess of P1. In this growth stage (case) 0.12 kg, 0.33 kg, and 9.61 kg were selected for P1, P2 and P3, respectively. A large amount of limestone selected in P3 can satisfy DMI ((I) in FIG. 6) and Ca ((E) in FIG. 6) due to the high content of Ca ((E) in FIG. 6) and lack of moisture content. made it For both P1 and P2, similar amounts of corn gluten diets were selected. The rice straw selected in P1 made it possible to better meet the forage at this point compared to P2.

2.2.2. Beef Cattle: Case 3

In the feed formulation of beef cattle case 3, four distinct points were selected and analyzed (FIG. 7(A)). P1 reasonably satisfied all prescribed nutrients except for roughage. However, moving from P1 to P2 to the left, the concentrated feed deviated from the prescribed amount by 18%, but the cost was reduced by 33%. As in Case 1, Level 2, similar trends were recorded in P3 and P4. In the results of Case 3, for the reasons explained in the formulation of Case 1, all the prescribed conditions in P2 were excluded, except for the enriched feed ((H) in FIG. 7) and the roughage ((G) in FIG. showed that the nutrients were met. Various raw materials and quantities were selected at different points. The main raw materials include corn gluten feed at P2 and P1, corn, molasses at P2, P3, and limestone at P4.

2.2.3. Beef Cattle: Case 4

The final case analyzed for beef feed formulations in the present invention was similar to the Pareto front of Case 3. P1 met all recommended nutritional requirements except for roughage. As in case 2, P2 ((A) in FIG. 8) was a satisfactory solution, except for the concentrated feed content, which was 21% insufficient ((H) in FIG. 8). All points did not meet the prescribed value for roughage (FIG. 8 (G)). As in case 3, P3 and P4 had different solutions and slightly different costs, but only met the recommended DMI at two points (Fig. 8(I)). Corn gluten feed, cottonseed meal, molasses and salt were the main raw materials selected in P1, soybean and wheat husks were the main raw materials in P2, and limestone of 5.41 kg, 5.53 kg and 1.23 kg were selected in P2, P3 and P4, respectively.

In the present invention, the existing feed formulation approach, which is a single-purpose pharmaceutical problem, has been formulated as a multi-purpose problem. The multi-purpose formula was based on observations from previous studies that a) mitigating some nutrient requirements did not affect animal growth or performance, and b) meeting nutrient requirements and cost of feed might sometimes be at odds. Thus, in the proposed multi-purpose feed formulation, feed cost and deviation of nutrients from prescribed requirements were considered for two purposes. Also, the use of the evolutionary multipurpose optimization (NSGA-II) method provided a full set of construct solutions in one run. The availability of a full Pareto Front helped the feed formulator to make better decisions, as it provided a relationship between several nutrients and the associated feed cost. Experimental simulations using different examples of cow and beef feed formulations demonstrated the applicability of the proposed framework.

The method described above may be implemented as a hardware component, a software component, and/or a combination of the hardware component and the software component. For example, the methods, apparatus and components described in the embodiments may include, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate (FPGA). array), a programmable logic unit (PLU), a microprocessor, or any other device capable of executing and responding to instructions, may be implemented using one or more general purpose or special purpose computers. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. A processing device may also access, store, manipulate, process, and generate data in response to execution of the software. For convenience of understanding, although one processing device is sometimes described as being used, one of ordinary skill in the art will recognize that the processing device includes a plurality of processing elements and/or a plurality of types of processing elements. It can be seen that it can include For example, the processing device may include a plurality of processors or one processor and one controller. Other processing configurations are also possible, such as parallel processors.

Software may include a computer program, code, instructions, or a combination of one or more thereof, which configures a processing device to operate as desired or is independently or collectively processed You can command the device. The software and/or data may be any kind of machine, component, physical device, virtual equipment, computer storage medium or apparatus, to be interpreted by or to provide instructions or data to the processing device. may be embodied in The software may be distributed over networked computer systems and stored or executed in a distributed manner. Software and data may be stored in one or more computer-readable recording media.

The method according to the embodiment may be implemented in the form of program instructions that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the embodiment, or may be known and available to those skilled in the art of computer software. Examples of the computer-readable recording medium include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic media such as floppy disks. - includes magneto-optical media, and hardware devices specially configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like.

As described above, although the embodiments have been described with reference to the limited embodiments and drawings, various modifications and variations are possible from the above description by those skilled in the art. For example, the described techniques are performed in an order different from the described method, and/or the described components of the system, structure, apparatus, circuit, etc. are combined or combined in a different form than the described method, or other components Or substituted or substituted by equivalents may achieve an appropriate result.

The above description is merely illustrative of the technical spirit of the present invention, and various modifications and variations will be possible without departing from the essential characteristics of the present invention by those skilled in the art to which the present invention pertains. Accordingly, the embodiments disclosed in the present invention are for explanation rather than limiting the technical spirit of the present invention, and the scope of the technical spirit of the present invention is not limited by these embodiments.

Therefore, the scope of protection of the present invention should be interpreted by the following claims rather than being limited by the above-described embodiments, and all technical ideas within an equivalent range should be interpreted as being included in the scope of the present invention.

Claims (4)

In a feed formulation method that minimizes feed cost and satisfies nutritional requirements for dairy cows,
The method satisfies the following Objectives 1 and 2 for cows,
Purpose 1: Feed cost

Objective 2: Deviation from prescribed nutritional requirements
Minimize｜MP - M｜+ ｜Lys - N｜ + ｜Ca - O｜ + ｜P - Q｜ +｜ME - R｜ + ｜Met - S｜
where n is the number of components under consideration, wi is the weight in kg, costi is the cost of feed ingredients (KRW/kg), MP is metabolic protein, Lys is lysine, Ca is calcium, P is phosphorus, ME is Metabolic energy, Met represents methionine, M, N, O, Q, R, S define the requirements for MP, Lys, Ca, P, ME, Met, respectively, and the requirements depend on the age and weight of the cow characterized by different
A feed formulation method that minimizes feed cost and meets nutritional requirements for dairy cows.
According to claim 1,
NSGA-II, an evolutionary multi-objective optimization algorithm, is used to optimize the multi-objective expression.
A feed formulation method that minimizes feed cost and meets nutritional requirements for dairy cows.
In a feed formulation method that minimizes feed cost and satisfies nutritional requirements for beef cattle,
The method satisfies the following Objective Expressions 3 and 4 for beef cattle,
Objective 3: Feed Cost

(4)
Objective 4: Deviation from prescribed nutritional requirements
Minimize｜DMI - A｜+ ｜CP - B｜+ ｜TDN - C｜ + ｜Ca - D｜+｜P - E｜+ ｜Rhage - F｜+ ｜MC - G｜+ ｜Conc. - H｜
where n is the number of ingredients under consideration, wi is the weight in kg, costi is the cost of feed ingredients (KRW/kg), DMI is dry matter intake, CP is crude protein, TDN is total digestible nutrients, and Ca is calcium , P is phosphorus, Rhage is roughage, MC is moisture content, Conc. is rich feed, A, B, C, D, E, F, G, H are DMI, CP, TDN, Ca, P, Rhage, A requirement for Mc, Conc.
A feed formulation method that minimizes feed cost and satisfies nutritional requirements for beef cattle.
4. The method of claim 3,
NSGA-II, an evolutionary multi-objective optimization algorithm, is used to optimize the multi-objective expression.
A feed formulation method that minimizes feed cost and satisfies nutritional requirements for beef cattle.

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