CN110378615B - A complete information game method for product configuration - Google Patents

Abstract

The invention aims at rapidly obtaining personalized customized products under limited resources in a product configuration process, and particularly relates to a complete information game method for product configuration. The technical scheme provided by the invention is as follows: firstly, dividing product parts into different functional modules according to user demands, taking each functional module as a central office, taking prices of alternative schemes of the functional modules as a strategy set, solving Nash balance in a game model of the product configuration by utilizing a genetic algorithm after determining a profit function, and solving contradiction between product performance and prices, thereby obtaining a product configuration scheme which best meets the user demands under limited resources. Taking the configuration of the civil unmanned aerial vehicle as an example, the method is verified to solve the personalized customization problem under the limited resources. The invention can help enterprises to quickly obtain the product configuration scheme meeting the requirements of users.

Description

A complete information game method for product configuration

Technical field

The invention relates to the field of product configuration, aiming at the problem of quickly obtaining personalized customized products under limited resources, and specifically relates to a complete information game method for product configuration.

Background technique

Since the reform and opening up, my country's manufacturing industry has developed rapidly. "Made in China 2025" has put forward higher requirements for my country's manufacturing industry. Enterprises need to continuously shorten the design and production cycle in the product life cycle to adapt to changing user needs.

Configurable products are a new concept that can be used to adapt to the above-mentioned changes and trends. Configurable products include some predefined components and rules between components, so that the combination of different components can meet the requirements of the rules. There are products required by different users, so by designing configurable products and configuring the configurable products through users and sales staff during the sales process, companies can obtain and produce products that meet user needs.

However, because modern industrial products are very complex in structure and function, complex products such as airplanes have hundreds of thousands of parts, relatively simple products such as cars have tens of thousands of parts, and simple daily products such as personal computers have several There are hundreds of parts, and there are complex constraint relationships between these parts. Therefore, it is difficult or even impossible to manually configure these products, and manual configuration is also prone to errors. Fortunately, with the computer With the development of information technology, computers can be used to build automatic configuration information systems to automatically and quickly complete the configuration tasks of products with complex structures and functions. This not only reduces the production iteration time of the product, but also ensures the correctness of the configuration. Product configuration methods based on user needs are an important means for companies to shorten product design cycles and improve customer satisfaction. The core issue in the product configuration process is the satisfaction of user needs. Only configuration solutions that meet user needs have actual value.

Contents of the invention

This invention is aimed at quickly obtaining personalized customized products with limited resources during the product configuration process. It introduces game theory to solve the conflict between product performance and price cost, and helps enterprises quickly obtain product configuration solutions that meet user needs.

In order to achieve the purpose of the present invention, the technical solutions provided by the present invention are:

A product configuration complete information game method. First, product parts are divided into different functional modules according to user needs. Each functional module is a player, and the prices of functional module alternatives are used as a strategy set. After determining the revenue function, the genetic algorithm is used to solve it. The Nash equilibrium in the product configuration game model resolves the contradiction between product performance and price, thereby obtaining the product configuration solution that best meets user needs under limited resources.

Further, the above method includes the following steps:

(1) Establish a DSM matrix. Taking components as row elements of the matrix, and the row and column elements of the square matrix are the same, if the components r _i in the DSM rows and the components c _i in the columns are combined to jointly provide a certain function of the product, then the matrix element m _ij =1 , otherwise m _ij =0, establish the DSM matrix M = [m _ij ], (i = 1, 2, L, m; j = 1, 2, L, m) according to this method

(2) Perform DSM clustering on the divided functional modules to form multiple sub-modules;

a) Identification and separation of independent elements. An independent element is an element in which all elements in its row and column are 0. The DSM is checked and moved to the end of the matrix;

b) Column transformation. Perform a row-column transformation on the DSM so that the non-zero elements in the DSM are as close as possible to the main diagonal of the DSM;

c) Clustering division. Select the rectangular blank area with the highest height in the lower triangular matrix, and establish a rectangular coordinate system with the upper right corner vertex of the blank area as the origin. This rectangular coordinate system divides the DSM into four quadrants. If there are columns truncated by the x-axis on the right side of the y-axis of the coordinate system, select the rectangular blank area with the next highest height in the lower triangular matrix, and perform the above operation again until there are no columns truncated by the x-axis in the area on the right side of the y-axis. At this time, the area in the second quadrant of the coordinate system is a sub-module obtained after the execution of the algorithm;

d) For the sub-blocks in the fourth quadrant, loop through step 3 until the x-axis coincides with the lower boundary of the DSM.

(3)Interpretation of DSM. All components in the same sub-module in DSM jointly provide a certain function of the product. Therefore, the i-th sub-module of DSM can be used as a whole as a player in the product configuration game model, and is moved to each last The independent element alone becomes a player.

If a product consists of m parts, after module division, all the parts of the product are combined into n different functional modules, then the set of players in the product configuration game process can be expressed as: P = { p _i |i∈N,i≤n}, p ₁ -p _n are n functional modules of the product.

(4) Strategy set in the model. During the configuration process, a product function module (player) is allowed to have multiple alternatives, and each alternative is a strategy for the player. Since this product configuration game model is driven by price factors, different strategies can be expressed in terms of the price of each alternative.

Assume that a certain functional module p _i contains j alternatives, use represents the price of the alternative, then in the product configuration game model, for this player p _i , its strategy set can be expressed as:/> is the jth strategy of player p _i ;/> is the price of the jth strategy of player p _i . Therefore, the strategy set of the product configuration game model is: S={S _i |i≤n}.

(5) Determine the profit function of the strategy according to user needs. Use the similarity comparison algorithm to compare user needs with the performance of product parts to determine whether existing product parts meet user needs. Based on the mapping relationship between customer needs and product structural unit characteristics in the product configuration process, a calculation method for attribute similarity and a calculation formula for entity similarity are proposed.

Assuming that the performance indicators of the product's alternative function modules fully match the user's needs, the similarity value is 1. Therefore, the performance indicators can be normalized and mapped to the [0,1] interval, and the following formula can be used to calculate the similarity Solution:

① If the product attributes are numerical, x _i is the value of the user demand parameter value mapped to the interval [0,1], and y _i is the value of the corresponding attribute parameter in the existing product configuration instance mapped to the interval [0,1]. value, then its similarity calculation formula is:

② If the product attributes are Boolean, x _i is the status value of the user demand parameter, and y _i is the status value of the corresponding attribute in the existing product configuration instance, then the similarity calculation formula is:

When the player p _i chooses to implement a certain strategy, he chooses to pay the price cost of the strategy to obtain the performance benefits of the module. Therefore, for a certain strategy of player p _i Its income function can be expressed as:

is the price cost of the strategy; C is the total price cost defined by the user;/> This is the sum of the price costs spent by the other players in the strategy except player p _i .

To sum up, for a certain group of players’ strategy combination, the income of the product allocation game model is:

(6) Use genetic algorithm to solve the Nash equilibrium problem in the product configuration process.

use Represents a strategy of player p _i in the product configuration process, assuming/> It is a Nash equilibrium strategy in the product allocation process. When any player's strategy choice deviates from the Nash equilibrium alone, its own income will not increase as a result, that is:/> It means that under the equilibrium solution S*, there is a strategy used by players in a certain game/> Replace the original strategy/>

In order to more conveniently calculate the income of the product allocation game model under each group of player strategy combinations, the income of the product allocation game model is simplified as:

At this time, according to the properties of the Nash equilibrium solution, the mixed payoff function in the game is defined as: 0|j＝1,2,…m}

Obviously, if and only if the game is a Nash equilibrium solution, the mixed payoff function H(S) takes the minimum value 0. Since the total price exceeds the user's needs, the solution obviously does not meet the user's needs, that is, when When , the individual fitness value is 0, and the price cost limit is introduced into the fitness value function. Select a sufficiently large real number N _max and define the fitness value of the genetic algorithm as:

Obviously, the fitness is highest when S obtains the Nash equilibrium solution.

Using the real number coding method, the alternative numbers of each product functional module are used as genes, and then these genes are connected into a complete chromosome of the strategy group _Si . Multiple chromosomes composed of different player strategies will hybridize and mutate respectively during the calculation iteration process, resulting in new mixed situations and mixed strategies. According to the process of biological evolution, the chromosome group with higher fitness will occupy the genetic advantage, thereby obtaining the Nash equilibrium solution.

The beneficial effects of the present invention are:

Game theory ideas are introduced into product configuration, and each functional module in the product configuration process is regarded as a player, and a product configuration game model is established. The genetic algorithm is used to solve the Nash equilibrium of the game model. It has good convergence and can quickly calculate the Nash equilibrium in a multi-player game. When the game model reaches Nash equilibrium, the product configuration plan is the maximum equilibrium of product performance under limited cost. The use of this method to configure civilian drones proves the effectiveness and feasibility of this configuration method, and can obtain user-satisfied product configuration solutions, which can help enterprises quickly configure product instances that meet user needs and help enterprises adapt to user personalization. need.

Description of the drawings

Figure 1 shows the establishment and clustering of DSM, where Figure 1(a) is the parts DSM and Figure 1(b) is the clustering matrix.

Figure 2 is the division of UAV functional modules. Figure 2(a) is a DSM composed of UAV components, and Figure 2(b) is the clustering result.

Figure 3 is the calculation result of individual fitness of the product configuration game model.

Specific implementation plan

The technical solution provided by the present invention is: firstly divide the parts into modules according to the system structure of the aerial photography drone, establish a DSM composed of the drone parts, and cluster them, and then interpret the DSM to combine all the parts into modules. The parts of the human machine are combined into different modules according to the requirements. Use the similarity comparison algorithm to compare user needs with the performance of product parts to determine whether existing product parts meet user needs. Finally, the genetic algorithm is used to calculate, and the individual fitness of the product configuration game model is obtained, and the Nash equilibrium solution of the product configuration game model is found.

The method of the present invention will be further described below in conjunction with the accompanying drawings and examples.

Implementation model library: aerial drone.

The technical solution of the present invention to solve the technical problem is: first divide the aerial photography drone into modules, establish a DSM composed of drone parts, see Figure 1 (a), and cluster them, see Figure 1 ( b) Obtain the set of players in the product configuration. The performance parameters and user requirements of the functional modules are brought into the formula for similarity calculation. Genetic algorithm is used for coding, functional module price and similarity data are input, individual fitness value is calculated, and the Nash equilibrium solution of the product configuration game model is obtained.

Taking the configuration of a certain aerial photography drone as an example, the user needs to configure an aerial photography drone with a wheelbase of 450mm, a controllable distance of 1000m, the ability to shoot 4K videos, and a battery capacity of 1500mAh. Since he is a novice user, he hopes The drone has a low battery protection function, and the price budget is up to 3,000 yuan. To sum up the above indicators, the specific implementation steps are as follows:

(1) Establish a DSM composed of UAV components, as shown in Figure 2(a), and cluster it. The clustering result is shown in Figure 2(b). Interpreting the DSM, the ESC, motor, propeller, and frame are merged into the shape module, the flight control and GPS are merged into the control module, the gimbal, camera, and tripod are merged into the shooting module, while the remote control and battery become Independent module, based on which the player set of product configuration is obtained as P = {P _moving , P _controlling , P _{photographing} , P _remote , P _electric }.

(2) According to market research, the performance parameters and selling prices of some UAV functional modules are shown in Table 1. According to user needs, the performance parameters corresponding to each functional module are shown in Table 2. Substitute the performance parameters and user requirements of the functional modules into the formula with formula/> The data obtained after calculating the similarity and mapping it to the [0,1] interval is shown in Table 3.

Table 1 UAV functional module prices

Table 2 UAV functional module performance parameters

Table 3 Performance similarity of UAV functional modules

(3) Encode the alternative number of the functional module as the gene of the genetic algorithm, and input the functional module price and similarity data into the program to calculate the individual fitness value. Set the population number to 40, the number of iterations = 200, and the hybridization probability =0.5, mutation probability =0.1, use genetic algorithm to calculate, and the result is shown in Figure 3. According to the algorithm output results, the functional module selection corresponding to the product configuration scheme that finally achieves Nash equilibrium is {2, 1, 3, 1, 2}, which can meet the user's personalized customization needs for drone products.

For those of ordinary skill in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims (1)

1. A product configuration complete information game method, which is characterized by first dividing the product parts into different functional modules according to user needs, with each functional module as a player, and the price of the functional module alternative as a strategy set to determine the income After the function, the genetic algorithm is used to solve the Nash equilibrium of the strategy set, to resolve the contradiction between product performance and price, so as to obtain the product configuration solution that best meets user needs under limited resources; The specific method includes the following steps: (1) Establish a DSM matrix: use components as row elements of the matrix, and the row and column elements of the square matrix are the same. If the components r _u in the DSM rows and the components r _v in the columns are combined to provide a certain function of the product, Then the matrix element a _uv =1, otherwise a _uv =0, according to this method, the DSM matrix A=[a _uv ], (u=1,2,...,z; v=1,2,..., is established according to this method z); (2) Perform DSM clustering on the divided functional modules to form multiple sub-modules; a) Identification and separation of independent elements: An independent element refers to an element where all elements in its rows and columns are 0. Check the DSM and move it to the end of the matrix; b) Row-column transformation: Perform row-column transformation on the DSM to make the non-zero elements in the DSM as close as possible to the main diagonal of the DSM; c) Clustering division: Select the rectangular blank area with the highest height in the lower triangular matrix, and establish a rectangular coordinate system with the upper right corner vertex of the blank area as the origin. This rectangular coordinate system divides the DSM into four quadrants; if the right side of the y-axis of the coordinate system If there are columns truncated by the x-axis, select the rectangular blank area with the next highest height in the lower triangular matrix, and perform the above operation again until there are no columns truncated by the x-axis in the area on the right side of the y-axis. At this time, the second highest value in the coordinate system The area in the quadrant is a sub-module obtained after the algorithm is executed; d) For the sub-blocks in the fourth quadrant, perform step 3 in a loop until the x-axis coincides with the lower boundary of the DSM; (3) Interpretation of DSM: All components in the same sub-module in DSM jointly provide a certain function of the product, so the i-th sub-module of DSM can be used as a whole as a player in the product configuration game model. Each independent element moved to the end becomes a player alone. If a product consists of m parts, after module division, all the parts of the product are combined into n different functional modules, then The set of players in the product configuration game process can be expressed as: P = {p _i |i∈N,i≤n}, where p ₁ -p _n are the n functional modules of the product; (4) Strategy set in the model; Assume that a certain functional module p _i contains m alternatives, use represents the price of the alternative, then in the product configuration game model, for this player p _i , its strategy set can be expressed as:/> is the jth strategy of player p _i ; is the price of the jth strategy of player p _i , so the strategy set of the product configuration game model is: S={S _i |i≤n}; (5) Determine the profit function of the strategy according to user needs; Assuming that the performance indicators of the product's alternative function modules fully match the user's needs, the similarity value is 1. Therefore, the performance indicators can be normalized and mapped to the [0,1] interval, and the following formula can be used to calculate the similarity Solution: ① If the product attributes are numerical, x _i is the value of the user demand parameter value mapped to the interval [0,1], and y _i is the value of the corresponding attribute parameter in the existing product configuration instance mapped to the interval [0,1]. value, then its similarity calculation formula is: ② If the product attributes are Boolean, x _i is the status value of the user demand parameter, and y _i is the status value of the corresponding attribute in the existing product configuration instance, then the similarity calculation formula is: When player p _i chooses to implement a certain strategy, he chooses to pay the price cost of the strategy to obtain the performance benefits of the module. Therefore, for a certain strategy of player p _i Its income function can be expressed as: is the price cost of the strategy; C is the total price cost defined by the user;/> is the sum of the price costs spent by the other players in this strategy except player p _i ; To sum up, for a certain group of players’ strategy combination, the income of the product allocation game model is: (6) Use genetic algorithm to solve the Nash equilibrium problem in the product configuration process.