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# Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model

###### Accepté: 17 Apr 2022
Détails du magazine
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Magazine
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2444-8656
Première parution
01 Jan 2016
Périodicité
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Anglais
Solving and analyzing the mathematical model of fuzzy constrained programming
Definition 1

For the construction and application of logistics public information management platform, it is easy to meet the phenomenon of ambiguity and ambiguity during the actual operation. At this time, using the mathematical model of fuzzy constraint planning as a solution tool can not only put forward effective decisions for optimization problems, but also master the optimal solution. Therefore, before studying the application demonstration of logistics public information management platform based on the mathematical model of fuzzy constraint programming, we should first understand the fuzzy and linear programming solution of Han elastic constraint.

Theorem 1

Suppose E represents the fuzzy set in the real number field R, and the membership function refers to E(x), xR. Suppose E (x) satisfies the condition E(0) = 1, then E (x) is a single increment right continuous function on the interval [−1, 0], and a single drop left continuous function on the interval (0,1). When x<−1 and x>−1 satisfy the condition, it is called fuzzy structural element in real number field R. Suppose E refers to any fuzzy structural element on R, and there exists membership function E (x), then F (x) is monotone bounded function on interval, and F (E) refers to bounded closed fuzziness on R, and the corresponding membership function is E (F−1 (x)).

Proposition 2

At this time, F−1 (x) refers to the rotationally symmetric function of relevant variables X and y. If f (x) is continuous and strictly monotonic, then f minus 1 (x) is the inverse of f (x). On the contrary, for a given regular fuzzy structure element E and any bounded closed fuzzy number Ā, there exists a monotone bounded function f on the interval [−1, 1], and thus the condition λ = f(E) is satisfied, then the fuzzy number Ā is said to be composed of structure element E. According to the analysis of the fuzzy linear programming solution with elastic constraints proposed by Verdegay et al., in general, the fuzzy linear programming model with elastic constraints is shown as follows: $maxZ=cx{ (Ax)i≤bi,i=1,2,…,mx≥0$ \eqalign{ & \max Z = cx \cr & \left\{ \matrix {\left( {Ax} \right)_i} \leqslant {b_i},i = 1,2, \ldots ,m \hfill \cr x \geqslant 0 \hfill \cr \endmatrix \right. \cr}

Lemma 3

The above formula meets the following conditions: $c,x∈Rn$ c,x \in {R^n}

A = (aij)m×n represents the real matrix, bi ∈(bi, bi + pi), pi represents tolerance, (Ax)ibi represents the JTH fuzzy constraint, and the corresponding membership function refers to: $μi(x)={ 1,(Ax)i≤bi1−[ (Ax)i−bi ]/pi,bi≤(Ax)i≤bi+pi0,(Ax)i≥bi+pi$ {\mu _i}(x) = \left\{ \matrix 1,{\left( {Ax} \right)_i} \leqslant {b_i} \hfill \cr 1 - \left[ {{{\left( {Ax} \right)}_i} - {b_i}} \right]/{p_i},{b_i} \leqslant {\left( {Ax} \right)_i} \leqslant {b_i} + {p_i} \hfill \cr 0,{\left( {Ax} \right)_i} \geqslant {b_i} + {p_i} \hfill \cr \endmatrix \right.

Conjecture 5

Verdegay et al. proposed an equivalent classical parameter programming model based on the above programming model in their study, as shown below: $maxz=cx{ x∈Xa((Ax)i≤bi+(1−a)pi,i=1,2,…,m)x≥0,∀a∈[ 0,1 ]$ \eqalign{ & \max z = cx \cr & \left\{ \matrix x \in {X_a}\left( {{{\left( {Ax} \right)}_i} \leqslant {b_i} + (1 - a){p_i},i = 1,2, \ldots ,m} \right) \hfill \cr x \geqslant 0,\forall a \in\left[ {0,1} \right] \hfill \cr \endmatrix \right. \cr}

In the above formula, Xα = {x|μi(x) ≥ α, x ≥ 0}, α ∈ [0,1] represents satisfaction.

Think of Ñc(R) as the bounded closed fuzzy whole. Corresponding definitions and properties are divided into the following points:

Example 6

First, it is assumed that the structure element of bounded fuzzy numbers refers to Ã = f(E), where E represents a definite fuzzy structure element and f represents the monotone function on the interval [−1,1], thus it can be obtained: $ρ(A˜)=∫−11ω(x)f(x)dx$ \rho \left( {\tilde A} \right) = \int_{ - 1}^1 {\omega (x)f(x)dx}

In the above formula, w (x) represents the weight function of bounded fuzzy number Ã, which actually meets the condition of ∀x ∈ [−1,1], ω(x)∈ [0,1], so ρ(Ã) is the weighted eigenvalue of fuzzy number Ã, which can also be called eigennumber of.

Second, assuming Ã1, $A˜2∈N¯c(R)$ {\tilde A_2} \in {\bar N_c}(R) , the corresponding structural element expression formula is: $A˜i=fi[ E ],i=1,2$ {\tilde A_i} = {f_i}\left[ E \right],i = 1,2

Note 7

In the above formula, E represents a given regular fuzzy structure element, the corresponding weight function is W (x), f1 and F2 represent the same order monotone function on the interval, and the order relation of the two fuzzy numbers is defined as follows: $A˜1≤A˜2⇔ρ(A˜1)≤ρ(A˜2)$ {\tilde A_1} \leqslant {\tilde A_2} \Leftrightarrow \rho \left( {{{\tilde A}_1}} \right) \leqslant \rho \left( {{{\tilde A}_2}} \right)

In the above formula, ≤ represents the weighted order of fuzzy numbers. At this point, it can be determined through analysis that ≤ represents the full order of ÑC(R).

Among them, ρ conforms to the following properties:

On the one hand, assuming that the condition kR, ÃÑC(R) is met, it can be obtained: $ρ(kA˜)=kρ(A˜)$ \rho \left( {k\tilde A} \right) = k\rho \left( {\tilde A} \right)

On the other hand, assuming that the condition Ã1, $A˜2∈N¯c(R)$ {\tilde A_2} \in {\bar N_c}(R) is met, it can be obtained: $ρ(A˜1+A˜2)=ρ(A˜1)+ρ(A˜2)$ \rho \left( {{{\tilde A}_1} + {{\tilde A}_2}} \right) = \rho \left( {{{\tilde A}_1}} \right) + \rho \left( {{{\tilde A}_2}} \right)

Open Problem 8

According to the above definition analysis, it can be seen that the succession of bounded fuzzy number Ã is: $supp(A˜)={ x|μλ(x)≥0 }$ \sup p\left( {\tilde A} \right) = \left\{ {x|{\mu _\lambda }(x) \geqslant 0} \right\}

The weight function w (x) represents the corresponding importance of each point on supp (Ã), the bearing set of bounded fuzzy numbers Ã.

For example, under the condition of ω(x) = 1 or ω(x) = E(x), the natural order and structural element weighted order of fuzzy numbers can be defined according to the order relation formed by the above definition.

If the weight function w (x) satisfies the condition $∫−11ω(x)dx=1$ \int_{ - 1}^1 {\omega (x)dx = 1} , then w (x) represents the standard weight function of the bounded fuzzy number Ã. For example, $ω(x)=34(1−x2)$ \omega (x) = \frac{3}{4}\left( {1 - {x^2}} \right) , $ω(x)=12(1+x)$ \omega \left( x \right) = \frac{1}{2}\left( {1 + x} \right) , $ω(x)=12(1−x)$ \omega \left( x \right) = \frac{1}{2}\left( {1 - x} \right) can be regarded as the standard weight function of bounded fuzzy numbers, from which three different forms of order relation can be obtained.

According to the above analysis of the weighted ordering of fuzzy numbers, the actual solving process of linear programming is shown as follows: the fuzzy linear programming model with elastic constraints is: $maxZ˜=e˜x{ d˜ix≤D˜i,i=1,…,n1ejx≤E^j,j=1,…,n2x≥0$ \eqalign{ & \max \tilde Z = \tilde ex \cr & \left\{ \matrix {{\tilde d}_i}x \leqslant {{\tilde D}_i},i = 1, \ldots ,{n_1} \hfill \cr {e_j}x \leqslant {{\hat E}_j},j = 1, \ldots ,{n_2} \hfill \cr x \geqslant 0 \hfill \cr \endmatrix \right. \cr}

Example 7

In the above formula, the fuzzy objective coefficient vector is $c˜=(c˜1,…c˜n)$ \tilde c = \left( {{{\tilde c}_1}, \ldots {{\tilde c}_n}} \right) , the coefficient of constraint condition is $d˜1=(d˜i1,…,d˜in)$ {\tilde d_1} = \left( {{{\tilde d}_{i1}}, \ldots ,{{\tilde d}_{in}}} \right) , MJ stands for tolerance, ej xÊj refers to the JTH special hu constraint, and the corresponding membership function is: $μj(x)={ 1,ejx≤Ej1−[ ejx−Ej ]/mj,Ej≤ejx≤Ej+mj0,ej≥Ej+mj$ {\mu _j}(x) = \left\{ \matrix 1,{e_j}x \leqslant {E_j} \hfill \cr 1 - \left[ {{e_j}x - {E_j}} \right]/{m_j},{E_j} \leqslant {e_j}x \leqslant {E_j} + {m_j} \hfill \cr 0,{e_j} \geqslant {E_j} + {m_j} \hfill \cr \endmatrix \right.

And meet the following conditions: $x=(x1,…,xn)T∈Rnej=(ej1,…,ejn),E^j∈[ Ej,Ej+mj ]$ \{ x = {\left( {{x_1}, \ldots ,{x_n}} \right)^T} \in {R^n} \cr & \{e_j} = \left( {{e_{j1}}, \ldots ,{e_{jn}}} \right),{{\hat E}_j} \in \left[ {{E_j},{E_j} + {m_j}} \right

According to the solution proposed by Verdegsy, the linear programming model obtained above is transformed into an equivalent fuzzy programming model, as shown below: $maxZ˜α=c˜x{ dix≤D˜i,i=1,…,n1x∈(μj(x))α(ejx≤Ej+(1−α)mj),j=1,…,n2x≥0$ \eqalign{ & \max {{\tilde Z}_\alpha } = \tilde cx \cr & \left\{ \matrix {d_i}x \leqslant {{\tilde D}_i},i = 1, \ldots ,{n_1} \hfill \cr x \in {\left( {{\mu _j}(x)} \right)_\alpha }\left( {{e_j}x \leqslant {E_j} + (1 - \alpha ){m_j}} \right),j = 1, \ldots ,{n_2} \hfill \cr x \geqslant 0 \hfill \cr \endmatrix \right. \cr}

In the above formula, (μj (x))α = {x|μj (x) ≥ α, x ≥ 0}, satisfaction refers to α ∈[0,1].

Thirdly, in the case of clear α ∈ [0,1], if xα = (xα1,..., xαn) conforms to the constraints of the above equivalent fuzzy programming model, xα = (xα1,..., xαn) is regarded as the α -feasible solution of the model, and the α -feasible solution set of the model is Xa. If the condition $x αφ=(x α1φ,…,x αnφ)∈Xα$ x_\alpha ^\phi = \left( {x_{\alpha 1}^\phi , \ldots ,x_{\alpha n}^\phi } \right) \in {X_\alpha } is met, there is no $x α'=(x α1',…,x αn')≠x αφ∈Xα$ x_\alpha ^' = \left( {x_{\alpha 1}^', \ldots ,x_{\alpha n}^'} \right) \ne x_\alpha ^\phi \in {X_\alpha } , but there is $c˜x α'≥c˜x αφ$ \tilde cx_\alpha ^' \geqslant \tilde cx_\alpha ^\phi , then it is said that $x αφ=(x α1φ,…,x αnφ)Xα$ x_\alpha ^\phi = \left( {x_{\alpha 1}^\phi , \ldots ,x_{\alpha n}^\phi } \right){X_\alpha } === represents the α -optimal feasible solution of the model. According to the above model analysis process, the solution research is carried out:

The model is: $maxρ(Z˜α)=ρ(c˜)x{ ρ(d˜i)x≤ρ(D˜i),i=1,…,n1ρ(ej)x≤ρ(E_j+(1−α)m_j),j=1,…,n2x≥0$ \eqalign{ & \max \rho \left( {{{\tilde Z}_\alpha }} \right) = \rho (\tilde c)x \cr & \left\{ \matrix \rho \left( {{{\tilde d}_i}} \right)x \leqslant \rho \left( {{{\tilde D}_i}} \right),i = 1, \ldots ,{n_1} \hfill \cr \rho \left( {{e_j}} \right)x \leqslant \rho \left( {{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {E} }_j} + (1 - \alpha ){{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {m} }_j}} \right),j = 1, \ldots ,{n_2} \hfill \cr x \geqslant 0 \hfill \cr \endmatrix \right. \cr}

Example 8

Assuming that $x*=(x 1*,…,x n*)$ {x^*} = \left( {x_1^*, \ldots ,x_n^*} \right) represents the α -optimal feasible solution of the above model, then $x*=(x 1*,…,x n*)$ {x^*} = \left( {x_1^*, \ldots ,x_n^*} \right) must represent the α -optimal feasible solution of the equivalent fuzzy programming model. Verification analysis of this theorem shows that:

Assuming that the α -feasible solution set of the equivalent fuzzy programming model after transformation is Xa, then the α -feasible solution set of the above model is X ‘A, and the corresponding α -optimal feasible solution is: $x*=x α*=(x α1*,…,x αn*)∈X α'$ {x^*} = x_\alpha ^* = \left( {x_{\alpha 1}^*, \ldots ,x_{\alpha n}^*} \right) \in X_\alpha ^'

According to the deterministic analysis proposed above, it can be concluded that: $∀xα=(xα1,…,xαn)∈X α'⇔ρ(d˜i)x≤ρ(D˜i),i=1,…,n;ρ(ej)x≤ρ(E_j+(1−α)m_j),j=1,…,n2⇔d˜jx≤D˜j,i=1,…,n1;ejx≤E_j+(1−α)m_j,j=1,…,n2⇔xα=(xα1,…,xαn)∈Xα$ \eqalign{ & \forall {x_\alpha } = \left( {{x_{\alpha 1}}, \ldots ,{x_{\alpha n}}} \right) \in X_\alpha ^' \Leftrightarrow \cr & \rho \left( {{{\tilde d}_i}} \right)x \leqslant \rho \left( {{{\tilde D}_i}} \right),i = 1, \ldots ,n; \cr & \rho \left( {{e_j}} \right)x \leqslant \rho \left( {{{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {E} }_j} + (1 - \alpha ){{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {m} }_j}} \right),j = 1, \ldots ,{n_2} \Leftrightarrow \cr & {{\tilde d}_j}x \leqslant {{\tilde D}_j},i = 1, \ldots ,{n_1}; \cr & {e_j}x \leqslant {{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {E} }_j} + (1 - \alpha ){{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to {m} }_j},j = 1, \ldots ,{n_2} \Leftrightarrow \cr & {x_\alpha } = \left( {{x_{\alpha 1}}, \ldots ,{x_{\alpha n}}} \right) \in {X_\alpha } \cr}

In other words: $X α'=Xα$ X_\alpha ^' = {X_\alpha }

And because $x*=x α*=(x α1*,…,x αn*)∈X α'$ {x^*} = x_\alpha ^* = \left( {x_{\alpha 1}^*, \ldots ,x_{\alpha n}^*} \right) \in X_\alpha^' refers to the α -optimal feasible solution of the model, if there is no: $x α'=(x α1',…,x αn')≠x α*∈X α'$ x_\alpha ^' = \left( {x_{\alpha 1}^', \ldots ,x_{\alpha n}^'} \right) \ne x_\alpha ^* \in X_\alpha^'

Then you can get: $ρ(c˜)x α'≥ρ(c˜)x α'⇔$ \rho \left( {\tilde c} \right)x_\alpha ^' \geqslant \rho \left( {\tilde c} \right)x_\alpha ^' \Leftrightarrow

There is no: $x α'=(x α1',…,x αn')≠x α*∈Xα$ x_\alpha ^' = \left( {x_{\alpha 1}^', \ldots ,x_{\alpha n}^'} \right) \ne x_\alpha ^* \in {X_\alpha }

There are: $c˜x α'≥c˜x α*.⇔$ \tilde cx_\alpha ^' \geqslant \tilde cx_\alpha ^*. \Leftrightarrow

There is no: $x*=x α*=(x α1*,…,x an*)∈X α'$ {x^*} = x_\alpha ^* = \left( {x_{\alpha 1}^*, \ldots ,x_{an}^*} \right) \in {X_\alpha }

There are: $c˜x α'≥c˜x α*.⇔$ \tilde cx_\alpha ^' \geqslant \tilde cx_\alpha ^*. \Leftrightarrow

$x*=x α*=(x α1*,…,x an*)∈Xα$ {x^} = x_\alpha ^ = \left( {x_{\alpha 1}^, \ldots ,x_{an}^} \right) \in {X_\alpha } represents the α -optimal feasible solution of the model after transformation.

According to the above theorem analysis, it is found that the model solving problem after the transformation can be transformed into the model solving problem after the theorem analysis, and the model α -optimal feasible solution between the two can be calculated and obtained mutually.

Use genetic algorithm to solve the system planning model

In this paper based on the operation of the logistics public information system, on the basis of the guarantee stable data transmission of information, due to the strict constraints will cause certain economic resources waste, so that the planning scheme of under certain conditions do not conform to the system constraints, to guarantee the probability under the condition of less than a certain confidence level. According to the fuzzy constraint programming solution of the above study, the mathematical model can be constructed as follows:[1.2] ${ minf(S)=∑j=1nCjLjsjs.t. Pr(PL≤PLmax)≥αBθ=PPG≤PGmax$ \left\{ \matrix \min f(S) = \sum\limits_{j = 1}^n {{C_j}{L_{jsj}}} \hfill \cr s.t.\,\,\Pr \left( {{P_L} \leqslant {P_{L\max }}} \right) \geqslant \alpha \hfill \cr B\theta = P \hfill \cr {P_G} \leqslant {P_{G\max }} \hfill \cr \endmatrix \right.

In the above formula, S represents the n-dimensional vector of the planning scheme, n represents the number of candidate systems, Sj represents the decision variable of the candidate system, Cj represents the investment and cost per unit length of the candidate system J, and Lj represents the candidate length, representing the confidence level of constraints.

The above models need to be solved and analyzed by genetic algorithm. Genetic algorithm is an optimization method proposed by combining computer science and natural genetics. Its essence is to abstract out the principles of genetic motivation and superiority, so as to form an application algorithm which is convenient for computer implementation. This content has been widely used in the construction planning of logistics public information management platform. The steps of analyzing mathematical model with fuzzy chance-constrained genetic algorithm are as follows: first, input original data information; Second, chromosomes are identified according to the number of candidates. Thirdly, a group of randomly generated initial schemes is regarded as the initial population of the genetic algorithm, and whether it meets the requirements of the model is judged. Fourthly, the quality of the corresponding objective function should be calculated. Fifthly, according to the values obtained by the above operations, the penalty function is used to study the chromosomes violating the constraints and their fitness. If the constraint conditions are not violated, the value of the above objective function can be directly regarded as fitness. Sixth, use roulette method to select chromosomes; Seventh, in the mutation crossover operation to obtain the new chromosome, also in the test analysis to judge whether it meets the requirements; Eighth, reach the expected set number of iterations in repeated operations; The resulting chromosome is the best planning scheme.[3.4]

Build a logistics public information management platform

Combined with the above mathematical model constructed by using fuzzy constraint programming, the construction and promotion of logistics public information management platform are discussed in depth, which can be divided into the following contents:

Core Technologies

As the basis of information system design and implementation, distributed architecture can not only facilitate users to install client programs on the computer platform, but also increase the difficulty and cost of design, development and maintenance. Therefore, B/S three-layer structure is selected in this study, as shown in the figure 1 below:

J2EE, as a distributed enterprise-level application standard defined by the company, can provide background services for all component types in the form of containers in platform design, so that each part of the complete enterpriselevel application is integrated into each container. Combined with the analysis of the architecture diagram shown in the figure 2 below, it can be seen that it is divided into four layers: first, the client layer mainly provides friendly visual interaction interface for end users; Second, the Web layer can provide the required parameters according to the user request, and use the business logic layer for scientific processing, so that the obtained processing results of the dynamic generation unit provided to the client layer for browsing; Third, the business layer mainly deals with the core business logic of the application. Fourthly, the enterprise information system layer is the system software that deals with the enterprise data information, and mainly completes the storage and management of data information and other persistent work.

Stuts, Hibernate and Spring are three open source framework technologies. The first can be used to develop a presentation layer, which can ensure the separation of processing between user interface and business logic. The second can be used to form a low intrusion extensibility framework, and use dynamic proxy mechanism to intercept external calls, so as to ensure the separation between the Web layer and the logical layer operation; The third allows the relationships between Java objects and the table relationships in a relational database to map each other, so as to meet the object-oriented development design ideas and reduce the actual development cost and consumption of time. MVC design model is mainly used to improve the general level of components in distributed application system and the flexibility of controlling things. Its core idea is to scientifically separate the relationship among data interaction, data representation, data and business logic, thus composing controller, view and model. The relationship among the three is shown in the following figure 3:[5]

Overall system architecture

First of all, the platform architecture regards J2EE as an open standard specification, and pays attention to fully reflect the characteristics of the development and design system, such as availability, scalability and portability, so as to meet the requirements of system analysis for the operation of the development platform. At the same time, the CHOICE of MVC design mode can not only scientifically separate data presentation and processing, but also enhance the flexibility and extensibility of system application, ensure that each function level is clear, and maintenance personnel can accurately grasp the system structure and business process. Combined with the analysis of fuzzy constrained programming mathematical model, the design of logistics public information management platform needs to systematically study a series of business activities when goods are received and shipped out, including transportation, storage, distribution and other routine business. In addition, the perfection of data structure should be ensured during the architecture study, and the functional design should be improved by combining rule description. The system structure model of the corresponding platform is shown in the figure 4 below:[6]

Second, the application framework. Since the logistics public information management platform studied in this paper is a distributed information system with B/S structure as the core, the actual environment architecture uses three-layer distributed application structure, so each layer structure has corresponding components, and the system provides universal components for universal services, the specific content involves the following points: First, the presentation layer can guarantee the interaction between the user and the system, has interface functions and defines related methods; Second, the business logic layer can process all the business logic to ensure the completeness and scientificity of the incoming data. The practical work involves BL logic processing, initialization of global variables and so on. Third, the persistence layer can provide excellent service for the business logic layer to operate efficiently on the database.

Platform design and implementation

In order to build a logistics public information management platform with perfect functions, the development and design of practical projects should ensure the effectiveness of the following three layers:

First, the persistence layer. This paper Outlines the system to use Hibernate framework to complete the access of persistence, which involves persistent objects and mapping files, mainly using DAO mode and the underlying database for interactive processing, Hibernate can be used to manage Java class to ROBMS table mapping, data search and program query in the database. In the process of program development and design, it is necessary to edit and configure persistent class object files, corresponding mapping files and basic accessory files. For example, part of the mapping file user. hbm. XML looks like this:

Second, the business logic layer. This content mainly implements business logic and provides service and transaction management for the other two layers, reducing not only coupling of program code but also component processing code. Generally speaking, this level of business logic components are implemented using the SpringOC container, and the corresponding business logic is integrated into the actual call action module using the configuration file Application Context-service.xml during the program run.

Third, the presentation layer. This work mainly refers to the specific interface presented to the user, so this paper studies the system using the Struts framework to complete the design and analysis of the presentation layer, its core controller will first intercept the user request, and pass it to the corresponding Action processing, thus pointing to the instance in the SpringOC container, that is, the processor that actually processes the user request. Eventually, the component delegates to invoke the business logic. Since Struts is made up of the Spring framework, the corresponding controller is managed by Spring in a carte Blanche manner, in which case Struts needs to obtain Spring support in the context in which the framework accesses Spring. Part of the code for configuring the Struts controller is as follows:

Part of the code for configuring the Struts controller

 Struts Org.Apache.Stryts.Dispatcher.Filter Dispatcher Struts /’Action

The core goal of the test and analysis of the above construction system is to find the problems existing during the operation of the system and ultimately provide customers with high-quality software products. This paper summarizes the system testing content involves the following points: first of all, to carry out functional testing, mainly for the design structure and functional module analysis, the final results prove that the operating process of each module meets the needs; The platform software system uses test tools to run test scripts in the specified environment, and carries out test analysis from the two aspects of load and pressure. The former mainly studies the limit value of an index of system application characteristics, and determines whether there is application failure. The latter requires frequent operations under data anomalies or multiple conditions to determine the level of resistance of the system performance program. The specific results are shown in the table 1 below. Finally, system security should be analyzed from two aspects, one is application-level security, the other is system-level security.[710]

Part of the user.hbm.xml code

 ...... ......

performance test results

Maximum load ≥500 people From the test results, the system can safely withstand the load of 500 people
Maximum concurrency ≥100 people The system can withstand the non-access of 100 people. When more than 100 people visit the system, the operation times out
Maximum system response time ≤20 seconds In general, the system response time is between 2 seconds and 6 seconds. Under the maximum number of concurrent requests, the system response time is less than 20 seconds
The stability of 7×24 hours uninterrupted operation Using the script and strategy of maximum load test, the system can run continuously for 7×24 hours from the test situation
Conclusion

Combined with the above analysis, it is found that the system’s various functional operations can be fully covered in the function test, the system operation and performance parameters under various conditions can be defined in the performance test, and the application performance such as data resources, permission control and login and access can be defined in the security test. From the overall point of view, the logistics public information management platform constructed by myself combined with the mathematical model of fuzzy constraint programming is feasible.

#### Part of the code for configuring the Struts controller

 Struts Org.Apache.Stryts.Dispatcher.Filter Dispatcher Struts /’Action

#### Part of the user.hbm.xml code

 ...... ......

#### performance test results

Maximum load ≥500 people From the test results, the system can safely withstand the load of 500 people
Maximum concurrency ≥100 people The system can withstand the non-access of 100 people. When more than 100 people visit the system, the operation times out
Maximum system response time ≤20 seconds In general, the system response time is between 2 seconds and 6 seconds. Under the maximum number of concurrent requests, the system response time is less than 20 seconds
The stability of 7×24 hours uninterrupted operation Using the script and strategy of maximum load test, the system can run continuously for 7×24 hours from the test situation

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