A quality-aware multi-objective cloud manufacturing service composition optimization method

Abstract

The present invention discloses a multi-objective cloud manufacturing service combination optimization method based on quality perception, and the steps include: 1. constructing a cloud manufacturing service combination optimization model; 2. setting algorithm parameters; 3. using a mirror strategy to generate an initial population; 4. selecting parent individuals; 5. using crossover and mutation operations to generate child individuals; 6. updating the archived population; 7. probability update; 8. judging whether the termination condition is met, and ending if it is met, otherwise going to step 4. The present invention optimizes from five dimensions of time, cost, reliability, availability and credibility at the same time, and can select the best parts supplier for automobile manufacturers, thereby saving time and cost for automobile manufacturers, increasing product reliability and availability, and providing a good reputation for the product, improving user satisfaction.

Description

Technical Field

[0001] The present invention relates to the technical field of cloud manufacturing service composition optimization, and in particular to a multi-objective cloud manufacturing service composition optimization method based on service quality perception. Background Art

[0002] The cloud manufacturing 3.0 system provides a new model of intelligent manufacturing system for the deep integration of manufacturing and information and communication technology. Cloud manufacturing technology integrates networked manufacturing and service technologies, cloud computing, high-performance technologies, the Internet of Things and other technologies to achieve the unification of classified manufacturing resources such as manufacturing hardware, computing systems, software, data, and knowledge, and centralized intelligent management and operation. It provides various types of manufacturing services that can be obtained at any time, on demand, safe and reliable, high-quality and low-cost for the entire manufacturing life cycle process. It is a service-oriented networked manufacturing model.

[0003] In a cloud manufacturing environment, users submit manufacturing tasks to a service platform, which decomposes the tasks by analyzing their complexity and selects suitable services from the platform to perform the user tasks according to user needs. However, as cloud computing service providers continue to provide cloud services with similar functions but different qualities, how to select and combine cloud services to meet users' quality of service (QoS) expectations, namely the QoS-aware cloud service composition (QoS-CSC) problem, has become a key issue in computing service provision.

[0004] For example, with the development of modern society, the customization of cars has gradually become a trend. A car can include five parts: foundation, external configuration, internal configuration, safety configuration, and special configuration. The foundation corresponds to the three major parts of the car, the engine, gearbox, and chassis, which are the main components of the car; the external configuration includes the type of sunroof, luggage rack, wheels, etc.; the internal configuration includes the steering wheel, LCD instrument, etc.; the safety configuration includes active safety and passive safety; the special configuration refers to the car refrigerator, the in-car fragrance device, etc. There are multiple suppliers for each module and component of the car. The parts provided by each supplier have the same functions but different functional attributes, such as cost, time, reliability, availability, credibility and other QoS. Therefore, how to select suitable manufacturer parts from different suppliers to complete the customization of the car and meet the needs of users is the key issue of Cloud Manufacturing Service Composition (CMSC).

[0005] With the increasing number of similar single services in cloud environments, the cloud manufacturing service composition problem has become an NP-hard (Non-deterministic Polynomial-Hard) problem. Due to the nonlinear characteristics of mathematical models and a large number of candidate services, it is usually not feasible to use precise methods such as linear and integer programming. Bao et al. used finite state machines to specify the legal call order of Web services and proposed an improved algorithm based on tree pruning to create a Web service composition tree. After generating all feasible execution paths, a simple weighting technique was used to select the best solution. Dou et al. changed the multi-objective optimization problem with constraints into two main objectives, namely, minimum QoS risk (minimizing the difference between QoS objectives and user constraints) and maximum QoS performance. Jian et al. proposed an improved bird flock optimization algorithm, which introduced a second-order oscillation equation and the historical position memory of birds on the basis of basic bird flock optimization to minimize the overall time cost of service composition. Zhou et al. proposed a hybrid artificial bee colony algorithm to transform the CMSC problem into a dual-objective problem for solution. Liang et al. divided CMSC into ascending and descending QoS standards and used a service selection model with dual constraints for optimization. Yang et al. proposed an enhanced gray wolf optimization algorithm to optimize both QoS and energy consumption. In addition, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), MOEAQI algorithm, etc. are also used to solve service combination problems, but these algorithms often simplify multi-objective problems into single-objective problems through weighted combination, and rarely consider optimizing four or more objectives at the same time. In the process of selecting suppliers for automobile manufacturers, there are many factors that automobile manufacturers need to consider, such as the processing time, processing cost, reliability, availability of parts, the credibility of suppliers, the delivery coordination of products, etc. The previous methods all used simple weighted combinations to solve such problems, and could not be well optimized from multiple dimensions at the same time, that is, there were great drawbacks in the selection process of parts suppliers. Summary of the invention

[0006] The present invention aims to overcome the shortcomings of the prior art and provide a multi-objective cloud manufacturing service portfolio optimization method based on quality perception, so as to simultaneously optimize the five dimensions of time, cost, reliability, availability and credibility, and select the best parts suppliers for automobile manufacturers, thereby saving time and cost for automobile manufacturers, increasing product reliability and availability, and improving user satisfaction.

[0007] The present invention adopts the following technical solutions to solve the technical problems:

[0008] The multi-objective cloud manufacturing service combination optimization method based on quality perception is characterized in that it is applied to a scenario in which an automobile manufacturer selects n parts of a whole vehicle from m×n parts suppliers producing the automobile, and the set of parts of the whole vehicle is recorded as C={C1,C2,…,C i ,…,C n}, C i represents the i-th component of the car, 1≤i≤n; let the i-th component C i The supplier set is denoted as Represents the i-th component C i The j-th supplier, 1≤j≤m; the multi-objective cloud manufacturing service composition optimization method is carried out in the following steps:

[0009] Step 1: Use equations (1) to (5) to build a cloud manufacturing service combination optimization model:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] In formula (1) to formula (5), Indicates that the automobile manufacturer obtains the i-th component C i Supplier Collection PS i Select the jth i suppliers, 1≤j i ≤m; T(·) and CS(·) represent the time function and cost function required for suppliers to produce parts, respectively; RB(·), AB(·), and RP(·) represent the reliability function, availability function, and reputation level function of suppliers, respectively;

[0016] Step 2.1, let the population size be N, the number of neighbor vectors be H, the probability of initial mating selection be Q, the minimum probability of mating selection be Δ1, the maximum probability of mating selection be Δ2, the number of updates of the mating selection probability Q be t, the interval generation be L, the probability of individual mutation be P, the archive population be EP, the current number of iterations be IT, and the maximum number of iterations be ITmax; let the number of individuals produced by near neighbor mating be r1 and the number of individuals produced by far neighbor mating be r2;

[0017] Step 2.2: Let the e-th supplier selection scheme randomly selected by the automobile manufacturer be in, Indicates that the automobile manufacturer selects from the supplier set PS in the e-th supplier selection scheme i Select the jth i suppliers, and the e-th supplier selects option X e As an individual, As the chromosomes of individuals, the initial first population P1 consisting of N individuals is generated;

[0018] Step 2.3: Calculate the C of the ith component using formula (6): i Suppliers The gap between the best suppliers

[0019]

[0020] In formula (6), Indicates supplier The time gap with the best supplier, T min (PS i ) represents the supplier set PS i Produce the i-th component C i Minimum time taken; Indicates the jth i The time it takes for a supplier to produce the i-th component C, Indicates supplier Cost gap with the best supplier, CS min (PS i ) represents the supplier set PS i The i-th component C is produced in i The minimum cost required; Indicates the jth i Suppliers produce component C i The cost required, Indicates supplier Reliability gap with the best supplier, RB max (PS i ) represents the supplier set PS i Highest reliability among parts suppliers; represents the jth production of the i-th component C i The reliability of each supplier; Indicates supplier Availability gap with best-in-class supplier, AB max (PS i ) represents the supplier set PS i Highest availability of parts suppliers; represents the jth production of the i-th component Ci the availability of suppliers; Indicates supplier The gap in credibility level with the best supplier, RP max (PS i ) represents the supplier set PS i The highest reputation among parts suppliers; represents the jth production of the i-th component C i The credibility of each supplier;

[0021] Step 2.4: Based on the gap For the i-th component C i Supplier Collection PS i Sort in ascending order to get the sorted supplier set PS′ i ;

[0022] Step 2.5: For each individual in the initial first population P1, the supplier set PS′ after sorting is calculated according to the chromosome of the individual i The position in the image is selected to replace the chromosome at the mirror position, thereby obtaining a new individual and forming the initial second population P2;

[0023] Step 2.6, merge the initial first population P1 and the initial second population P2, and compare the individuals in the merged populations in turn according to Chebyshev's rule, and retain half of the better individuals, so as to obtain the evolved population P;

[0024] According to the Pareto optimality principle, the non-dominated individuals in the evolving population P are added to the archive population EP;

[0025] Step 3: Generate a uniform reference vector in the target space, and correspond each individual in the evolution population P to the reference vector one by one;

[0026] Step 4: Determine H nearest neighbor reference vectors and H far neighbor reference vectors of each reference vector according to the Euclidean distance between each reference vector and other reference vectors;

[0027] Step 5.0, initialize IT=1;

[0028] Step 5.1, at the ITth iteration, initialize t = 0; r1 = r2 = 0;

[0029] Step 5.2: Generate a random number for each individual in the evolving population P, and determine whether the current random number is greater than the probability Q. If so, assign r2+1 to r2, randomly select two vectors from the H distant neighbor vectors of the current individual, and record the individuals corresponding to the two vectors as x1 and x2, and execute step 5.4; otherwise, assign r1+1 to r1, and go to step 5.3;

[0030] Step 5.3: First determine the number u of non-dominated individuals among the individuals corresponding to the H nearest neighbor reference vectors of the current individual. If u>2, two random non-dominated individuals are recorded as x1 and x2. Otherwise, two individuals are randomly selected from the individuals corresponding to the H nearest neighbor reference vectors of the current individual and recorded as x1 and x2.

[0031] Step 5.4, perform crossover and mutation operations on the two individuals x1 and x2 to obtain two new individuals y1 and y2;

[0032] Step 5.5, add the two new individuals y1 and y2 to the evolving population P, and update the evolving population P according to the Pareto optimal principle, deleting the two dominant individuals, so as to keep the population size unchanged;

[0033] Step 5.6, adding the non-dominated individuals in the evolving population P to the archived population EP, thereby updating the archived population EP;

[0034] Step 5.7, assign IT+1 to IT, assign t+1 to t, if IT>IT max , then each individual in the archived population EP is used as an optimized parts supplier selection scheme and recommended to the user, otherwise go to step 5.8;

[0035] Step 5.8: If t>L, go to step 5.9; otherwise, go to step 5.2;

[0036] Step 5.9: Calculate the new mating selection probability Q′ using formula (7):

[0037]

[0038] Step 5.10, if Δ1≤Q′≤Δ2, assign Q′ to Q and go to step 5.1; otherwise, go to step 5.11;

[0039] Step 5.11. If 0≤Q′≤Δ1, set Q=Δ2 and go to step 5.1; otherwise, set Q=Δ1 and go to step 5.1.

[0040] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0041] 1. Aiming at the problem of simultaneously optimizing time, cost, reliability, availability and credibility of service combination, the present invention proposes an evolutionary algorithm based on adaptive selection and reverse learning strategy (ARSEA). Firstly, the reverse learning strategy is adopted to increase the diversity of the initial population. In the iterative process, the selection probability is dynamically adjusted to adaptively select the parent individuals participating in mating, so as to maintain the unity of algorithm diversity and convergence. The invention solves the problem of simultaneous optimization of multiple objectives of cloud manufacturing service combination, realizes the quality optimization of the combination scheme, thereby saving time and cost and improving user satisfaction.

[0042] 2. The present invention adopts a reverse learning strategy in the population initialization process, so that the initial solution is more evenly distributed in the solution space, which improves the diversity of the population and provides automobile manufacturers with more comprehensive options in multiple dimensions during the selection of parts suppliers.

[0043] 3. In the process of population iteration, the present invention adopts an adaptive parent mating probability selection and update strategy, automatically adjusts the probability of mating selection according to the contribution of the new solution, makes the archived population closer to the real Pareto frontier of the problem, effectively balances the global and local search capabilities of the algorithm, improves the diversity and convergence performance of the algorithm, and thus helps automobile manufacturers select better parts suppliers in terms of five dimensions: time, cost, reliability, availability and credibility, thereby improving the product strength of the automobile. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 A flow chart of the cloud manufacturing service combination of the present invention;

[0045] Figure 2 This is a flow chart of the multi-objective cloud manufacturing service composition optimization method based on service quality awareness proposed in the present invention. DETAILED DESCRIPTION

[0046] In this embodiment, a multi-objective cloud manufacturing service composition optimization method based on service quality perception is provided, and its process is as follows: Figure 1 As shown in the figure, it is applied to a scenario where an automobile manufacturer selects n parts for a whole vehicle from m×n parts suppliers producing automobiles. Let the set of parts for the whole vehicle be denoted as C = {C1, C2, …, C i ,…,C n}, C i represents the i-th component of the car, 1≤i≤n; let the i-th component C i The supplier set is denoted as Represents the i-th component C i The jth supplier, 1≤j≤m; for such a complex manufacturing task as manufacturing a car, each component of the car can be regarded as a subtask, and each subtask has a set of suppliers. Each supplier in the supplier set can complete the task, and the car can be manufactured by selecting a supplier from the supplier set under each subtask. The present invention optimizes from five dimensions simultaneously: time, cost, reliability, availability, and credibility. It can select the best parts supplier for automobile manufacturers, thereby saving time and cost for automobile manufacturers, increasing product reliability and availability, and providing a better reputation for the product, thereby improving user satisfaction. Specifically, if Figure 2 As shown in the figure, the multi-objective cloud manufacturing service composition optimization method is carried out in the following steps:

[0047] Step 1: Use equations (1) to (5) to build a cloud manufacturing service combination optimization model:

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] In formula (1) to formula (5), Indicates that the automobile manufacturer obtains the i-th component C i Supplier Collection PS i Select the jth i suppliers, 1≤j i ≤m; T(·) and CS(·) represent the time function and cost function required for suppliers to produce parts, respectively; RB(·), AB(·), and RP(·) represent the reliability function, availability function, and reputation level function of suppliers, respectively;

[0054] Step 2.1, let the population size be N, the number of neighbor vectors be H, the probability of initial mating selection be Q, the minimum probability of mating selection be Δ1, the maximum probability of mating selection be Δ2, the number of updates of the mating selection probability Q be t, the interval generation be L, the probability of individual mutation be P, the archive population be EP, the current number of iterations be IT, and the maximum number of iterations be ITmax; let the number of individuals produced by near neighbor mating be r1 and the number of individuals produced by far neighbor mating be r2;

[0055] Step 2.2: Let the e-th supplier selection scheme randomly selected by the automobile manufacturer be in, Indicates that the automobile manufacturer selects from the supplier set PS in the e-th supplier selection scheme i Select the jth i suppliers, and the e-th supplier selects option X e As an individual, As the chromosomes of individuals, the initial first population P1 consisting of N individuals is generated;

[0056] Step 2.3: Calculate the C of the ith component using formula (6): i Suppliers The gap between the best suppliers

[0057]

[0058] In formula (6), Indicates supplier The time gap with the best supplier, T min (PS i ) represents the supplier set PS i Produce the i-th component C i Minimum time taken; Indicates the jth i The time it takes for a supplier to produce the i-th component C, Indicates supplier Cost gap with the best supplier, CS min (PS i ) represents the supplier set PS i The i-th component C is produced in i The minimum cost required; Indicates the jth i Suppliers produce component C i The cost required, Indicates supplier Reliability gap with the best supplier, RB max (PS i ) represents the supplier set PS i Highest reliability among parts suppliers; represents the jth production of the i-th component C i The reliability of each supplier; Indicates supplier Availability gap with best-in-class supplier, AB max (PS i ) represents the supplier set PS i Highest availability of parts suppliers; represents the jth production of the i-th component Ci the availability of suppliers; Indicates supplier The gap in credibility level with the best supplier, RP max (PS i ) represents the supplier set PS i The highest reputation among parts suppliers; represents the jth production of the i-th component C i The credibility of each supplier;

[0059] Step 2.4: Based on the gap For the i-th component C i Supplier Collection PS i Sort in ascending order to get the sorted supplier set PS′ i ;

[0060] Step 2.5: For each individual in the initial first population P1, the supplier set PS′ after sorting is calculated according to the chromosome of the individual i The position in the image is selected to replace the chromosome at the mirror position, thereby obtaining a new individual and forming the initial second population P2. The mirror method can generate a more comprehensive supplier selection scheme in multiple dimensions, increase the diversity of the population, and provide a solid foundation for subsequent evolutionary optimization.

[0061] Step 2.6, merge the initial first population P1 and the initial second population P2, and compare the individuals in the merged populations in turn according to Chebyshev's rule, and retain half of the better individuals, so as to obtain the evolved population P;

[0062] According to the Pareto optimality principle, the non-dominated individuals in the evolving population P are added to the archive population EP;

[0063] Step 3: Generate a uniform reference vector in the target space, and correspond each individual in the evolution population P to the reference vector one by one;

[0064] Step 4: Determine H nearest neighbor reference vectors and H far neighbor reference vectors of each reference vector according to the Euclidean distance between each reference vector and other reference vectors;

[0065] Step 5.0, initialize IT=1;

[0066] Step 5.1, at the ITth iteration, initialize t = 0; r1 = r2 = 0;

[0067] Step 5.2: For each individual in the evolving population P, generate a random number and determine whether the current random number is greater than the probability Q. If so, assign r2+1 to r2, randomly select two vectors from the H distant neighbor vectors of the current individual, and record the individuals corresponding to the two vectors as x1 and x2, and execute step 5.4; otherwise, assign r1+1 to r1, and go to step 5.3. The individuals corresponding to the distant neighbor vectors perform mating operations to increase the diversity of the population and the diversity of the supplier selection scheme.

[0068] Step 5.3, first determine the number u of non-dominated individuals among the individuals corresponding to the H nearest neighbor reference vectors of the current individual. If u>2, two random non-dominated individuals are recorded as x1 and x2. Otherwise, two individuals are randomly selected from the individuals corresponding to the H nearest neighbor reference vectors of the current individual and recorded as x1 and x2. The mating operation of the individuals corresponding to the nearest neighbor vectors can increase the convergence of the algorithm and make the population evolve toward the Pareto optimal point, which is conducive to reducing the time cost of the selected supplier and increasing the reliability, availability and credibility of the selected supplier.

[0069] Step 5.4, perform crossover and mutation operations on the two individuals x1 and x2 to obtain two new individuals y1 and y2;

[0070] Step 5.5, add the two new individuals y1 and y2 to the evolving population P, and update the evolving population P according to the Pareto optimal principle, deleting the two dominant individuals, so as to keep the population size unchanged;

[0071] Step 5.6, adding the non-dominated individuals in the evolving population P to the archived population EP, thereby updating the archived population EP;

[0072] Step 5.7, assign IT+1 to IT, assign t+1 to t, if IT>IT max , then each individual in the archived population EP is used as an optimized parts supplier selection scheme and recommended to the user, otherwise go to step 5.8;

[0073] Step 5.8: If t>L, go to step 5.9; otherwise, go to step 5.2;

[0074] Step 5.9: Calculate the new mating selection probability Q′ using formula (7):

[0075]

[0076] Step 5.10, if Δ1≤Q′≤Δ2, assign Q′ to Q and go to step 5.1; otherwise, go to step 5.11;

[0077] Step 5.11, if 0≤Q′≤Δ1, set Q=Δ2 and go to step 5.1; otherwise, set Q=Δ1 and go to step 5.1. The adaptive update of mating probability can make the population automatically adjust the evolution direction of the population according to the evolution process of the individuals, which is conducive to balancing the convergence and diversity of the algorithm and making the supplier selection plan move towards overall optimization.

Claims

1. A multi-objective cloud manufacturing service composition optimization method based on quality perception, characterized by Applied to a scenario where an automobile manufacturer selects n parts for a vehicle from m×n parts suppliers, let the set of vehicle parts be C = {C1, C2, …, C i ,…,C n }, C i represents the i-th component of the car, 1≤i≤n; let the i-th component C i The supplier set is denoted as Represents the i-th component C i The j-th supplier, 1≤j≤m; the multi-objective cloud manufacturing service composition optimization method is carried out in the following steps: Step 1: Use equations (1) to (5) to build a cloud manufacturing service combination optimization model: In formula (1) to formula (5), Indicates that the automobile manufacturer obtains the i-th component C i Supplier Collection PS i Select the jth i suppliers, 1≤j i ≤m; T(·) and CS(·) represent the time function and cost function required for suppliers to produce parts, respectively; RB(·), AB(·), and RP(·) represent the reliability function, availability function, and reputation level function of suppliers, respectively; Step 2.1, let the population size be N, the number of neighbor vectors be H, the probability of initial mating selection be Q, the minimum probability of mating selection be Δ1, the maximum probability of mating selection be Δ2, the number of updates of the mating selection probability Q be t, the interval generation be L, the probability of individual mutation be P, the archive population be EP, the current number of iterations be IT, and the maximum number of iterations be ITmax; let the number of individuals produced by near neighbor mating be r1 and the number of individuals produced by far neighbor mating be r2; Step 2.2: Let the e-th supplier selection scheme randomly selected by the automobile manufacturer be in, Indicates that the automobile manufacturer selects from the supplier set PS in the e-th supplier selection scheme i Select the jth i suppliers, and the e-th supplier selects option X e As an individual, As the chromosomes of individuals, the initial first population P1 consisting of N individuals is generated; Step 2.3: Calculate the C of the ith component using formula (6): i Suppliers The gap between the best suppliers In formula (6), Indicates supplier The time gap with the best supplier, T min (PS i ) represents the supplier set PS i Produce the i-th component C i Minimum time taken; Indicates the jth i The time it takes for a supplier to produce the i-th component C, Indicates supplier Cost gap with the best supplier, CS min (PS i ) represents the supplier set PS i The i-th component C is produced in i The minimum cost required; Indicates the jth i Suppliers produce component C i The cost required, Indicates supplier Reliability gap with the best supplier, RB max (PS i ) represents the supplier set PS i Highest reliability among parts suppliers; represents the jth production of the i-th component C i The reliability of each supplier; Indicates supplier Availability gap with best-in-class supplier, AB max (PS i ) represents the supplier set PS i Highest availability of parts suppliers; represents the jth production of the i-th component C i the availability of suppliers; Indicates supplier The gap in credibility level with the best supplier, RP max (PS i ) represents the supplier set PS i The highest reputation among parts suppliers; represents the jth production of the i-th component C i The credibility of each supplier; Step 2.4: Based on the gap For the i-th component C i Supplier Collection PS i Sort in ascending order to get the sorted supplier set PS′ i ; Step 2.5: For each individual in the initial first population P1, the supplier set PS′ after sorting is calculated according to the chromosome of the individual i The position in the image is selected and the chromosome at the mirror position is replaced to obtain a new individual and form the initial second population P2; Step 2.6, merge the initial first population P1 and the initial second population P2, and compare the individuals in the merged populations in turn according to Chebyshev's rule, and retain half of the better individuals, so as to obtain the evolved population P; According to the Pareto optimality principle, the non-dominated individuals in the evolving population P are added to the archive population EP; Step 3: Generate a uniform reference vector in the target space, and correspond each individual in the evolution population P to the reference vector one by one; Step 4: Determine H nearest neighbor reference vectors and H far neighbor reference vectors of each reference vector according to the Euclidean distance between each reference vector and other reference vectors; Step 5.0, initialize IT=1; Step 5.1, at the ITth iteration, initialize t = 0; r1 = r2 = 0; Step 5.2: Generate a random number for each individual in the evolving population P, and determine whether the current random number is greater than the probability Q. If so, assign r2+1 to r2, randomly select two vectors from the H distant neighbor vectors of the current individual, and record the individuals corresponding to the two vectors as x1 and x2, and execute step 5.4; otherwise, assign r1+1 to r1, and go to step 5.3; Step 5.3: First determine the number u of non-dominated individuals among the individuals corresponding to the H nearest neighbor reference vectors of the current individual. If u>2, two random non-dominated individuals are recorded as x1 and x2. Otherwise, two individuals are randomly selected from the individuals corresponding to the H nearest neighbor reference vectors of the current individual and recorded as x1 and x2. Step 5.4, perform crossover and mutation operations on the two individuals x1 and x2 to obtain two new individuals y1 and y2; Step 5.5, add the two new individuals y1 and y2 to the evolving population P, and update the evolving population P according to the Pareto optimal principle, deleting the two dominant individuals, so as to keep the population size unchanged; Step 5.6, adding the non-dominated individuals in the evolving population P to the archived population EP, thereby updating the archived population EP; Step 5.7: After assigning IT+1 to IT and t+1 to t, if IT>IT max , then each individual in the archived population EP is used as an optimized parts supplier selection scheme and recommended to the user, otherwise go to step 5.8; Step 5.8: If t>L, go to step 5.9; otherwise, go to step 5.2; Step 5.9: Calculate the new mating selection probability Q′ using formula (7): Step 5.10, if Δ1≤Q′≤Δ2, assign Q′ to Q and go to step 5.1; otherwise, go to step 5.11; Step 5.

11. If 0≤Q′≤Δ1, set Q=Δ2 and go to step 5.1; otherwise, set Q=Δ1 and go to step 5.1.

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