A novel approach to adaptive robust service composition and optimization selection in cloud manufacturing

Abstract

This invention discloses a novel method for adaptive robust service composition and optimal selection in cloud manufacturing, belonging to the field of cloud manufacturing technology. The method includes the following steps: 1) establishing an Adaptive Robust Service Composition and Optimal Selection (ARSCOS) model; 2) solving the model in step 1) using the Enhanced Multi-Objective Artificial Hummingbird Algorithm (EMOAHA). The ARSCOS model of this invention enhances the anti-interference capability of CMS and reduces the negative impact of uncertainty on the task execution process.

Description

Technical Field

[0001] This invention belongs to the field of optimization algorithm technology and relates to a new method for adaptive robust service composition and optimization selection in cloud manufacturing. Background Technology

[0002] Cloud Manufacturing (CMfg), as a novel intelligent manufacturing model, leverages information technologies such as cloud computing and the Internet of Things to achieve collaborative utilization of geographically dispersed manufacturing resources. Service Composition and Optimization Selection (SCOS) is crucial for optimizing resource allocation on the CMfg platform and has garnered significant attention from scholars. However, the actual execution of Composite Manufacturing Services (CMS) frequently encounters various uncertainties, such as equipment failures, service outages, and task cancellations. These uncertainties are random and unpredictable, potentially significantly impacting the successful execution of tasks. This is particularly true for complex cloud manufacturing tasks in aerospace equipment manufacturing, characterized by multi-level complex supply chains, high quality requirements, diverse product types, and small batches. These tasks typically involve dozens or even hundreds of sub-tasks undertaken by different companies, with manufacturing cycles often exceeding one year. Frequent temporary adjustments or reorganizations during task execution inevitably lead to increased execution costs, order delays, decreased service quality, and even task failure. Therefore, ensuring the smooth execution of CMS in uncertain environments is paramount.

[0003] However, existing SCOS methods have very limited research on CMS inefficiency or even failure caused by uncertain events in real-world environments. Some studies focus on emergency response methods after theoretical architecture and service anomalies. The performance of these methods largely depends on the predefined CMS and real-time resource status, so they are prone to producing low-quality temporary adjustment solutions, or even failing to find feasible solutions. Therefore, in CMfg systems, the ability of the CMS to withstand a certain degree of abnormal events becomes an important consideration. Therefore, this paper proposes an Adaptive Robust Service Composition and Optimal Selection Model (ARSCOS) to enhance the CMS's ability to withstand certain uncertain events during the SCOS planning phase.

[0004] Furthermore, with the rapid increase in user demand and service resources on the CMfg platform, the Cloud Manufacturing Candidate Service Set (CMCSS) is growing larger and larger. How to efficiently select the optimal service combination that meets user needs from massive cloud service resources, thereby improving service resource utilization and manufacturing capabilities, has become a key factor in enhancing the core competitiveness of the CMfg platform, improving user satisfaction, and promoting regional collaborative manufacturing. However, despite extensive research on methods for solving the SCOS problem, problems such as low efficiency and unsatisfactory results still exist.

[0005] In recent years, the Multi-objective Artificial Hummingbird Algorithm (MOAHA) has been applied to solve complex engineering problems such as energy system management and multi-reservoir operation due to its advantages such as simple structure and strong global search capability. It has shown great potential in solving the SCOS problem.

[0006] Service Composition and Optimal Selection (SCOS), a crucial component of cloud manufacturing, involves selecting a set of cloud services from a candidate service set (CMCSS) according to specific processes and rules to accomplish complex tasks, thereby enhancing the value and efficiency of service resources within the cloud manufacturing system. As is well known, the SCOS problem is essentially an NP-hard constrained combinatorial optimization problem. Over the past decade, numerous scholars have conducted extensive research on SCOS models from various perspectives. Research on single-objective SCOS models includes considerations such as geographic location, service relevance, task similarity and credibility, crowdsourcing patterns, and sustainability. Research on multi-objective SCOS models involves cloud entropy, customer preference attributes, energy consumption, short-term user profits and long-term supplier profits, as well as the interests of multiple stakeholders.

[0007] Although scholars have studied the optimization objectives and constraints of the SCOS problem model from multiple perspectives, there is relatively little research on methods for handling uncertainties in the execution of CMfg tasks. Some scholars have proposed solutions, such as the paper "Wei Le, Zhao Qiuyun, Shu Hongping. Adaptive adjustment of QoS-based combined cloud services in cloud manufacturing environment [J]. Journal of Lanzhou University (Natural Science Edition), 2012, 48(04):98-104.DOI:10.13885 / j.issn.0455-2059.2012.04.015", which proposes a high-quality service adaptive adjustment model for cloud services. This model adapts to changes in service quality and user needs in the cloud manufacturing environment by dynamically adjusting the service combination scheme. The paper “Zhao Qiuyun, Wei Le, Shu Hongping. Anomaly Handling Model for Cloud Services of Manufacturing Equipment in Cloud Manufacturing Environment [J]. Journal of Graphics, 2014, 35(06): 840-846” proposes an anomaly handling model for cloud services of manufacturing equipment, which ensures the reliability and stability of services in the cloud manufacturing environment by classifying, identifying and handling abnormal events. In addition, the paper “GAO B, WANG S, KANG L, et al. Anomaly Diagnosis and Handling in Cloud Manufacturing [C / OL] / / 2018 Diagnosis and System Health Management Conference (PHM-Chongqing). 2018: 866-870. DOI: 10.1109 / PHM-Chongqing.2018.00155” proposes an anomaly diagnosis and handling model based on cloud manufacturing, which includes three stages: anomaly detection, cause analysis and anomaly handling. The paper "WANG Y, WANG S, YANG B, et al. An effective adaptive adjustment method for service composition anomaly handling in cloud manufacturing [J / OL]. Intelligent Manufacturing Journal, 2022, 33(3):735-751. DOI:10.1007 / s10845-020-01652-4" studies the anomaly handling model of cloud manufacturing service composition and proposes three different methods: The first method is to use service anomaly replacement in CMfg to adaptively adjust the service composition to solve the problem of individual service anomalies. However, this method is limited by the number of services in CMfg, and it is difficult to find an effective solution. Therefore, the paper "WANG Y, WANG S, KANG L, et al. An effective dynamic service composition reconstruction method for service anomalies in real-world cloud manufacturing [J / OL]. Robotics and Computer Integrated Manufacturing, 2021, 71: 102143. DOI: 10.1016 / j.rcim.2021.102143" proposes a second method, namely, using dynamic service composition reconstruction to handle service anomalies in cloud manufacturing. This method can reconstruct cloud manufacturing service compositions under specific constraints, but it cannot well show the relationships between multiple objectives.Finally, the paper "WANG Y, WANG S, GAO S, et al. Adaptive multi-objective service composition reconstruction method considering dynamic real-world constraints in cloud manufacturing [J / OL]. Knowledge-based Systems, 2021, 234:107607. DOI:10.1016 / j.knosys.2021.107607" further considers the actual constraints of manufacturing resource coupling relationships, the selection of processing and transportation methods, and the adjustment of manufacturing resource reconstruction, and proposes a robust service composition reconstruction method that incorporates multiple real-world constraints in real-world cloud manufacturing.

[0008] It's easy to see that these studies primarily focus on emergency handling after service anomalies occur. Their performance heavily relies on the CMS and real-time resource status, easily leading to low-quality temporary adjustments, or even causing the entire task to fail due to the lack of feasible solutions. Therefore, in the CMfg system, the ability of the CMS obtained during the SCOS phase to withstand a certain degree of anomalies becomes a crucial consideration. Summary of the Invention

[0009] The technical problem to be solved by this invention is to provide a new method for adaptive robust service composition and optimization selection in cloud manufacturing, so as to solve the technical problems existing in the prior art.

[0010] The technical solution adopted in this invention is: a new method for adaptive robust service composition and optimization selection in cloud manufacturing, which includes the following steps:

[0011] 1) Establish an Adaptive Robust Service Composition and Optimal Selection (ARSCOS) model;

[0012] 2) The enhanced multi-objective artificial hummingbird algorithm (EMOAHA) is used to solve the model in step 1).

[0013] Furthermore, the steps for establishing the aforementioned Adaptive Robust Service Composition and Optimal Selection (ARSCOS) model are as follows:

[0014] 101) Requirements Analysis and Task Decomposition Phase: The complex cloud manufacturing task is decomposed into a finite number of STs according to actual needs, and each ST is executed by a suitable MCS;

[0015] 102) Service Search and Matching: For each subtask, retrieve all MCSs that meet the functional requirements and form its candidate Manufacturing Cloud Service Set (CMCSS), representing the number of MCSs in the CMCSS;

[0016] 103) Service Composition and Optimization Selection (SCOS): Select a candidate MCS for each subtask (ST) from the CMCSS to generate a composite manufacturing service (CMS) with the best overall quality of service (QoS);

[0017] 104) Task Execution: After user confirmation, the task is executed according to the optimal CMS.

[0018] In step 103), each subtask ST is assigned a preferred MCS and a backup AMCS. The number of subtasks is set to n, and the number of MCSs corresponding to each ST is assumed to be the same, set to m. The preferred MCSs constitute the preferred composite manufacturing service (pCMS). If no anomaly occurs, the task will be completed according to pCMS; otherwise, if the preferred MCS of a certain ST has an anomaly, the ST will repair the anomaly or be replaced by its AMCS. When a service anomaly occurs, the task execution delay time caused by the following three decisions is considered:

[0019] A) Select to call the alternative service: (1-P) f )×R t (i), where P f Let R represent the probability of choosing to wait for service i to perform fault repair when service i encounters an anomaly. t (i) is the preferred MCS for the i-th ST. i An anomaly occurred and its AMCS i Delay time when it is called;

[0020] B) Select service i to handle the exception, and service i is able to complete the exception handling: P f ×P c ×R f (i), where P c R represents the probability that the service can successfully repair the exception. f (i) is the preferred MCS for the i-th ST. i Time required to handle exceptions;

[0021] C) Select service i to handle the exception. If service i cannot complete the exception handling, then call the alternative service: P. f ×(1-P c )×(R f (i)+R t (i)).

[0022] Furthermore, the above-mentioned use of task execution delay time when service exceptions occur to describe the robustness of the CMS, serving as a symbol of the CMS's ability to resist abnormal events. Based on this, the following assumptions and preconditions should be met during the SCOS process:

[0023] (a) The probability of a service failure E(i) and the probability of choosing to wait for the service to handle the failure P f The probability P that the service can successfully complete exception handling c This can be obtained through statistical analysis;

[0024] (b) Ignore the case where the preferred MCS and AMCS of a certain ST fail simultaneously;

[0025] Based on the robustness definition of CMS, the quantitative robustness criterion of ARSCOS is defined as follows:

[0026]

[0027] Furthermore, the maximum value and maximum robustness of the average Quality of Service (QoS) in the aforementioned Adaptive Robust Service Composition and Optimal Choice (ARSCOS) model are represented by the following functions:

[0028]

[0029] Pareto optimality sets are used to compare multi-objective solutions F.

[0030] Furthermore, the steps of the enhanced multi-objective artificial hummingbird algorithm described above are as follows:

[0031] 201) Initialize the population; initialize the population using the Opposition Based Learning (OBL) method; when the original solution x i When randomly generated in the search space, its mirror solution x i ′ will be generated between the lower boundary Low and the upper boundary Up, and the relationship between them satisfies:

[0032]

[0033] Where Low and Up are the upper and lower boundaries of the d-dimensional problem, respectively, r is a random vector in [0,1], and x i Let N represent the location of the i-th food source in the solution to the given problem, and N represent the population size.

[0034] 202) Initialize the food source access table;

[0035] 203) During the foraging process, the MOAHA algorithm makes full use of three flight techniques, including omnidirectional flight, diagonal flight and axial flight;

[0036] 204) Guided Foraging: In the guided foraging phase, once the target food source is determined, the hummingbird flies towards it to forage. Each hummingbird tends to visit the food source with the highest access level from the food source with the largest nectar content. The mathematical model for guided foraging is as follows:

[0037] v i (t+1)=x i,tar (t)+D·a·(x i (t)-x i,tar (t)) (11)

[0038] Where, x i (t) is the i-th iteration at the t-th iteration. th The location of the food source, x i,tar (t) is the i-th th The location of the target food source that the hummingbird intends to visit; 'a' is a guiding factor that follows a standard normal distribution N(0,1); 'D' is the direction matrix used to control the hummingbird's flight; after guiding the foraging, the visit table is updated.

[0039] 205) Improved Territory Foraging: A global leader α is selected from the external archive using a roulette wheel strategy. α is then used to guide individuals in the population to search for the most promising regions. The selection of α is accomplished using a roulette wheel method, with the following probabilities for each hypercube:

[0040]

[0041] Where c is a constant greater than 1, and N is the number of Pareto optimal solutions obtained in the i-th segment; the search always proceeds towards the most promising region of the search space;

[0042] The improved territory foraging formula is as follows:

[0043]

[0044] Where, x α (t) is the position vector corresponding to the global leader α selected from the external archive through the roulette wheel strategy, b is the region factor, which follows a standard normal distribution N(0,1). After the domain foraging strategy is executed, the access table is updated.

[0045] 206) Migratory foraging: When food becomes scarce in their current location, hummingbirds tend to migrate to areas far from their current location to forage. In MOAHA, the worst-case front solution based on the Non-Dominated Sorting (NDS) is defined as the worst food source. Therefore, hummingbird migratory foraging behavior in MOAHA is represented as follows:

[0046]

[0047] Among them, F endIt is the worst frontier, r is a random number in [0,1], and Up and Low are the upper and lower boundaries; when the migration foraging is completed, the access table is updated, and the update process is similar to the other two foraging strategies.

[0048] 207) Improved Differential Evolution Strategy: Embed the Differential Evolution (DE) algorithm into MOAHA. The standard differential evolution algorithm includes mutation, crossover, and selection operations. After executing the improved differential evolution strategy, update the access table.

[0049] Furthermore, in the above mutation operations, individual x i (t) produces variant individuals v i The expression for (t) is:

[0050] v i (t)=x best (t)+F'·(x r1 (t)-x r2 (t)) (25)

[0051] In the formula, x best (t) represents the current optimal solution, and x is used in this invention. α (t) as x best (t); x r1 (t) and x r2 (t) are two individuals randomly selected from the current generation, r1≠r2≠best; Levy's flight stride F' is as follows:

[0052]

[0053] In the formula, α0 is the step size factor;

[0054] Furthermore, the above crossover operation is based on the crossover factor CR, which is used to cross the variant individuals v i (t) and parent individual x i (t) The experimental individual u is obtained by operating according to formula (18). i (t):

[0055]

[0056] In the formula, j = 1, 2, ..., d; j = j ran d is a randomly selected integer in [1, d], which guarantees that the experimental individual u i (t) at least v must be obtained from the mutated individuals i(t) yields an element with a CR value ranging from [0.1, 0.9]. The crossover factor CR = 0.5 * (1 + Rand) is set to dynamically change the CR value around 0.75, increasing the randomness of the algorithm and improving population diversity. Rand is a random number between [0, 1].

[0057] Furthermore, the above selection operation employs a "greedy" selection strategy, that is, in the parent individual x... i (t) and the experimental individual u i The better individual among (t) is selected as the next generation of the population. The expression for the selection operation is:

[0058]

[0059] In the formula, f(u) i (t))<f(x i (t) represents the individual u i (t) is better than x i (t).

[0060] Furthermore, the food source access table in step 202 above is initialized as follows:

[0061]

[0062] Where i = j, VT i,j =null indicates that the hummingbird feeds at its specific food source; for i≠j, VT i,j =0 indicates that in the current iteration, the j-th food source has just been consumed by the i-th food source. th The hummingbird visited.

[0063] The beneficial effects of the present invention are as follows: Compared with the prior art, the present invention has the following advantages:

[0064] 1) The Adaptive Robust Service Composition and Optimal Selection Model (ARSCOS) of this invention aims to enhance the anti-interference capability of CMS and reduce the negative impact of uncertainty on the task execution process;

[0065] 2) Each ST is assigned a preferred MCS and an alternative AMCS. The preferred MCSs constitute the preferred composite manufacturing service (pCMS), and the task will be completed according to the pCMS if no anomalies occur. Since the preferred MCSs are already booked, production preparation can be made in advance, thus requiring no additional time. Conversely, if an anomaly occurs in the preferred MCS of an ST, the ST will either repair the anomaly or be replaced by its AMCS.

[0066] 3) Considering that multiple factors influence production decisions in the actual environment, variable P is introduced. fThis represents the probability of choosing to wait for the service to repair itself when an exception occurs. Furthermore, due to various uncertainties in the real-world environment, a service exception may not necessarily be successfully repaired. Therefore, referencing variable P... c This indicates the probability that the service can successfully repair the anomaly;

[0067] 4) Use the delay time of task execution when a service exception occurs to describe the robustness of the CMS, as a symbol of the CMS's ability to resist abnormal events. The greater the robustness, the better.

[0068] 5) When considering two or more optimization objectives, there are often conflicts between decision variables. The concept of Pareto optimal set is used to compare multi-objective solutions.

[0069] 6) The MOAHA algorithm is a biologically-based metaheuristic algorithm that solves optimization problems by iteratively searching the initial population of the search space. The diversity of the initial population has a positive impact on search efficiency. However, in the population initialization phase, randomly generated initial positions may lead to uncertainty in search efficiency and quality. To address this issue, an Opposition Based Learning (OBL)-based population initialization method is adopted to improve the quality and diversity of the initial population. Specifically, OBL can generate new solutions that are the opposite of the original solutions and select better solutions as initial solutions, thereby improving the search efficiency and diversity of the population.

[0070] 7) In the standard MOAHA territorial foraging phase, hummingbirds use solutions randomly selected from an external archive to search their territory. This external archive stores the best non-dominated solutions obtained so far. However, the random selection method has limitations because it doesn't account for crowding in the solution set of the external archive, potentially causing the population to continuously search towards a particular region, leading to overly concentrated solutions and local optima. Therefore, this section first addresses this by using a roulette wheel strategy.

[49] Select a global leader α from the external archive, and then use α to guide the population individuals to search for the most promising areas;

[0071] 8) In each iteration, the roulette wheel selection method is used instead of the original random selection. The location information of the best and most promising solutions obtained so far is communicated with the location information of individuals in the population, which effectively enhances the global search capability and solution diversity of the algorithm.

[0072] 9) Embedding the Differential Evolution (DE) algorithm into MOAHA increases the population diversity and convergence speed of MOAHA by increasing information exchange between individuals and between individuals and external archives;

[0073] 10) As the population evolves, each individual's position is updated by exchanging information with the best position to date within a small range. However, this can cause the algorithm to prematurely fall into local optima. The Lévy fly strategy is a special type of random walk strategy that involves frequent short-distance walks and occasional long-distance walks during the walk process, effectively balancing the algorithm's local exploitation and global exploration capabilities, helping it escape local optima. Therefore, the Lévy fly strategy is introduced into the mutation phase of the DE algorithm, and the Lévy fly step size is used instead of the mutation factor F in the conventional mutation algorithm; with α0 = 0.3, after 100 runs divided into 20 groups, the histogram of F' values ​​is as follows. Figure 3 As shown, most values ​​lie within the interval [-0.5, 0.5], which helps improve the algorithm's convergence speed. Meanwhile, a small portion of values ​​lie outside the interval [-0.5, 0.5], which helps the algorithm escape local optima with a certain probability. Replacing the original F with F' improves both the algorithm's convergence speed and helps it escape local optima with a certain probability. Attached Figure Description

[0074] Figure 1 A schematic diagram of SCOS in CMfgCMfg;

[0075] Figure 2 A schematic diagram of ARSCOS in CMfgCMfg;

[0076] Figure 3 The histogram is shown when α0 = 0.3;

[0077] Figure 4 The results of different algorithms on the test function UF2 are shown in the graph;

[0078] Figure 5 The results of different UF3 algorithms on the test function UF3 are shown in the graph.

[0079] Figure 6 The results of different algorithms on the test function ZDT1 are shown in the figure;

[0080] Figure 7 The results of different algorithms on the test function ZDT2 are shown in the graph;

[0081] Figure 8 The results of different algorithms on the test function CF1 are shown in the graph.

[0082] Figure 9The results of different algorithms on the test function CF6 are shown in the graph.

[0083] Figure 10 A diagram illustrating task breakdown;

[0084] Figure 11 A distribution map of the optimal solution;

[0085] Figure 12 Statistical results of different algorithms for solving the ARSCOS problem;

[0086] Figure 13 A comparison chart of the time consumption of different algorithms;

[0087] Figure 14 This is a flowchart of the present invention. Detailed Implementation

[0088] The present invention will be further described below with reference to specific embodiments.

[0089] Example 1: As Figure 1-14 As shown, a new method for adaptive robust service composition and optimization selection in cloud manufacturing includes the following steps:

[0090] First, an Adaptive Robust Service Composition and Optimal Choice (ARSCOS) model was established to improve the ability of CMS to resist certain uncertain events during the planning phase of Service Composition and Optimal Choice (SCOS).

[0091] In the CMfg platform, complex manufacturing requirements submitted by service requesters can be viewed as a task T, which is then decomposed into multiple subtasks (ST) executed by different Manufacturing Cloud Services (MCS). This enables the collaboration of geographically dispersed manufacturing resources to achieve the highest user satisfaction. The steps for establishing the Adaptive Robust Service Composition and Optimal Selection (ARSCOS) model are as follows:

[0092] 101) Requirements Analysis and Task Decomposition Phase: The complex cloud manufacturing task is decomposed into a finite number of STs according to actual needs, and each ST is executed by a suitable MCS;

[0093] 102) Service Search and Matching: For each subtask, retrieve all MCSs that meet the functional requirements and form its candidate Manufacturing Cloud Service Set (CMCSS), representing the number of MCSs in the CMCSS;

[0094] 103) Service Composition and Optimization Selection (SCOS): Select a candidate MCS for each subtask (ST) from the CMCSS to generate a composite manufacturing service (CMS) with the best overall quality of service (QoS);

[0095] 104) Task Execution: After user confirmation, the task is executed according to the optimal CMS.

[0096] It is evident that the quality of the optimal CMS obtained in the SCOS stage directly affects the efficiency and accuracy of task execution. The focus of this invention is the third stage, with the number of subtasks set to n. To simplify the model, it is assumed that the number of MCSs corresponding to each ST is the same, set to m.

[0097] Encoding Method: Candidate services are encoded using integer encoding, and the combined services are mapped to position vectors. Each integer value in the vector dimension represents the index of a specific service in the candidate set. Assume a task consists of n subtasks. Under the integer array encoding scheme, the hummingbird i's position vector is represented by an n-dimensional array x. i ={x i1 ,x i2 ,...,x in Let}, i = 1, 2, ..., N represent the sequence of elements x, where each element x ij This represents the index of the specific service in the corresponding candidate set, and N represents the population size. For example... Figure 1 The array corresponding to the position vector shown is x. i ={1,m,...,i,...1}.

[0098] Quality of Service (QoS) is an important standard for measuring basic cloud services and composite cloud services, and it has been widely applied to the SCOS problem. Currently, there are many evaluation metrics for measuring the QoS of MCSs. The four most commonly used metrics in SCOS are selected as: time, cost, reliability, and quality. Since the definitions and descriptions of these metrics are already available in many other documents, this invention will not repeat them. Furthermore, the literature “QUE Y, ZHONG W, CHENH, et al. An improved adaptive immune genetic algorithm for optimal QoS-aware service composition selection in cloud manufacturing [J / OL]. International Journal of Advanced Manufacturing Technology, 2018, 96:4455-4465. DOI:10.1007 / s00170-018-1925-x” has already considered the transformation of four classic cloud manufacturing internal structures. Therefore, this invention only considers the sequential structure case. Therefore, the average QoS calculation formula for SCOS is as follows:

[0099]

[0100] Where, ω c ,ω T ,ω Re ,ω Q ω represents the weights of cost, time, reputation, and product quality, respectively. c ,ω T,ω Re ,ω Q ∈[0,1], and ω c +ω T +ω Re +ω Q =1. The descriptions of the four QoS attributes and aggregation functions above are shown in Table 1.

[0101] Table 1. Overall QoS Attributes for Sequential Types

[0102]

[0103]

[0104] Considering that the value range and dimensions of each attribute in QoS are different, the QoS value of each indicator needs to be normalized before calculating the overall QoS value. According to the practical meaning, QoS attribute indicators can be divided into positive attribute indicators and negative attribute indicators. Through equation (2), the four attribute indicators under consideration can be normalized to the range [0,1].

[0105]

[0106] In the formula, x max and x min These are the maximum and minimum values ​​of the evaluation index, respectively. Furthermore, when x... max =x min At that time, q k =1.

[0107] In step 103), the Adaptive Robust Service Composition and Optimal Selection Model (ARSCOS) has the following structure: Figure 2 As shown in the diagram, this structure assigns a preferred MCS and a backup AMCS to each subtask ST. The number of subtasks is set to n, and the number of MCSs corresponding to each ST is assumed to be the same, set to m. The preferred MCSs constitute the preferred composite manufacturing service (pCMS). If no anomalies occur, the task will be completed according to the pCMS. Since the preferred MCSs are already pre-booked, production preparation can be done in advance, thus requiring no additional time. Conversely, if an anomaly occurs in the preferred MCS of a certain ST, the ST will either repair the anomaly or be replaced by its AMCS.

[0108] Considering that various factors influence production decisions in real-world environments, this invention introduces the variable P. f Let P represent the probability of choosing to wait for service i to repair itself when service i encounters an anomaly. Furthermore, due to various uncertainties in the real-world environment, a service may not be able to successfully repair itself after an anomaly occurs. Therefore, referencing variable P... cLet be the probability that the service can successfully recover from the exception. Therefore, the possible decisions that a service might face after an exception can be represented using probability as follows:

[0109] • Select alternative service: 1-P f ;

[0110] • Select service i to handle the exception, and service i is able to complete the exception handling: P f ×P c

[0111] • If service i is selected to handle the exception, but service i is unable to complete the exception handling, then the alternative service P is called. f ×(1-P c )

[0112] Since it's unrealistic to have all AMCSs ready for production, additional time is needed for production scheduling and material delivery when calling AMCSs. This is addressed using R... t (i) represents this. Similarly, the time required for the service to handle exceptions is represented by R. f (i) indicates.

[0113] In summary, when a service exception occurs, consider the delay in task execution caused by the following three decisions:

[0114] A) Select to call the alternative service: (1-P) f )×R t (i), where P f Let R represent the probability of choosing to wait for service i to perform fault repair when service i encounters an anomaly. t (i) is the preferred MCS for the i-th ST. i An anomaly occurred and its AMCS i Delay time when it is called;

[0115] B) Select service i to handle the exception, and service i is able to complete the exception handling: P f ×P c ×R f (i), where P c R represents the probability that the service can successfully repair the exception. f (i) is the preferred MCS for the i-th ST. i Time required to handle exceptions;

[0116] C) Select service i to handle the exception. If service i cannot complete the exception handling, then call the alternative service: P. f ×(1-P c )×(R f (i)+R t(i)).

[0117] The above description uses the delay time of task execution when service exceptions occur to describe the robustness of the CMS, serving as a symbol of the CMS's ability to resist abnormal events; the greater the robustness, the better. Based on this, the following assumptions and preconditions should be met during the SCOS process:

[0118] (a) The probability of a service failure E(i) and the probability of choosing to wait for the service to handle the failure P f The probability P that the service can successfully complete exception handling c This can be obtained through statistical analysis;

[0119] (b) Ignore the case where the preferred MCS and AMCS of a certain ST fail simultaneously;

[0120] Based on the robustness definition of CMS, the quantitative robustness criterion of ARSCOS is defined as follows:

[0121]

[0122] After simplification:

[0123]

[0124] Where: n is the number of STs, R t (i) is the preferred MCS for the i-th ST. i An anomaly occurred and its AMCS i Delay time when R is called f (i) is the preferred MCS for the i-th ST. i The time required for exception handling, q t (j) represents the duration of the j-th ST executed by its preferred MCS, E(i) is the anomaly probability of the i-th ST, and P f P represents the probability of choosing to wait for the service to handle the exception when an exception occurs. c The probability of successfully handling and repairing an anomaly in the service. In this invention, R is taken as... t (i) The range is (0.01, 20], q t The anomaly probability E(i) of the i-th ST is randomly generated within the range of [0.02, 0.1] obtained from statistical analysis, with a parameter setting that does not lose generality. In this invention, R... f (i), P f P c The values ​​for these parameters are (0.01, 20], [0.7, 1], and [0.7, 1], respectively. It should be noted that these parameters can be set according to the actual situation without affecting the effectiveness of the proposed method.

[0125] The maximum value and maximum robustness of the average Quality of Service (QoS) in the Adaptive Robust Service Composition and Optimal Choice (ARSCOS) model described above are represented by the following functions:

[0126]

[0127] in,

[0128] In equation (1), ω c ω T ω Re and ω Q ω represents the weights of cost, time, reputation, and product quality, respectively. c ∈[0,1]、ω T ∈[0,1]、ω Re ∈[0,1] and ω Q ∈[0,1], and ω c +ω T +ω Re +ω Q =1;

[0129] When considering two or more optimization objectives, there are often conflicts between decision variables. Pareto optimality sets are used to compare multi-objective solutions F.

[0130] Secondly, the enhanced multi-objective artificial hummingbird algorithm (EMOAHA) is used to solve the model in step 1). The improved strategies of the enhanced multi-objective artificial hummingbird algorithm (EMOAHA) include: using a strategy based on reverse learning for population initialization, using a roulette wheel strategy to improve domain foraging, and using an improved differential evolution algorithm to embed the standard MOAHA.

[0131] The multi-objective artificial hummingbird algorithm (MOAHA) is a highly efficient multi-objective optimization algorithm extended from the standard artificial hummingbird algorithm (AHA). It employs a dynamic elimination-based crowding distance (DECD) method to maintain an external archive, simulating three foraging behaviors: guided foraging, territorial foraging, and migratory foraging, as well as three flight skills: axial flight, diagonal flight, and omnidirectional flight. Furthermore, the algorithm utilizes an access table to represent the hummingbird's memory capacity when selecting ideal food sources.

[0132] The enhanced multi-objective artificial hummingbird algorithm steps are as follows:

[0133] 201) Initializing the Population; The MOAHA algorithm is a biologically based metaheuristic algorithm that solves optimization problems by iteratively searching the initial population of the search space. The diversity of the initial population has a positive impact on search efficiency. However, in the population initialization phase, randomly generated initial positions may lead to uncertainty in search efficiency and quality. To address this issue, an Opposition Based Learning (OBL)-based population initialization method is adopted to improve the quality and diversity of the initial population. Specifically, OBL can generate new solutions that are the opposite of the original solution and select better solutions as the initial solutions, thereby improving the search efficiency and diversity of the population. When the original solution x... i When randomly generated in the search space, its mirror solution x i ′ will be generated between the lower boundary Low and the upper boundary Up, and the relationship between them satisfies:

[0134]

[0135] Where Low and Up are the upper and lower boundaries of the d-dimensional problem, respectively, r is a random vector in [0,1], and x i Let N represent the location of the i-th food source in the solution to the given problem, and N represent the population size.

[0136] 202) Initialize the food source access table; the food source access table is initialized as follows:

[0137]

[0138] Where i = j, VT i,j =null indicates that the hummingbird feeds at its specific food source; for i≠j, VT i,j =0 indicates that in the current iteration, the j-th food source has just been consumed by the i-th food source. th The hummingbird visited;

[0139] 203) During the foraging process, the MOAHA algorithm makes full use of three flight techniques, including omnidirectional flight, diagonal flight and axial flight;

[0140] Axial flight: Axial flight means that the hummingbird flies along any coordinate axis in the search space. The hummingbird's axial flight is given as follows:

[0141]

[0142] Diagonal flight: Diagonal flight means that the hummingbird flies from one corner of a rectangle to the opposite corner of the search space. The diagonal flight of the hummingbird is given as follows:

[0143]

[0144] Omnidirectional flight: Omnidirectional flight means that the hummingbird flies in the direction projected onto each coordinate axis in the search space. The omnidirectional flight of the hummingbird is given as follows:

[0145] D (i) =1 i=1,...,d (10)

[0146] 204) Guided Foraging: In the guided foraging phase, once the target food source is determined, the hummingbird flies towards it to forage. Each hummingbird tends to visit the food source with the highest access level from the food source with the largest nectar content. The mathematical model for guided foraging is as follows:

[0147] v i (t+1)=x i,tar (t)+D·a·(x i (t)-x i,tar (t)) (11)

[0148] Where, x i (t) is the i-th iteration at the t-th iteration. th The location of the food source, x i,tar (t) is the i-th th The location of the target food source that the hummingbird intends to visit, 'a' is a guiding factor that follows a standard normal distribution N(0,1); 'D' is the direction matrix used to control the hummingbird's flight, which is the direction matrix obtained from one of the three flight techniques in step 203; after performing guided foraging, update the visit table;

[0149] 205) Improved Territory Foraging: In the standard MOAHA territory foraging phase, hummingbirds use solutions randomly selected from an external archive to search their territory. The external archive stores the best non-dominated solutions obtained so far. However, the random selection method has limitations because it does not consider the crowding of the solution set in the external archive, which may cause the population to keep searching towards a certain region, resulting in overly concentrated solutions and getting trapped in local optima. Therefore, a global leader α is selected from the external archive using a roulette wheel strategy, and then α is used to guide the population to search towards the most promising region. The selection of α is accomplished using the roulette wheel method, and the probabilities of each hypercube are as follows:

[0150]

[0151] Where c is a constant greater than 1, and N is the number of Pareto optimal solutions obtained in the i-th segment; the search always proceeds towards the most promising region in the search space; it can be seen from equation (15) that the probability of α being selected is inversely proportional to the crowding level in the hypercube, and the more crowded the hypercube, the lower the probability of being selected as the leader. Therefore, the search always proceeds towards the most promising region in the search space;

[0152] The improved territory foraging formula is as follows:

[0153]

[0154] Where, x α (t) is the position vector corresponding to the global leader α selected from the external archive through the roulette wheel selection strategy, b is the regional factor, which follows a standard normal distribution N(0,1). After executing the domain foraging strategy, the access table is updated. In each iteration, the roulette wheel selection method is used instead of the original random selection to exchange the position information of the best solution and the most promising solution obtained so far with the position information of individuals in the population, which effectively enhances the global search capability and solution diversity of the algorithm.

[0155] 206) Migratory foraging: When food becomes scarce in their current location, hummingbirds tend to migrate to areas far from their current location to forage. In MOAHA, the worst-case front solution based on the Non-Dominated Sorting (NDS) is defined as the worst food source. Therefore, hummingbird migratory foraging behavior in MOAHA is represented as follows:

[0156]

[0157] Among them, F end It is the worst frontier, r is a random number in [0,1], and Up and Low are the upper and lower boundaries; when the migration foraging is completed, the access table is updated, and the update process is similar to the other two foraging strategies.

[0158] 207) Improved Differential Evolution Strategy: The Differential Evolution (DE) algorithm is embedded into MOAHA to increase information exchange between individuals and between individuals and external archives, thereby improving the population diversity and convergence speed of MOAHA. The Differential Evolution algorithm is a population-based global optimization algorithm characterized by its simplicity, fewer control parameters, and good robustness. The standard Differential Evolution algorithm includes mutation, crossover, and selection operations. After implementing the improved Differential Evolution strategy, the access table is updated.

[0159] The mutation operation described above is a key step that fully embodies the idea of ​​differential evolution. There are various strategies, the most classic and commonly used being "DE / best / 1". As the population evolves, each individual's position is updated by exchanging information with the best position to date within a small range. However, this can cause the algorithm to prematurely get trapped in local optima. (Levi's flight strategy) [54,55]This is a special random walk strategy that involves frequent short-distance walks and occasional long-distance walks during the walk process. This effectively balances the algorithm's local exploitation and global exploration capabilities, helping it escape local optima. Therefore, the Lévy flight strategy is introduced into the mutation phase of the DE algorithm, and the Lévy flight step size is used instead of the mutation factor F.

[0160] The formula for updating Levi's flight position is as follows:

[0161]

[0162] Where, x i (t) represents the position of the i-th individual in generation t; This represents point-to-point multiplication; α represents the step size control variable, which can be expressed as:

[0163] α=α0·(x i (t)-x best (t)) (21)

[0164] Where α0 is the step size factor, typically taken as 0.01, x i (t) represents the i-th solution in the t-th generation, x best (t) represents the current optimal solution, and x is used in this invention. α (t) as x best Let Levy(t) represent a random path following a Levy distribution, and let s be the step size of the Levy flight. In practical engineering, the Mantegna algorithm is often used to simulate Levy flight. The formula for calculating the step size s is:

[0165]

[0166] Where μ and v follow a normal distribution, defined as follows:

[0167]

[0168] In formula (23), Γ represents the gamma function; β is usually taken as 1.5.

[0169] The Lévy flight stride F' is used to replace the mutation factor F, and in the mutation operation, individual x i (t) produces variant individuals v i The expression for (t) is:

[0170] v i (t)=x best (t)+F'·(x r1 (t)-x r2 (t)) (25)

[0171] In the formula, x best(t) represents the individual with the best fitness in the current generation. In this invention, x is used. α (t) as x best (t); x r1 (t) and x r2 (t) are two individuals randomly selected from the current generation, r1≠r2≠best; Levy's flight stride F' is as follows:

[0172]

[0173] In the formula, α0 is the step size factor;

[0174] The value of the mutation factor F typically ranges between [0, 2]. Generally, a smaller value allows for a finer search near already found good solutions, further optimizing the individual. A larger value allows for a broader search of the search space, helping to discover new solutions or escape local optima. With α0 = 0.3, running 100 times and divided into 20 groups, the histogram of F' values ​​is as follows. Figure 3 As shown, most values ​​lie within the interval [-0.5, 0.5], which helps improve the algorithm's convergence speed. Meanwhile, a small portion of values ​​lie outside the interval [-0.5, 0.5], which helps the algorithm escape local optima with a certain probability. Replacing the original F with F' improves both the algorithm's convergence speed and helps it escape local optima with a certain probability.

[0175] The above crossover operation is based on the crossover factor CR, which is used to cross the mutant individuals v i (t) and parent individual x i (t) The experimental individual u is obtained by operating according to formula (18). i (t):

[0176]

[0177] In the formula, j = 1, 2, ..., d; j = j rand It is a randomly selected integer within [1, d], guaranteeing that the experimental individual u i (t) at least v must be obtained from the mutated individuals i (t) yields an element with a CR value ranging from [0.1, 0.9]. The crossover factor CR = 0.5 * (1 + Rand) is set to dynamically change the CR value around 0.75, increasing the randomness of the algorithm and improving population diversity. Rand is a random number between [0, 1].

[0178] The above selection operation employs a "greedy" selection strategy, that is, in the parent individual x i (t) and the experimental individual u i The better individual among (t) is selected as the next generation of the population. The expression for the selection operation is:

[0179]

[0180] In the formula, f(u) i (t))<f(x i (t) represents the individual u i (t) is better than x i (t).

[0181] Furthermore, the food source access table in step 202 above is initialized as follows:

[0182]

[0183] Where i = j, VT i,j =null indicates that the hummingbird feeds at its specific food source; for i≠j, VT i,j =0 indicates that in the current iteration, the j-th food source has just been consumed by the i-th food source. th The hummingbird visited.

[0184] The EMOAHA algorithm was designed to address the proposed ARSCOS problem, and its pseudocode is shown in Figure 1.

[0185]

[0186]

[0187] The computational complexity of the EMOAHA algorithm depends primarily on the size of the hummingbird population (N), the maximum number of iterations (T), the number of targets (M), the population dimension (D), and the size of the external archive being equal to the population size (N). The following operators measure the computational complexity of EMOAHA in the worst-case scenario.

[0188] (1) The complexity of NDS is O(TMN) 2 ).

[0189] (2) Removing the element with the smallest crowding distance from the archive and updating the archive requires O(TMN) 2 The computational complexity of the DECD method is at most O(2TMN), which requires O(logN) to calculate the crowding distance between adjacent elements. 2 logN)+O(2TMN)).

[0190] (3) The computational complexities of guided foraging, territorial foraging, migration foraging and differential evolution operations are O(0.5TMN), O(0.5TMN), O(0.5TM / N), and O(TMND), respectively.

[0191] (4) The initialization complexity of the population based on reverse learning is O(MND). Therefore, the computational complexity of EMOAHA is: O(EMOAHA) = max(O(TMN)). 2 ),O(TMN 2 logN+2TMN),O(TMN+0.5TM / N+TMND),O(MND)).

[0192] Therefore, the overall complexity is: O(EMOAHA) = O(TMN) 2 logN).

[0193] Two sets of experiments were conducted to explore the performance of the proposed algorithm. The first set of experiments evaluated the effectiveness of the proposed algorithm on 17 well-known test functions. The second set of experiments aimed to evaluate the performance of the proposed method in real-world cloud manufacturing cases.

[0194] The performance of multi-objective optimization algorithms is generally evaluated from two aspects: diversity and convergence. Since a single performance index cannot well describe these two evaluation criteria, this invention uses commonly used comprehensive indices, inversion generation distance (IGD) and hypervolume (HV), to simultaneously evaluate the convergence and diversity of the algorithm.

[0195] EMOAHA's effectiveness against benchmark functions: Seventeen well-known standard test functions, including UF1-7, ZDT1-3, and CF1-7, were selected from previous literature. The performance of these functions was evaluated using the IGD and HV metrics. The parameter settings for all algorithms are shown in Table 2.

[0196] Table 2 Parameter settings for each algorithm

[0197]

[0198]

[0199] The calculation results of IGD and HV metrics for all algorithms are shown in Tables 3 and 4. The optimal results obtained by different algorithms are highlighted in bold, and Mean / Std represents the mean and standard deviation. Statistical results from Tables 3 and 4 show that, regarding the IGD metric, EMOAHA achieves the best results on all benchmark functions except UF3, UF7, CF1, and CF5. For MOAHA, the best IGD values ​​are only obtained on UF7 and CF1; for SMOGWO, the best value is only obtained on UF3; and for NSGA-III, the best value is only obtained on CF5. The remaining algorithms do not achieve the best average. The results for the HV metric are similar to those for the IGD metric, as both evaluate algorithm performance based on overall performance. EMOAHA achieves the best values ​​on all benchmark functions except UF3, ZDT3, CF1, and CF5. Among them, MOAHA achieved the best value on CF1, SMOGWO on UF3, NSGA-II on ZDT3, and NSGA-III on CF5. The remaining algorithms did not achieve the best average value. The results in Tables 3 and 4 show that MOAHA has a significant advantage over other algorithms in solving the benchmark function.

[0200] To examine the significant differences between EMOAHA and the comparison algorithms in terms of IGD and HV metrics, the Wilcoxon Signed Rank Test (WSRT) was used to compare EMOAHA with other algorithms. The statistical results of the WSRT are given in Tables 5 and 6. In the tables, "+" indicates that EMOAHA's metrics are superior to the other algorithm, "-" indicates that EMOAHA's metrics are inferior to the other algorithm, and "≈" indicates that there is no significant difference between EMOAHA and the other algorithm.

[0201] Table 5 shows that the WSRT results for IGD demonstrate that EMOAHA outperforms MOAHA, SMOGWO, MOGWO, MODE, MOMVO, MOPSO, NSGA-II, NSGA-III, MOEA / D, MAOA, and MOAOVA on 13, 15, 16, 17, 17, 16, 16, 16, 17, 16, and 17 out of 17 functions, respectively. The results indicate a significant difference between EMOAHA and the comparison algorithms, and EMOAHA exhibits better overall performance in IGD metrics than other optimization methods. Table 6 shows that the WSRT results for HV demonstrate that EMOAHA outperforms MOAHA, SMOGWO, MOGWO, MODE, MOMVO, MOPSO, NSGA-II, NSGA-III, MOEA / D, MAOA, and MOAOVA on 15, 15, 16, 17, 17, 17, 13, 14, 17, 17, and 17 out of 17 functions, respectively. The results show that EMOAHA differs significantly from the comparison algorithms, and EMOAHA has better overall performance on the HV index than other optimization methods.

[0202] To more intuitively compare the solutions of each algorithm, two functions were selected as representatives from each test function series. For example... Figure 4-9 As shown, the distribution of optimal solutions obtained by the above algorithms on the benchmark functions UF2, UF3, ZDT1, ZDT2, CF2, and CF6 is presented. Black solid dots represent PF (Power Factor), and red solid dots represent the optimal solution set obtained by the algorithms. It can be observed that for UF2, compared with other algorithms, EMOAHA provides the best convergence and coverage, followed by MOAHA and NSGA-II. For UF3, EMOAHA did not obtain a good value; instead, SMOGWO is significantly closer to PF, a result consistent with that in Tables 3 and 4. For ZDT1, ZDT2, and CF1, EMOAHA and MOAHA provide the best convergence and coverage, possibly due to their unique solution update mechanisms and archive maintenance methods. For CF6, EMOAHA provides the best convergence and coverage.

[0203] To rank the overall performance of all algorithms, the Friedman test was used, which is performed on the average solution provided by the algorithms. A better algorithm is ranked lower. Table 7 shows the Friedman test results for the IGD and HV indices. The p-values ​​are less than the significance level α = 0.05. Here, the smaller the p-value, the more significant the difference. This result indicates significant differences among the algorithms compared above.

[0204] As shown in Table 7, EMOAHA ranks first in both IGD and HV metrics, demonstrating strong competitiveness compared to other algorithms. MOAHA ranks second in IGD but third in HV. SMOGWO ranks third in IGD but fifth in HV. NSGA-III ranks fourth in IGD and second in HV. NSGA-II ranks fifth in IGD and fourth in HV. It is evident that the different rankings of each algorithm across the two metrics reflect performance variations from different perspectives. Therefore, it can be concluded that EMOAHA exhibits superior convergence and versatility when solving various MOPs.

[0205] The combined results of all comparisons demonstrate that EMOAHA is superior in solving test functions, and also verify the effectiveness of the strategy designed in this invention.

[0206] Table 3. IGD Measurement Results on the Benchmark Function

[0207]

[0208] Table 4. HV Measurement Results on the Benchmark Function

[0209]

[0210]

[0211] Table 5. WSRT results for the IGD index

[0212]

[0213]

[0214] Table 6 shows the HV results for the IGD index.

[0215]

[0216] Table 7. Friedman's test for IGD and HV measures on the benchmark function (significance level α = 0.05)

[0217]

[0218]

[0219] EMOAHA's effectiveness in solving ARSCOS problems: The practicality of EMOAHA in solving ARSCOS problems was verified. Taking the production of a certain type of civilian unmanned aerial vehicle (UAV) by an aviation equipment manufacturing company in Guizhou Province as an example, the manufacturing of the UAV's airframe structure needs to be outsourced through the CMfg service platform. After the task requirement was submitted to the CMfg platform, it was broken down into 10 sub-tasks, such as... Figure 10 As shown. This includes: airframe structure design, raw material procurement, fuselage manufacturing, nose manufacturing, V-tail manufacturing, main wing manufacturing, aileron manufacturing, flap manufacturing, airframe assembly, and inspection and testing.

[0220] If there are 50 candidate services for each subtask, the size of the ARSCOS problem can be represented by "nm", where n represents the number of subtasks and m represents the number of candidate service tasks. Therefore, this aircraft airframe structure manufacturing task instance can be represented as "10-50".

[0221] Before calculating QoS, cost (C) and time (T) should be normalized using formula (2), and the weights w for cost, time, reliability, and quality should be set to 0.25. The parameter settings for all algorithms are consistent with those described above, as shown in Table 2. Without loss of generality, the relevant parameters of the candidate services are randomly generated within a certain range during initialization, and the value range is shown in Table 8.

[0222] Table 8 Range of Candidate Service Index Values

[0223]

[0224] Furthermore, to further verify the applicability of the model and algorithm to ARSCOS problems of different scales, this case study is expanded to nine ARSCOS problems of different scales. The number of subtasks (STs) is increased to 10, 20, and 30, and the number of candidate services (MCS) corresponding to each subtask is increased to 50, 100, and 150. Therefore, a total of nine ARSCOS problems of different scales are obtained, denoted as: "10-50, 10-100, 10-150, 20-50, 20-100, 20-150, 30-50, 30-100, 30-150".

[0225] The Inverse Geometric Value (IGD) and Hypogean Value (HV) indices were used for evaluation. Since the true frontier (PF) of the ARSCOS problem is unknown, the non-dominated frontiers obtained from all algorithm runs were used as approximate frontiers for calculating the IGD index. Considering the randomness of the algorithms, each algorithm was run independently 20 times. The IGD and HV index calculation results for all algorithms are shown in Tables 9 and 10. The optimal results obtained by different algorithms are highlighted in bold, and Mean / std represents the mean and standard deviation.

[0226] Statistical results from Tables 9 and 10 show that, regarding the IGD metric, EMOAHA achieves the best results for all ARSCOS problems of all sizes except for "10-50", "30-100", and "30-150". For MOAHA, it only achieves the best IGD value for "10-50". For NSGA-III, it only achieves the best values ​​for "30-100" and "30-150", with no other algorithms achieving the best average. Regarding the HV metric, EMOAHA achieves the best value for all nine ARSCOS problems. The significant performance difference between EMOAHA and the HV metric could be due to the non-uniformity of the approximate front used to calculate the IGD metric.

[0227] To examine the significant differences between EMOAHA and the comparison algorithms in terms of IGD and HV metrics, we used the Wilcoxon Signed Rank Test (WSRT) to compare EMOAHA with other algorithms. In Tables 11 and 12, "+" indicates that EMOAHA's metrics are superior to the other algorithm, "-" indicates that EMOAHA's metrics are inferior to the other algorithm, and "≈" indicates that there is no significant difference between EMOAHA and the other algorithm.

[0228] In Table 11, the WSRT results for IGD show that EMOAHA significantly outperforms SMOGWO, MOGWO, MODE, MOPSO, MOEA / D, MAOA, and MOAVOA across all nine scales; and outperforms MOAHA, MOMVO, NSGA-II, and NSGA-III on scales 7, 8, 6, and 3, respectively. In Table 12, the WSRT results for HV show that EMOAHA significantly outperforms MOAHA, SMOGWO, MOGWO, MODE, MOMVO, MOPSO, MOEA / D, MAOA, and MOAVOA across all nine scales; and outperforms NSGA-II and NSGA-III on scales 7 and 6, respectively. These results indicate that EMOAHA differs significantly from the comparative algorithms, and that EMOAHA demonstrates better overall performance in both IGD and HV metrics compared to other optimization methods.

[0229] Table 9. IGD metrics for ARSCOS problems of different sizes.

[0230]

[0231] Table 10 HV metric results for ARSCOS problems of different sizes

[0232]

[0233] Table 11 shows the WSRT results for the IGD index.

[0234]

[0235] Table 12 shows the WSRT results for the HV index.

[0236]

[0237] To intuitively compare the solution performance of each algorithm, Figure 11 The optimal solution distributions obtained by all algorithms for ARSCOS problems of nine sizes are presented. It can be seen that the red dots obtained by EMOAHA are mostly distributed in the outermost part and are relatively dispersed, reflecting its good convergence and diversity. Secondly, the solution distributions obtained by NSGA-III, NSGA-II, and MOAHA are close to those of EMOAHA.

[0238] In addition, to visually demonstrate the distribution of the calculation results of each algorithm, Figure 12 Box plots of the sum and HV values ​​for all algorithms are provided. Based on the mean values ​​(circles) shown in the box plots, it can be seen that EMOAHA's data is distributed at the top of the graph at all scales, indicating that the solution set obtained by the EMOAHA algorithm is of higher quality than the other algorithms. Furthermore, the MOEA / D box plots are distributed at the bottom of the graph at all scales, indicating that the MOEA / D solution results are of lower quality.

[0239] Table 13 Friedman test for IGD and HV indices of different algorithms (significance level α = 0.05)

[0240]

[0241] Finally, computation time statistics for ARSCOS problems of different sizes were performed, and the time consumption was quantitatively analyzed. Table 14 shows the average computational cost of all algorithms for solving nine different sizes of ARSCOS problems. For easy comparison, the time consumption of each algorithm is expressed as... Figure 13 middle.

[0242] from Figure 13As can be seen, MOMVO, MOPSO, and MODE exhibit lower time consumption across all problem scales. MOGWO, MOAVOA, MOEA / D, MOAHA, SMOGWO, MAOA, and MOAVOA all have lower time consumption than EMOAHA across all scales. Closer observation reveals that MOAHA's time consumption is higher than most algorithms across all scales. This is due to MOAHA's integration of a method based on Dynamically De-Crowding Distance (DECD) for maintaining external archives. Therefore, when EMOAHA incorporates improved strategies based on MOAHA, its time consumption will inevitably be higher than some algorithms, including MOAHA. Nevertheless, NSGA-II and NSGA-III still significantly outperform EMOAHA across all scales, approximately three times that of EMOAHA. In summary, while NSGA-II and NSGA-III achieve the best results in the ARSCOS problem, second only to EMOAHA, this comes at the cost of significantly higher time consumption. Under high-performance requirements, EMOAHA's computational time consumption remains within an acceptable range. Therefore, it is easy to infer that EMOAHA is an efficient algorithm for solving the ARSCOS problem.

[0243] In summary, statistical analysis of the experimental results shows that EMOAHA achieves better overall performance than its competitors on the ARSCOS problem, validating the effectiveness of the proposed improvement strategy.

[0244] Table 14 Time consumption of different algorithms in solving ARSCOS problems of different sizes

[0245]

[0246] With the deepening research on Service Composition and Optimal Selection (SCOS) in cloud manufacturing, it is urgent to consider the impact of uncertainties in the real-world environment on the efficiency of composite manufacturing services to ensure their efficient execution. This paper first establishes an ARSCOS model, taking robustness as one of the independent optimization objectives for response time, and considering two decision-making scenarios in case of service anomalies. Then, three improved strategies are proposed for the standard MOAHA: (a) using an inverse learning (OBL) strategy to improve the quality of the initial population; (b) using a roulette wheel strategy to improve the local foraging strategy and enhance the global search capability of the population; and (c) introducing an improved differential evolution strategy to improve population diversity and convergence speed. Finally, two sets of experiments are designed to verify the performance of the proposed methods. Experimental results show that the MOAHA algorithm outperforms other algorithms in both the ARSCOS problem and the selected benchmark function, exhibiting the best overall performance. This research is of great significance for improving the efficiency and robustness of composite manufacturing services in the CMfg platform, providing valuable reference and guidance for practical applications and further research.

[0247] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of protection of the claims.

Claims

1. A novel method for adaptive robust service composition and optimization selection in cloud manufacturing, characterized in that: The method includes the following steps: Step 1) Establish the Adaptive Robust Service Composition and Optimal Selection Model (ARSCOS); The steps for establishing the ARSCOS adaptive robust service composition and optimal selection model are as follows: Step 101) Requirements Analysis and Task Decomposition Phase: Decompose complex cloud manufacturing tasks into a finite number of STs based on actual needs, with each ST executed by a suitable MCS; Step 102) Service Search and Matching: For each subtask, retrieve all MCSs that meet the functional requirements, forming a candidate Manufacturing Cloud Service Set (CMCSS). Indicates the number of MCSs in CMCSS; Step 103) Service Composition and Optimization Selection SCOS: Select a candidate MCS for each subtask ST from CMCSS to generate a composite manufacturing service CMS with the best overall quality of service (QoS); Step 104) Task Execution: After user confirmation, execute the task according to the optimal CMS; In step 103), each subtask ST is assigned a preferred MCS and a backup AMCS. The number of subtasks is set to n, and the number of MCSs corresponding to each ST is assumed to be the same, set to m. The preferred MCSs constitute the preferred composite manufacturing service pCMS. If no anomaly occurs, the task will be completed according to the pCMS; otherwise, if the preferred MCS of a certain ST has an anomaly, the ST will repair the anomaly or be replaced by its AMCS. When a service anomaly occurs, the following three decisions will be considered to cause delays in task execution: A) Select an alternative service: ,in, To indicate service Choose to wait for service when an error occurs. The probability of performing an anomaly repair. For the first The preferred choice for ST An anomaly occurred and its Delay time when it is called; B) Select Waiting for Service Perform exception handling and service. Capable of handling exceptions: ,in, This indicates the probability that the service can successfully repair the anomaly. For the first The preferred choice for ST Time required to handle exceptions; C) Select Waiting for service Perform exception handling if the service Unable to complete exception handling, then an alternative service is invoked: ; Step 2) Solve the model in Step 1) using the Enhanced Multi-Objective Artificial Hummingbird Algorithm (EMOAHA). The enhanced multi-objective artificial hummingbird algorithm EMOAHA improvement strategies include: using a back-learning-based strategy for population initialization, using a roulette wheel strategy to improve foraging in the local area, and using an improved differential evolution algorithm to embed the standard MOAHA.

2. The novel method for adaptive robust service composition and optimization selection in cloud manufacturing according to claim 1, characterized in that: The robustness of a CMS is described by the delay in task execution when a service exception occurs, serving as a symbol of the CMS's ability to resist abnormal events. Based on this, the following assumptions and preconditions should be met during the SCOS process: (a) Probability of service failure Select the probability of waiting for service to handle exceptions. The probability that the service can successfully complete exception handling This was obtained through statistical analysis; (b) Ignore the case where the preferred MCS and AMCS of a subtask ST fail simultaneously; Based on the robustness definition of CMS, the quantitative robustness criterion of ARSCOS is defined as follows: （3）， After simplifying equation (3): （4）， in: For the number of STs, For the first The preferred choice for ST An anomaly occurred and its Delay time when called, For the first The preferred choice for ST Time required for exception handling For its first choice Execute the The duration of each ST, For the first The probability of an anomaly in each ST. This determines the probability of waiting for the service to handle the exception when an exception occurs. The probability of performing exception handling for the service and successfully repairing the exception.

3. A novel method for adaptive robust service composition and optimization selection in cloud manufacturing according to claim 2, characterized in that: The maximum value and maximum robustness of the average Quality of Service (QoS) in the Adaptive Robust Service Composition and Optimal Choice (ARSCOS) model are represented by the following functions: （5）， in, (1), In equation (1), , , and These represent the weights of cost, time, reputation, and product quality, respectively. , , and ,and ; Pareto optimality sets are used to compare multi-objective solutions F.

4. A novel method for adaptive robust service composition and optimization selection in cloud manufacturing according to claim 3, characterized in that: The enhanced multi-objective artificial hummingbird algorithm steps are as follows: Step 201) Initialize the population; initialize the population using a population initialization method based on reverse learning; reverse learning can generate a new solution that is the opposite of the original solution, and select a better solution as the initial solution. When randomly generated in the search space, its mirror solution At the lower boundary and upper boundary They are generated from each other, and the relationship between them satisfies: （14）， in, and They are The upper and lower bounds of the dimension problem, It is a random vector in [0,1]. Denotes the first solution to a given problem. The location of a food source Indicates population size; Step 202) Initialize the food source access table; Step 203) During the foraging process, the MOAHA algorithm includes omnidirectional flight, diagonal flight, and axial flight; Axial flight: Axial flight means that the hummingbird flies along any coordinate axis in the search space. The hummingbird's axial flight is given as follows: （8）， Diagonal flight: Diagonal flight means that the hummingbird flies from one corner of a rectangle to the opposite corner of the search space. The diagonal flight of the hummingbird is given as follows: （9）， Omnidirectional flight: Omnidirectional flight means that the hummingbird flies in the direction projected onto each coordinate axis in the search space. The omnidirectional flight of the hummingbird is given as follows: （10）， Step 204) Guided Foraging: In the guided foraging phase, once the target food source is determined, the hummingbird flies towards it to forage. Each hummingbird tends to visit the food source with the highest access level from the food source with the largest nectar content; the mathematical model for guided foraging is as follows: （11）， in, It is in the During the nth iteration Location of food source It is the first The location of the target food source that the hummingbird intends to visit. is the guiding factor that follows a standard normal distribution N(0,1); D is the direction matrix used to control the hummingbird's flight; after guiding foraging, the access table is updated; Step 205) Improved Territory Foraging: Select a global leader from the external archive using a roulette strategy. Then use This guides individuals within the population to search for the most promising areas. The selection is done through a roulette wheel method, with the following probabilities for each hypercube: （15）， in, It is a constant greater than 1. It is the first The number of Pareto optimal solutions obtained in a segment; the search always proceeds towards the most promising region of the search space; The improved foraging formula is as follows: （16）， in, The global leader selected from external archives via a roulette wheel strategy. The corresponding position vector, It is a regional factor that follows a standard normal distribution N(0,1). After implementing the territorial foraging strategy, the access table is updated. Step 206) Migration and Foraging: The migratory foraging behavior of hummingbirds in MOAHA is represented as follows: （13）， in, It is the worst possible frontier. It is a random number in [0,1]. and These are the upper and lower boundaries; the access table is updated when the migration foraging is complete. Step 207) Improve the differential evolution strategy: Embed the differential evolution algorithm (DE) into MOAHA. The standard differential evolution algorithm includes mutation, crossover and selection operations. After executing the improved differential evolution strategy, update the access table.

5. A novel method for adaptive robust service composition and optimization selection in cloud manufacturing according to claim 4, characterized in that: Individuals in mutation operations Generate variant individuals The expression is: （25）， In the formula, For the individual with the best fitness in the current generation, use As ; and It refers to two individuals randomly selected from the current generation. Levi's flight stride as follows: （24）， In the formula, It is the step size factor. It's the step length.

6. A novel method for adaptive robust service composition and optimization selection in cloud manufacturing according to claim 5, characterized in that: Crossover operations are based on the crossover factor. , will mutated individuals and parental individuals The experimental individuals were obtained by following the procedure in formula (18). : （18）， In the formula, ; It is a randomly selected integer within [1, d], the cross factor. The value ranges from [0.1, 0.9], and the cross factor is taken. , It is a random number between [0,1].

7. A novel method for adaptive robust service composition and optimization selection in cloud manufacturing according to claim 6, characterized in that: The selection operation employs a "greedy" selection strategy, meaning that in the parent individual... With test individuals The better individual is selected from the remaining individuals to form the next generation of the population. The selection operation expression is: （19）， In the formula, Represents an individual Superior .

8. A novel method for adaptive robust service composition and optimization selection in cloud manufacturing according to claim 4, characterized in that: In step 202), the food source access table is initialized as follows: （7）， in, , = This indicates that hummingbirds feed at their specific food sources; for , = This indicates that in the current iteration, the... The food source was just... The hummingbird visited.

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