Cloud manufacturing service composition optimization method based on improved multi-objective artificial bee algorithm

Abstract

The present application relates to cloud manufacturing service technical field, especially based on the cloud manufacturing service combination optimization method of improved multi-objective artificial swallow algorithm, through the establishment of a double target SCOS model, the service quality (QoS) and energy consumption are considered simultaneously, to realize the sustainable green development of cloud manufacturing and ensure the efficient solution of SCOS problem, through the design of an efficient improved multi-objective artificial swallow algorithm (IMOAHA) for solving SCOS problem.IMOAHA adopts the reverse learning strategy to strengthen the exploration of initial population, and redesigns a kind of improved field foraging strategy based on leader mechanism, the comprehensive performance of IMOAHA algorithm is significantly improved, and the solving efficiency and accuracy are higher than existing algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cloud manufacturing service, and particularly relates to a cloud manufacturing service combination optimization method based on an improved multi-objective artificial bee algorithm. BACKGROUND

[0002] Service composition and optimization selection (SCOS) is the key to realize the optimal configuration of cloud manufacturing (CMfg) platform resources. In recent years, with the growing concern for sustainable development, the environmental problems of manufacturing industry have become increasingly urgent. This is particularly evident in CMfg, because the manufacturing resources are widely distributed and diversified, resulting in huge energy consumption during the execution of combined services, especially for some unreasonable service combinations. However, the current research on SCOS problem rarely considers the perspective of sustainable development, and the existing models are often out of touch with the actual situation, thus limiting the application.

[0003] In addition, with the sharp increase of manufacturing resources and user demand in the CMfg platform, metaheuristic algorithms are more suitable for solving SCOS problems than traditional branch and bound, linear programming and other methods. For example, genetic algorithm (GA), artificial bee colony algorithm (ABC), grey wolf algorithm (GWO) and various algorithm variants and hybrids. These algorithms have certain subjectivity in the solving process, and it is difficult to meet the actual engineering requirements. Therefore, multi-objective optimization algorithms should be used to solve SCOS. Recently, some scholars have developed enhanced multi-objective gray wolf algorithm (EMOGWO), adaptive multi-population multi-objective whale optimization algorithm (AMPOWOA) and the like.

[0004] Although a large number of researches have been conducted on the algorithm for solving SCOS problem, there are still problems of low solving efficiency and unsatisfactory effect. SUMMARY

[0005] Therefore, the purpose of the present application is to propose a cloud manufacturing service combination optimization method based on an improved multi-objective artificial bee algorithm to solve the problem of unsatisfactory effect of the existing algorithm.

[0006] Based on the above purpose, the application provides a cloud manufacturing service combination optimization method based on an improved multi-objective artificial swallow algorithm, comprising the following steps:

[0007] S1, splitting a complex manufacturing requirement into multiple sub-tasks;

[0008] S2, establishing a multi-objective SCOS model for evaluating service quality and energy consumption for searching and matching cloud manufacturing services for the sub-tasks;

[0009] S3, performing service combination and optimization selection on the multi-objective SCOS model by using an improved multi-objective artificial swallow algorithm to obtain optimal cloud manufacturing service combination, wherein the improved multi-objective artificial swallow algorithm performs population initialization based on a reverse learning strategy and improves field foraging based on a leader mechanism.

[0010] Preferably, the multi-objective SCOS model is as follows:

[0011]

[0012] wherein n is the number of tasks after decomposition, F is an SCOS optimization target, f1 is a service quality optimization target, f2 is an energy consumption optimization target, QoS(CMS) is the service quality of service combination, and EC(CMS) is the energy consumption of service combination.

[0013] Preferably, the calculation formula of QoS(CMS) is as follows:

[0014] QoS(CMS)=ω c ×Q C +ω T ×Q T +ω Re ×Q Re +ω Av ×Q Av ;

[0015] wherein Q C , Q T , Q Re , Q Av respectively represent a cost index, a time index, a reliability index and an availability index, ω c , ω T , ω Re , ω Av respectively represent the weights of cost, time, reliability and availability, ω c , ω T , ω Re , ω Av ∈[0,1], and ω c +ω T +ω Re +ω Av =1.

[0016] Preferably, when evaluating the quality of service, the cost index, time index, reliability index and availability index are normalized to have a value range of [0, 1];

[0017]

[0018] wherein q k represents the normalized single task evaluation index, x max and x min are the maximum and minimum values of the evaluation index, respectively.

[0019] Preferably, the calculation formula of EC(CMS) is:

[0020]

[0021] wherein, represents the unit processing energy consumption of the ith service combination; t i represents the processing time of the corresponding service; represents the unit logistics energy consumption of the ith service combination, d i represents the delivery distance of the corresponding service, λ i is the road type coefficient, represents the fuel type coefficient.

[0022] Preferably, the process of improving the multi-objective artificial bee algorithm includes:

[0023] S31, initialize parameters: population size, maximum iteration number, external archive size, access table, initialize population position according to the reverse learning strategy;

[0024] S32, evaluate the objective function of all bees, add the current population to the archive, and update according to the dominance relationship;

[0025] S33, judge whether the archive exceeds the maximum value, if yes, execute the dynamic elimination method strategy based on the crowding distance, judge whether the iteration number reaches the stop condition, if yes, return the archive and end the algorithm, if not, execute step S34;

[0026] S34, update the population using non-dominated sorting, judge whether rand is greater than 0.5 after updating, if yes, execute guided foraging and update the access table, jump to step S35, if not, execute the leader mechanism improved field foraging and update the access table, jump to step S35;

[0027] S35, add the population to the archive and update according to the dominance relationship, judge whether mod(t,2n)==0, if yes, execute migration foraging and update the access table, add the population to the archive and update according to the dominance relationship, then return to step S33, if not, directly jump back to step S33, wherein t represents the tth iteration.

[0028] Preferably, in step S31, the population position is initialized according to the reverse learning strategy, which satisfies the formula:

[0029]

[0030] Wherein, x i represents the original solution, x′ i represents its mirror solution, Low represents the lower boundary, Up represents the upper boundary, and r is a random number ranging from 0 to 1.

[0031] Preferably, in step S34, the improved domain foraging of the leader mechanism is executed according to the following formula:

[0032]

[0033] Wherein, x best (t) is a global leader selected from the external archive by a roulette selection strategy α corresponding position vector, D represents the flight of hummingbird, b represents the region factor, which obeys the standard normal distribution N(0,1), v i represents the foraging behavior of hummingbird, and the selection of the global leader α is completed by a roulette method, and the probability of each hypercube is:

[0034]

[0035] Wherein, c is a constant greater than 1, and N is the number of Pareto optimal solutions obtained in the ith section.

[0036] Advantages of the present application: the present application establishes a double target SCOS model, which considers the quality of service (QoS) and energy consumption at the same time, to realize the sustainable green development of cloud manufacturing and ensure the efficient solution of SCOS problem, and an improved multi-objective artificial hummingbird algorithm (IMOAHA) is designed for solving the SCOS problem. IMOAHA adopts a reverse learning strategy to strengthen the exploration of the initial population, and redesigns a domain foraging strategy based on the improved leader mechanism, so that the comprehensive performance of the IMOAHA algorithm is significantly improved, and the solving efficiency and accuracy are higher than those of the existing algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0037] In order to make the technical solutions in the present application or prior art clearer, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only a part of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort based on these drawings.

[0038] Figure 1 A cloud manufacturing service combination optimization method flowchart of an embodiment of the present application;

[0039] Figure 2 A SCOS process framework diagram of an embodiment of the present application;

[0040] Figure 3 An IMOAHA algorithm flowchart of an embodiment of the present application;

[0041] Figure 4 Pareto boundary diagrams obtained by nine algorithms in case 1 of the present application on HV10-50, 10-100 and 10-150;

[0042] Figure 5 Pareto boundary diagrams obtained by nine algorithms in case 1 of the present application on HV20-50, 20-100 and 20-150;

[0043] Figure 6 Pareto boundary diagrams obtained by nine algorithms in case 1 of the present application on HV30-50, 30-100 and 30-150;

[0044] Figure 7 A box plot of values of nine algorithms in case 1 of the present application;

[0045] Figure 8 An average running time diagram of nine algorithms running 20 times in case 1 of the present application. DETAILED DESCRIPTION

[0046] In order to make the technical solutions in the present application or prior art clearer, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only a part of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort based on these drawings.

[0047] It should be noted that the technical terms or scientific terms used in the present application should be understood as the general meaning understood by those skilled in the art to which the present application belongs, unless otherwise defined. The "first", "second" and similar words used in the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Include" or "contain" and similar words mean that the elements or objects before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connected" or "connected" and similar words are not limited to physical or mechanical connection, but can include electrical connection, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to represent relative positional relationship, when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0048] As Figure 1 shown, the embodiment of the present specification provides a cloud manufacturing service combination optimization method based on improved multi-objective artificial bee algorithm, comprising the following steps:

[0049] S1, split the complex manufacturing demand into multiple sub-tasks;

[0050] In the cloud manufacturing (CMfg) platform, the complex manufacturing demand submitted by the service demander can be regarded as a task T, which is then split into n sub-tasks ST, which are executed by multiple manufacturing cloud services MCS. Such decomposition and execution mode realizes the cooperation between geographically dispersed manufacturing resources, aiming to achieve the highest user satisfaction. The manufacturing cloud service set corresponding to the sub-task ST is regarded as a path, and each path represents a manufacturing cloud service set (CMCSS). Therefore, the mapping relationship can be expressed by the following simple mathematical model:

[0051]

[0052]

[0053] Wherein, the dimension of the search space P is m x n, T m is the search space of the mth ST, represents the nth candidate service of the mth ST; CMS t is the tth scheme, and is the MCS selected for the jth ST in the tth CMS, as shown in the framework. Figure 2

[0054] S2, establish a multi-objective SCOS model for evaluating service quality and energy consumption for searching and matching cloud manufacturing services for sub-tasks;

[0055] ​In the SCOS problem, the quality of service (QoS) is an important standard for measuring the basic cloud service and the combined cloud service, and in the present application, only the case of taking the cost (C), the time (T), the reliability (Re) and the availability (Av) as the measuring indexes is considered, i.e., QoS={C, T, Re, Av}. The QoS calculation formula of the SCOS problem is as follows:

[0056] QoS(CMS)=ω c ×Q C +ω T ×Q T +ω Re ×Q Re +ω Av ×Q Av ;

[0057] Wherein Q C , Q T , Q Re , Q Av respectively represent the cost index, the time index, the reliability index and the availability index, ω c , ω T , ω Re , ω Av respectively represent the weight of the cost, the time, the reliability and the availability, ω c , ω T , ω Re , ω Av ∈[0,1], and ω c +ω T +ω Re +ω Av =1, and the description of the above four QoS attributes and the aggregation function is shown in Table 1.

[0058] Table 1

[0059]

[0060] Since the value range and the dimension of each evaluation index are different, the actual value of the evaluation index should be normalized according to a unified quantification method, and according to the actual meaning, the QoS attribute index can be divided into positive attribute index and negative attribute index, and through the following formula, the four attribute indexes can be normalized so that their value ranges are all in [0,1].

[0061]

[0062] In the formula, q k represents the normalized single task evaluation index, x max and x min are respectively the maximum value and the minimum value of the evaluation index, and in addition, when xmax = x min when q k = 1.

[0063] In addition to the quality of service, the method also considers the energy consumption evaluation. In the manufacturing service, the total energy consumption (EC) is mainly composed of manufacturing energy consumption and logistics energy consumption. Manufacturing energy consumption is mainly affected by processing energy consumption, which depends on the level of processing and the characteristics of production equipment. While logistics energy consumption is affected by factors such as transportation distance, fuel type and road type. Therefore, the energy consumption evaluation function of cloud manufacturing service is as follows:

[0064]

[0065] In the formula: represents the unit processing energy consumption of the i th MCS; t i indicates the processing time of the corresponding service; represents the unit logistics energy consumption of the i th MCS, d i represents the delivery distance corresponding to the service, λ i is the road type coefficient, represents the fuel type coefficient.

[0066] In summary, the method considers two optimization objectives of maximum QoS and minimum energy consumption in the SCOS problem to ensure that the combined manufacturing service CMS has high quality and low energy consumption, which is a target SCOS problem, which can be represented by the following function:

[0067]

[0068] Where n is the number of tasks after decomposition, F is the SCOS optimization objective, f1 is the service quality optimization objective, f2 is the energy consumption optimization objective, QoS(CMS) is the service quality of service combination, and EC(CMS) is the energy consumption of service combination.

[0069] S3, using the improved multi-objective artificial hummingbird algorithm (IMOAHA) to combine and optimize the selection of the multi-objective SCOS model to obtain the optimal service combination of cloud manufacturing, the improved multi-objective artificial hummingbird algorithm is based on the reverse learning strategy for population initialization and the leader mechanism for improving the field foraging.

[0070] The core of the original multi-objective artificial hummingbird algorithm (MOAHA) is to search for the optimal solution in the solution space by simulating the three flight skills and foraging behavior of hummingbirds.

[0071] (1) Three flight skills

[0072] Axial flight: Axial flight means that hummingbirds can fly along any coordinate axis in the search space. The axial flight of the hummingbird is given as follows:

[0073]

[0074] Diagonal flight: Diagonal flight means that the hummingbird can fly from one corner of a rectangle to the opposite corner of the search space. The hummingbird's diagonal flight is given below:

[0075]

[0076] Omnidirectional flight: Omnidirectional flight means that the hummingbird can fly in the search space in directions projected onto each coordinate axis. The omnidirectional flight of a hummingbird is given below:

[0077] D (i) =1i=1,...,d.

[0078] (2) Three foraging behaviors

[0079] Guided foraging: Each hummingbird tends to access the highest-level food source from the food source with the largest nectar availability. The mathematical model for guided foraging is as follows:

[0080] v i (t+1)=x i,tar (t)+D·a·(x i (t)-x i,tar (t))

[0081] 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, where 'a' is a guiding factor that follows a standard normal distribution N(0,1).

[0082] Territorial foraging: During the territorial foraging phase, hummingbirds tend to search their own neighborhood rather than visit other known food sources.

[0083]

[0084] Where x a (t) is a solution randomly selected from the external archive, and b is the region factor that follows a standard normal distribution N(0,1).

[0085] 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 non-dominated sorting (NDS) is defined as the worst food source. Therefore, hummingbird migratory foraging behavior in MOAHA can be represented as follows:

[0086]

[0087] where F end is the non-dominated front based on the worst, r is a random number in [0, 1], and Up and Low are the upper and lower boundaries.

[0088] In the present application, in order to overcome the problem that random generation of initial positions may lead to low population quality, insufficient diversity and unstable search efficiency, the Opposition-Based Learning (OBL) strategy is introduced for population initialization. OBL can generate new solutions opposite to the original solutions and select better solutions as initial solutions, thereby improving the search efficiency and diversity of the population. As shown in the following formula, when the original solution x i When randomly generated in the search space, the mirror solution x' i will be generated between the lower boundary Low and the upper boundary Up, and their relationship satisfies.

[0089]

[0090] In the formula, r is a random number in the range of [0, 1]. OBL introduces prior knowledge, making the algorithm more targeted in search, reducing uncertainty, and making the algorithm's performance more stable and reliable, better exploring the search space, avoiding the population falling into local optimal solution too early, and thus increasing the global search ability of the algorithm.

[0091] In the present application, in order to overcome the limitations of the random selection method of traditional algorithms, which ignores the congestion of the solution set in the external archive, the population may always search in a certain area repeatedly when performing field search, cannot fully utilize the remaining more promising search areas, and may lead to problems such as premature falling into local optimum, slow convergence speed, etc. By introducing the roulette selection strategy, a solution is selected from the external archive, defined as the global leader alpha, and then alpha is used to guide the population individuals to search in the most promising area, thereby overcoming the limitations of the original algorithm and improving the global search ability of the algorithm. The improved field foraging strategy based on the leader mechanism is shown in the following formula:

[0092]

[0093] where x best (t) is the position vector corresponding to the global leader alpha selected from the external archive by the roulette selection strategy. By introducing the global leader alpha, the hummingbird can exchange information with the most promising individual obtained so far at a probability of one-half each time it performs field foraging, guiding the current individual to explore the most promising area.

[0094]

[0095] where c is a constant greater than 1, and N is the number of Pareto optimal solutions obtained in the ith segment. As can be seen from the above formula, the probability of being selected is inversely proportional to the degree of crowding in the hypercube, and the more crowded the hypercube is, the lower the probability of being selected as the leader, ensuring that the search is always conducted towards the most 'promising' area of the search space.

[0096] Based on the above improvement strategies, the flow of the designed IMOAHA algorithm is as shown in Figure 3 The flow is as follows:

[0097] S31, initialize parameters: population size, maximum iteration number, external archive size, access table, initialize population position according to the reverse learning strategy;

[0098] S32, evaluate the objective function of all hummingbirds, add the current population to the archive, and update according to the dominance relationship;

[0099] S33, judge whether the archive exceeds the maximum value, if yes, execute the dynamic elimination-based crowding distance (DECD) strategy, judge whether the iteration number reaches the stop condition, if yes, return the archive and end the algorithm, if not, execute step S34, and the iteration number can be set to 300.

[0100] S34, update the population using non-dominated sorting, judge whether rand is greater than 0.5 after updating, if yes, execute guided foraging and update the access table, jump to step S35, if not, execute the improved leader mechanism foraging and update the access table, jump to step S35;

[0101] S35, add the population to the archive and update according to the dominance relationship, judge whether mod(t, 2n) == 0, if yes, execute migration foraging and update the access table, add the population to the archive and update according to the dominance relationship, then return to step S33, if not, directly jump back to step S33, where t represents the tth iteration.

[0102] The method provided by the application is verified as follows, first, the complexity is calculated.

[0103] The calculation complexity of the IMOAHA algorithm is affected by multiple factors, including the size of the hummingbird population (N), the maximum iteration number (T), the target number (M) and the population dimension (D), in addition, the size of the external archive (N) is equal to the population size. The calculation complexity of the IMOAHA algorithm is analyzed as follows:

[0104] Firstly, the complexity of NDS is O(TMN^2). This is because the non-dominated sorting (NDS) operation involves sorting and comparing all individuals in the population, which requires O(TMN^2) computational complexity in the worst case.

[0105] Secondly, deleting the element with the minimum crowded distance from the archive and updating the archive requires O(TMN^2logN), and calculating the crowded distance of the neighboring elements requires O(2TMN). Therefore, the computational complexity of the DECD method is max(O(TMN^2logN)+O(2TMN)).

[0106] Next, the computational complexity of guided foraging, improved field foraging, and migration foraging is O(0.5TMN), O(0.5TMN), and O(0.5TM / N), respectively.

[0107] Finally, the complexity of population initialization based on reverse learning is O(MND).

[0108] Combining the above computational complexities, the overall computational complexity of the IMOAHA algorithm is O(IMOAHA) = max(O(TMN^2), O(TMN^2logN+2TMN), O(TMN+0.5TM / N), O(MND)). Therefore, the overall complexity of IMOAHA is O(IMOAHA) = O(TMN^2logN). It is worth noting that the improvement strategies added in IMOAHA do not increase the computational complexity of the algorithm compared to the standard MOAHA.

[0109] In order to verify the effectiveness of the method, two groups of experiments are designed in this specification.

[0110] Case 1: Effectiveness of IMOAHA on SCOS problem.

[0111] For the designed 9 experimental examples, the number of subtasks n is between 10 and 30 with a step of 10, and the number of candidate services corresponding to each subtask m is between 50 and 150 with an increment of 50. It is worth mentioning that MOGWO, MOPSO, NSGA-II, MOEA / D, and other classic algorithms have been widely used in various multi-objective optimization problems due to their good solving performance. MAOA, MOAVOA, MOAHA, and SMOGWO, which were proposed recently, are highly praised for their excellent convergence and diversity, and perform well in solving multi-objective optimization problems. In addition, the parameter settings of all algorithms are consistent with the original literature, as shown in Table 2. Considering the randomness of the algorithm, each algorithm is independently run 20 times.

[0112] Table 2

[0113]

[0114] Before calculating QoS, each indicator value should be normalized, and the weights w of cost, time, reliability, and availability are set to 0.25. Without loss of generality, the related parameters of candidate services are randomly generated in a certain range at initialization, and the value range is shown in Table 3.

[0115]

[0116] Because the true Pareto front (PF) of the custom SCOS problem is unknown, this specification takes the Pareto boundary obtained in all algorithm running results as the true PF to calculate the IGD indicator. The IGD and HV indicator calculation results of all algorithms on different scale SCOS problems are shown in Tables 4 and 5, and Mean / std represents the mean and standard deviation. In order to test the significant difference between IMOAHA and the comparison algorithm in IGD and HV indicators, we use Wilcoxon signed-rank test (WSRT) to compare IMOAHA and other algorithms. "+" indicates that the indicator of IMOAHA is better than that of another algorithm, "-" indicates that the indicator of IMOAHA is worse than that of another algorithm, and "≈" indicates that there is no significant difference between IMOAHA and another algorithm.

[0117] The IGD indicator results are shown in Table 4. It can be seen that IMOAHA achieves the best results on all 9 scales of SCOS problems. From the last row of Table 4, it can be seen that IMOAHA has a significant advantage over all other algorithms, which is better than MOAHA, SMOGWO, MOGWO, MOPSO, MOEAD, MAOA, MOAVOA 9 times, and better than NSGA-II 8 times.

[0118] Table 4

[0119]

[0120] The HV indicator results are shown in the table. It can be seen that IMOAHA is significantly better than MOAHA, SMOGWO, MOGWO, MOPSO, NSGA-II, MOEA / D, MAOA, and MOAVOA on all 9 scales.

[0121]

[0122] Figure 4The Pareto frontiers obtained by all algorithms are shown. It can be seen that the Pareto frontier obtained by IMOAHA is distributed in the outermost part of the other frontiers, and is the most extensive and uniform, which reflects its better convergence and diversity. Secondly, it can be found that the frontiers obtained by NSGA-II and MOAHA are distributed close to the frontier obtained by IMOAHA, indicating that NSGA-II and MOAHA have better comprehensive performance than IMOAHA. This corresponds to Table 4 and Table 5.

[0123] Figure 5 The box plots of the sum of HV values of all algorithms are given to intuitively show the distribution of the calculation results of each algorithm. It can be seen that the distribution of the results obtained by all algorithms in the 9 instances is slightly similar, because the 9 instances have the same objective function. In addition, according to the circles (mean values) shown in the box plots, it can be seen that the circles of IMOAHA are distributed in the uppermost part of the image in all scales, indicating that the solution set obtained by IMOAHA has higher quality than the rest of the algorithms; and the box plot corresponding to IMOAHA is the narrowest in most scale problems, indicating that IMOAHA has better stability.

[0124] On the basis of the above statistical results, we further analyze the performance differences between algorithms. MOGWO uses three head wolves to guide the search of the entire population by simulating the social hierarchy and leadership mechanism of the gray wolf group, and is greatly affected by the three head wolves, which can easily lead to premature convergence or fall into local optimum. Compared with MOGWO, SMOGWO improves the comprehensive performance of MOGWO to some extent, but still has a significant gap compared with IMOAHA. MOPSO is easily affected by the initial population distribution and parameter settings, which can lead to premature convergence or loss of diversity. NSGA-II algorithm is a classic multi-objective optimization algorithm, which has the advantages of fast convergence and wide application. However, this algorithm needs to adjust many parameters, such as crossover probability, mutation probability, population size, etc., and the algorithm performance is greatly affected by the parameters and has a large time cost. The limitation of the MODE algorithm is that it is easily affected by parameter settings and initial population distribution, which can lead to premature convergence or loss of diversity. MAOA simulates the four arithmetic rules used by humans when solving mathematical problems, and needs to adjust many parameters, such as operator probability, archive size, etc., which can affect the algorithm performance. MOAVOA needs to adjust many parameters, which affects the convergence and stability.

[0125] IMOAHA significantly outperforms other algorithms on all scale SCOS problems. This is due to its introduction of the OBL-based population initialization strategy and the improved domain search strategy based on the leader mechanism on the basis of MOAHA. The main advantages of the OBL-based population initialization strategy include: (1) increase diversity: the OBL strategy generates the initial population from the characteristics of known excellent solutions, making the individuals in the population more diverse. This can help the algorithm better explore the solution space and avoid falling into local optimal solutions too early; (2) improve algorithm performance: an excellent initial population can provide a better starting point for the subsequent optimization process, making the algorithm more likely to find the global optimal solution or a solution close to the global optimal solution. The main advantages of the domain search strategy based on the leader mechanism include: (1) enhanced global search capability: the leader mechanism transmits the information of excellent individuals in the population to other group members, prompting the entire population to move towards the excellent solution. This helps to improve the global search capability of the algorithm, making it more likely to find the global optimal solution or a solution close to the global optimal solution; (2) fast convergence: the leader mechanism can quickly spread the information of excellent solutions to the entire population, which helps to speed up the convergence process of the population. In the early stages of the optimization algorithm, the population members can be quickly gathered around the excellent solution, thereby reducing the search space and improving the convergence speed.

[0126] Table 6 shows the results of the Friedman test for the IGD and HV indicators. In the table, the better the algorithm performance, the lower the ranking; the smaller the p-value, the more significant the difference between algorithms. As can be seen from Table 6, IMOAHA ranks first in both IGD and HV comprehensive indicators, showing its strong competitiveness. NSGA-II ranks second in IGD and HV indicators. MOAHA ranks third in IGD and HV indicators. The remaining algorithms have almost the same ranking in IGD and HV indicators, because both HV and IGD indicators are comprehensive performance evaluation indicators.

[0127] Table 6

[0128]

[0129]

[0130] Figure 6The average running time of all algorithms running 20 times is given to quantitatively analyze the time consumption. It can be seen that MOPSO shows lower time consumption on all scale problems, and MOGWO, MOAVOA, MOAHA, SMOGWO, MAOA show close time consumption on all scales and are lower than IMOAHA. IMOAHA increases the time consumption by introducing the proposed enhancement strategy, and the running time is slightly higher than MOAHA. Nevertheless, the time consumption of NSGA-II and MOEA / D is still much higher than IMOAHA and the remaining algorithms on all scales, about 3 times of IMOAHA. It can be seen that although NSGA-II can obtain results second only to IMOAHA on SCOS problems, it is at the cost of huge time consumption. Careful observation also shows that as the scale of SCOS problem increases, the time consumption of IMOAHA does not increase significantly.

[0131] Therefore, in the case of high performance requirements, the calculation time consumption of IMOAHA is still within an acceptable range, and has a stronger comprehensive performance than all other competitors, while also verifying the effectiveness of the improvement strategy proposed in the specification, providing a reference for solving SCOS problems.

[0132] Case 2: Effectiveness of IMOAHA on benchmark functions

[0133] This case is to evaluate the effectiveness of the IMOAHA algorithm on 17 well-known benchmark functions. The selected benchmark functions include UF1-7, ZDT1-3 and CF1-7, and for these test functions, the number of decision variables is 30, and the parameters of all algorithms are the same as in Case 1. Similarly, IGD and HV indicators are used for evaluation, and all algorithms are independently run 20 times, and the results are shown in Tables 7 and 8.

[0134] The statistical results of the data in Table 7 can be seen. On the IGD index, except for UF3, ZDT2, CF5, and CF7, IMOAHA achieves the best results on all remaining benchmark test functions. For MOAHA, only on ZDT2, the best IGD value is obtained, for SMOGWO, only on UF3, the best value is obtained, for NSGA-III, only on CF5 and CF7, the best value is obtained. The remaining algorithms do not achieve the best average value. From the last row of Table 7, it can be seen that IMOAHA is superior to MOAHA, SMOGWO, NSGA-II, MAOA and MOAVOA on 15 of the 17 functions, and superior to MOGWO, MOPSO and MOEA / D on 17 functions. This shows that IMOAHA has better comprehensive performance than other optimization methods on the IGD index of benchmark functions.

[0135] Table 8 gives the statistical results of HV indicator. It can be seen that IMOAHA is superior to MOAHA, SMOGWO, MOGWO, MOPSO, NSGA-II, MOEA / D, MAOA and MOAOVA on 13, 13, 16, 16, 11, 16, 14, 14 of 17 functions respectively. It further verifies the effectiveness of the strategy introduced by IMOAHA. It is worth noting that when solving function CF7, the HV value of the solution result of most solving algorithms is 0, which indicates that the algorithm has poor performance in solving this function.

[0136] Similarly, Table 9 gives the Friedman test results of IGD and HV indicators. It can be seen that the p value is less than the significance level a = 0.05, and there is a significant difference between the above comparison algorithms. IMOAHA ranks first in IGD and HV indicators. MOAHA ranks second in IGD and HV indicators. SMOGWO ranks third in IGD indicator, but ranks fourth in HV indicator. NSGA-II ranks fourth in IGD indicator, and ranks third in HV indicator. This result is similar to Case 1, and the top-ranked are IMOAHA, MOAHA, SMOGWO and NSGA-II.

[0137] In summary, IMOAHA has better comprehensive performance than competitors in solving test functions. The results show that compared with the comparison algorithm, the proposed IMOAHA algorithm still has the best comprehensive performance in solving different types of multi-objective problems, which further verifies the effectiveness of the improved strategy.

[0138] Table 7

[0139]

[0140]

[0141] Table 8

[0142]

[0143] Table 9

[0144]

[0145]

[0146] Those skilled in the art should understand that the above discussion of any embodiment is only intended to be exemplary in nature and is not intended to suggest any limitation on the scope of the present application (including the claims) as a mere representation of representative samples. Under the concept of the present application, the above embodiments or technical features among different embodiments can be combined, the steps can be implemented in any order, and there are many other changes of different aspects of the present application as described above. In order to be brief, they are not provided in details.

[0147] The present application is intended to cover all such alternatives, modifications, and variations as fall within the broad scope of the appended claims. Accordingly, any one of the above-described embodiments of the present application can be further modified than or combined with other embodiments without departing from the scope and spirit of the present application.

Claims

1. A cloud manufacturing service composition optimization method based on an improved multi-objective artificial hummingbird algorithm, characterized in that, The method includes the following steps: S1. Break down complex manufacturing requirements into multiple sub-tasks; S2. Establish a multi-objective SCOS model for evaluating service quality and energy consumption for sub-task search and matching of cloud manufacturing services; S3. An improved multi-objective artificial hummingbird algorithm is used to perform service combination and optimization selection on the multi-objective SCOS model to obtain the optimal service combination for cloud manufacturing. The improved multi-objective artificial hummingbird algorithm is based on the reverse learning strategy for population initialization and on the leader mechanism to improve domain foraging. The improved multi-objective artificial hummingbird algorithm includes the following steps: S31. Initialize parameters: population size, maximum number of iterations, external archive size, access table, and initialize the population position according to the reverse learning strategy; S32. Evaluate the objective function of all hummingbirds, add the current population to the profile, and update it according to the dominance relationship; S33. Determine if the archive exceeds the maximum value. If so, execute the dynamic elimination strategy based on congestion distance. Determine if the number of iterations reaches the stopping condition. If the stopping condition is reached, return to the archive and end the algorithm. If the stopping condition is not reached, execute step S34. S34. Update the population using non-dominated sorting. After the update, check if rand is greater than 0.

5. If it is, execute guided foraging and update the access table, then jump to step S35. Otherwise, execute the leader mechanism improved domain foraging and update the access table, then jump to step S35. S35. Add the population to the archive and update it according to the dominance relationship. Check if mod(t,2n)==0. If yes, perform migration foraging and update the access table. Add the population to the archive and update it according to the dominance relationship. Then return to step S33. Otherwise, directly jump back to step S33, where t represents the t-th iteration.

2. The cloud manufacturing service composition optimization method based on the improved multi-objective artificial hummingbird algorithm according to claim 1, characterized in that, The multi-objective SCOS model is as follows: ； in, Let F represent the number of tasks after decomposition, f1 represent the SCOS optimization objective, f2 represent the service quality optimization objective, and f3 represent the energy consumption optimization objective. For the service quality of the service package, Energy consumption for the service mix.

3. The cloud manufacturing service composition optimization method based on the improved multi-objective artificial hummingbird algorithm according to claim 2, characterized in that, The calculation formula is: ； in , , , These represent cost metrics, time metrics, reliability metrics, and availability metrics, respectively. These represent the weights for cost, time, reliability, and availability, respectively. ,and .

4. The cloud manufacturing service composition optimization method based on the improved multi-objective artificial hummingbird algorithm according to claim 3, characterized in that, When evaluating service quality, cost, time, reliability, and availability metrics are normalized so that their values ​​are all within the range of [0, 1]. ； In the formula, Represents a normalized evaluation metric for a single task. and These are the maximum and minimum values ​​of the evaluation indicators, respectively.

5. The cloud manufacturing service composition optimization method based on the improved multi-objective artificial hummingbird algorithm according to claim 1, characterized in that, The calculation formula is: ； in, Indicates the first Unit processing energy consumption of each service combination; This refers to the processing time of the corresponding service; This represents the unit logistics energy consumption of the i-th service combination. Indicates the delivery distance for the corresponding service. This is the road type coefficient. This represents the fuel type coefficient.

6. The cloud manufacturing service composition optimization method based on the improved multi-objective artificial hummingbird algorithm according to claim 1, characterized in that, In step S31, the population position satisfaction formula is initialized according to the reverse learning strategy: ； in, This represents the original solution. This represents its mirror solution, Low represents the lower boundary, Up represents the upper boundary, and r is a random number in the range [0,1].

7. The cloud manufacturing service composition optimization method based on the improved multi-objective artificial hummingbird algorithm according to claim 6, characterized in that, In step S34, the domain foraging improved by the leader mechanism is performed according to the following formula: ； in To select a global leader from an external archive using a roulette wheel selection strategy. The corresponding position vector, D, represents the hummingbird's flight path, and b represents the region factor, follows a standard normal distribution N(0,1). This refers to the foraging behavior of hummingbirds, and the overall leader. The selection is done using a roulette wheel method, with each hypercube having a probability of: ； in It is a constant greater than 1. It is the first The number of Pareto optimal solutions obtained in the segment.

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