Strojniški vestnik - Journal of Mechanical Engineering 62(2016)10, 577-590 © 2016 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2016.3545 Original Scientific Paper Received for review: 2016-03-01 Received revised form: 2016-07-05 Accepted for publication: 2016-07-06 Multi-objective Optimization of Cloud Manufacturing Service Composition with Cloud-Entropy Enhanced Genetic Algorithm Yongxiang Li - Xifan Yao* - Jifeng Zhou School of Mechanical & Automotive Engineering, South China University of Technology, China To consider the service-matching degree, the composition harmony degree, and the service composition complexity in cloud manufacturing service composition optimization problems, a new composition optimization approach, called cloud-entropy enhanced genetic algorithm (CEGA), is put forward to solve such problems with multi-objectives. The definitions of service-matching degree, composition harmony degree, and cloud-entropy and the corresponding calculation methods are given. A multi-objective optimization mathematical model of cloud manufacturing service composition is built. The manufacturing task of AGV (automated guided vehicle) is taken as an example to verify the proposed CEGA algorithm on the established composition model. The studied result shows that CEGA converges faster than a standard genetic algorithm with shorter time. Keywords: cloud manufacturing, service composition optimization, cloud-entropy, service-matching degree, composition harmony degree, genetic algorithm Highlights • Cloud-entropy enhanced genetic algorithm (CEGA) is proposed. • Service-matching degree, composition harmony degree, and cloud-entropy are defined, and the corresponding calculation methods are given. • The multi-objective optimization mathematical model of cloud manufacturing service composition is built. • The manufacturing task of AGV is taken as an example to verify the proposed CEGA algorithm on its feasibility and effectiveness. • The proposed CEGA converges faster than a standard genetic algorithm with shorter time. 0 INTRODUCTION With the rise of cloud computing [1] and the development of Internet of things [2] and other related technologies, the cloud manufacturing based on them provides a new way to realize centralized management, unified scheduling, on-demand use of all kinds of distributed manufacturing resources [3]. Cloud manufacturing, in the form of cloud services, for the whole manufacturing life cycle, provides all kinds of manufacturing resources which can obtain and pay for use at any time [4]. A single cloud service is often difficult to meet customer's manufacturing requirements. Therefore, with service composition, a cloud manufacturing service platform assembles a number of fine-grained simple cloud services into coarse-grained complex cloud services to meet customer's complex manufacturing requirements [5]. Implementation of cloud manufacturing is a collaborative process that requires the participation of multiple distributed manufacturing resources. In the cloud manufacturing service platform, it is shown as a series of activities, such as manufacturing demand decomposition, service matching with tasks, service composition optimization, service execution monitoring, etc. [6]. According to the opening degree of services to users, cloud manufacturing services can be divided into public cloud services and private cloud services [7]. The manufacturing resources of private cloud services are limited to internal use, not for providing services directly to users outside the enterprise. The manufacturing resources of public cloud services are not only available for internal users but also directly provide services to users outside the enterprise. In manufacturing processes, there are a variety of information interaction and material transportation among cloud manufacturing services. It is a kind of complex relationship that is full of mutual dependence, constraints and competition [8]. Therefore, assembling appropriate fine-grained cloud services according to the customer's manufacturing needs is an important part of the implementation process of cloud manufacturing. Some scholars have done research on the optimization of service composition. For example, Lartigau et al. [9] proposed an improved artificial bee colony optimization algorithm for solving the cloud manufacturing service composition model based on QoS with geo-perspective transportation; Jeong and Lee [10] proposed a web service composition formal model with business logic process buffer based on CSP (Communication Sequential Process); Castejon *Corr. Author's Address: School of Mechanical & Automobile Engineering , South China University of Technology, Guangzhou 510640, China, mexfyao@scut.edu.cn 577 Strojniski vestnik - Journal of Mechanical Engineering 62(2016)10, 577-590 et al. [11] proposed multi-objective optimal design procedure applied to a robotic arm for service tasks; Jovanovic et al. [12] described production cycle scheduling algorithm on the grounds of investigations of manufacturing capacity utilization levels and causes of loss for special-purpose products in complex manufacturing environments; Gaaloul et al. [13] proposed a dynamic mining algorithm based on a statistical technique to discover composite web service patterns from execution logs; Stegaru and Stanescu [14] presented a methodological modeling framework for quality driven web service composition that tackles quality from the user, final product, and process views; Omid et al. [15] proposed a framework for context-aware web service composition using planning techniques; Iordache and Moldoveanu [16] introduced a QoS-aware end-to-end web service composition approach that handles all the stages from the web service discovery step to the actual binding of the services, using a genetic algorithm to compute and compare the aggregated QoS of the composite services; Berlec et al. [17] proposed basic and extended models that take into account the tied-up capital in a production to calculate the optimal batch quantity; Avitabile et al. [18] used component modes from unconnected components as projection matrices to identify the system level full field response; Florjanic et al. [19] proposed an artificial neural network model to address the problem of estimating the volume of manufacturing hours in model manufacturing; Suzic et al. [20] studied mass customized production by using group technology and production flow analysis in a panel furniture manufacturing company; Chifu et al. [21] presented an ant-inspired method for selecting the optimal solution in semantic web service composition; Xiao et al. [22] proposed an improved shuffled frog leaping algorithm for solving the optimization problems of multi-objective production transportation scheduling in a cloud manufacturing environment; Dong and Guo [23] proposed a cloud manufacturing service evaluation and selection optimization model based on a global trust degree and composite template; Jing et al. [24] presented a cloud manufacturing service composition optimization algorithm based on discrete particle swarm optimization and execution reliability; Zhao et al. [25] proposed the service capability evaluation model of small and medium enterprise design knowledge resources and the mathematical model of design knowledge resource serialization combination under a cloud manufacturing environment, and a quantum harmony search algorithm for solving the model was given; Bao et al. [26] divided the service composition into three stages: the matching of adjacent nodes, the cleaning of broken branch nodes and the combination of atomic services, and put forward three steps service composition algorithm of the combination of atomic services based on knowledge. The above documents built service composition models and the corresponding solution algorithms mainly based on the analysis of service composition targets, most of which idealized a cloud manufacturing service as a kind of "rigid body", which was separated from the social relationship, seldom considering the relationships between the cloud manufacturing services and manufacturing tasks, and between cloud manufacturing services on the service composition optimization. However, to meet the personalized needs in the cloud manufacturing environment, it requires collaborative participation among customers and cloud manufacturing service providers and others [27]. The matching degree of cloud manufacturing services and manufacturing tasks, the harmony degree of cloud manufacturing services in service composition, and the complexity of service composition have great influence on the completion of customized/personalized product manufacturing tasks. Therefore, it is imperative to consider those factors for studying the optimization of cloud manufacturing service composition. This study constructs a cloud manufacturing service composition optimization mathematical model with the consideration of the matching degree of service and task in the process of cloud manufacturing service composition, the composition harmony degree, and the complexity of service composition, and then proposes a cloud-entropy enhanced genetic algorithm (CEGA) to solve the problem. Finally, the model and the algorithm are verified by an example of an automatic guided vehicle manufacturing task. The remainder of this paper is organized as follows: Section 1 analyzes the objectives and the strategies of cloud manufacturing service composition; Section 2 gives the definitions of service-matching degree, composition harmony degree, and cloud-entropy, as well as the corresponding calculation methods; Section 3 proposes CEGA algorithm; Section 4 analyzes the application case; and Section 5 concludes the whole paper and gives future work. 1 CLOUD MANUFACTURING SERVICE COMPOSITION ANALYSIS In a cloud manufacturing environment, customers can organize multiple distributed manufacturing resources to complete manufacturing tasks using cloud 578 Li, Y.X. - Yao, X.F. - Zhou, J.F. Strojniski vestnik - Journal of Mechanical Engineering 62(2016)10, 577-590 manufacturing service platform service composition modules. The goal of cloud manufacturing service composition is that various product manufacturing tasks are allocated to private cloud services and the most appropriate public cloud services, making the service composition meet the technical requirements of product, process time constraints and other conditions, and to obtain the maximum economic benefit [28]. The matching degree of cloud manufacturing services and manufacturing tasks, the harmony degree of cloud manufacturing services in service composition, and the complexity of service composition have significant impacts on the service composition, so cloud service composition should not only consider the product delivery period, manufacturing cost and other traditional factors, but also address service-matching degree, composition harmony degree and cloud-entropy. In the cloud manufacturing service composition, matching manufacturing tasks with public cloud services and/or enterprise private cloud services is necessary. If the cloud manufacturing service provider cannot understand its customers' manufacturing needs completely, or in the cloud manufacturing service platform it is hard to accurately express customers' requirement, customers and cloud manufacturing service providers need to communicate, coordinate, and collaboratively participate in product manufacturing processes. If the cloud service customer belongs to a branch of a group company, due to the restriction of its equipment manufacturing capacity and technical level, it is difficult for the customer to complete a manufacturing task alone, so it needs to be completed with the enterprise private cloud services or public cloud services. The main effect of customers' participation in manufacturing processes is the verification and feedback of product manufacturing requirements. Such a manufacturing model in which customers are directly involved in the product manufacturing processes is different than traditional closed-door manufacturing and networked manufacturing based on the knowledge of the customers' description of manufacturing requirements. Its outstanding advantage is that customers can directly inspect and provide feedback on a manufacturing process or even some parts and components in the process of product development or manufacturing, and without any need to wait for all the manufacturing tasks to be completed before the product information feedback. To a certain extent, it can reduce a product's defect rate and ensure that the product meets customer's customized manufacturing needs with high standards. Moreover, it also shortens the time of trial production and the rework time of unqualified products, reduces production costs, and ensures the product's quality and delivery time. In the composition process, first of all, determining the service composition strategy based on the decomposition of customer's manufacturing requirements should be considered, specifically, the basic strategies for selecting cloud manufacturing services according to the manufacturing tasks; secondly, service-matching degree, composition harmony degree, cloud-entropy, and other problems should be addressed. Based on the above analysis, the following cloud manufacturing service composition strategies are given: 1. All manufacturing tasks must be allocated to one or more corresponding public cloud services or private cloud services to complete. 2. Manufacturing tasks that include core product technologies and need to be kept strictly confidential must be allocated to enterprise private cloud services to be completed. 3. The comprehensive optimization objective of the cloud manufacturing service composition scheme should be as close to the ideal value as possible, which is composed of service-matching degree, composition harmony degree, cloud-entropy, and so on. Service composition according to the above strategies could provide support for the construction of a scientific and rational organization structure of the cloud manufacturing and the optimization of the use of distributed manufacturing resources. 2 MODELING CLOUD MANUFACTURING SERVICE COMPOSITION 2.1 Problem Description Suppose that a customized product manufacturing project can be broken down into l sub-tasks, namely W= {w1, ..., wl}, it is necessary to select the appropriate public cloud services in n public cloud service sets and enterprise private cloud services in m private cloud service sets from the cloud resource pool to complete. The m private cloud service sets are represented as Q1, ..., Qm. The number of private cloud services contained in each set is represented as k1, ..., km. The ith private cloud service set is represented as Qi = {Q^, ..., Qi>ki}. The n public cloud service sets are represented as Qm+1, ..., Qm+n. The number of public cloud services contained in each set is represented as km+1, ..., km+n. The ith public cloud service set is represented as Qi = {Q^, ..., Qi>ki}. The l Multi-objective Optimization of Cloud Manufacturing Service Composition with Cloud-Entropy Enhanced Genetic Algorithm 579 Strojniski vestnik - Journal of Mechanical Engineering 62(2016)10, 577-590 manufacturing tasks are allocated to the most m+n j appropriate public cloud services in ^ ki and the most suitable enterprise private cloud services in / i ,_1 Ki to compete for the task collaboratively. The allocation relationship is shown in Fig. 1. Qi={Q„, e12,-, Qltl} e2={e21, Q*,-, Q2h} Qm = {Qm 1, Qm2,-, Qmk, } Qm+1 = {Qm+1,1' Qm+1,2 ,—, Qm+1,km+1 } Qm+2 = {Qm+21 Qm+2,2, —, Qm+2,k„2 } Qm+n = {Qm+n.1, Qm+r,2—', Qm+nKJ Fig. 1. Cloud manufacturing service composition mapping relationship 2.2 Service-Matching Degree Definition and Calculation In cloud manufacturing, whether manufacturing services are suitable for manufacturing tasks has a significant influence on the cloud manufacturing service composition. The higher the suitability of cloud manufacturing services for manufacturing tasks, the greater the ability to control the manufacturing tasks, the better the completion quality of the manufacturing tasks. Therefore, in the process of service composition, considering the suitability of cloud manufacturing services for manufacturing tasks is of great significance, which is defined as the service-matching degree. • Definition 1: Service-matching degree: the quantitative level of suitability of cloud manufacturing services (including private and public cloud services) for the manufacturing tasks. Many factors may affect the suitability of public and private cloud services for manufacturing tasks, such as the geographic location of manufacturing resources mapped by cloud manufacturing services, the frequency and experience of implementation of similar manufacturing tasks, the software and hardware strength of manufacturing resources mapped by cloud manufacturing services, the interest in undertaking the manufacturing tasks, and so on. The specific description is as follows: 1. Capacity factor. Capacity matrix C=(ciJ)(m+n)Xl is introduced to describe the manufacturing capacity of m private cloud services and n public ones. ciJ-(1 < i cmax and pcmin respectively represent the maximum mutation and minimum crossover probabilities of the population; pmmax and pmmin respectively represent the maximum and minimum mutation probabilities of the population; and &b ..., k4 are constants of [0,1] with kl = k2 = 0.5, and k3 = k4 = 1. According to Eqs. (12) and (13), the initial values of pc and pm are larger, but gradually reduced with the continuous evolution of the population. In the same generation, different individuals have different crossover and mutation probabilities. The individuals with high fitness value should be protected, and their crossover and mutation probabilities are reduced. The individuals with low fitness value should increase their crossover and mutation probabilities. Therefore, each individual in each generation has different crossover and mutation probabilities, so as to realize the adaptive crossover and mutation. Entropy En, expected value Ex, hyper entropy He and standard deviation Enn are important control parameters of the normal cloud model. Among them, the value of standard deviation Enn is mainly affected by the two parameters of entropy En and hyper entropy He. Entropy En reflects the steepness of the cloud model; expected value Ex reflects the horizontal position of the cloud model; hyper entropy He reflects the cloud particle discrete degree [34]. Cloud particles fluctuate near the expected value, and the fluctuation degree is controlled by He. The stability of the normal cloud model is decreased when the hyper entropy He is too large, and the randomness of the normal cloud model is declined when the hyper entropy He is too small. The algorithm ensures that the best individuals around the maximum fitness value maintain the stable tendency of a normal cloud model, improving the search ability of the individual with a lower fitness value, thus, producing new individuals in larger space, improving the randomness of the algorithm effectively, and restraining premature convergence. The specific steps of the cloud-entropy genetic algorithm are discussed as follows. 3.1 Encoding Strategy The algorithm uses a binary encoding method, in which each chromosome is divided into l segments, and each gene segment represents a manufacturing task. Assuming that the number of the candidate public cloud services to complete the ith manufacturing task is ni, and that of the candidate private ones to complete the ith manufacturing task is mi, then the total number of the candidate cloud manufacturing services to complete the ith manufacturing task is mi+ni. In encoding, the genetic value of 0 indicates that the manufacturing task corresponding to the gene segment is not allocated to any public or private cloud c m 584 Li, Y.X. - Yao, X.F. - Zhou, J.F. Strojniski vestnik - Journal of Mechanical Engineering 62(2016)10, 577-590 services; whereas the genetic value of 1 indicates that the manufacturing task corresponding to the gene segment is allocated to a public/ private cloud service. Such encoding can also be used to decode the chromosome. An example of such encoding is given in Fig. 4, which indicates that the manufacturing task w1 is allocated to the first service of the private cloud service set Q1 with a genetic value of 1. In the same segment, the other genetic values corresponding to the other candidate cloud services are 0. Similarly, the manufacturing task w{ is allocated to the third service of the public cloud service set Qm+n. 3.2 Fitness Function Cloud manufacturing service composition is a nonlinear and multi-objective optimization problem, and there is a certain link among multiple objectives. It is difficult to directly give the optimal value of such a multi-objective optimization problem, but the ideal positive point (i.e. the most desired value) and the ideal negative point (i.e. the least expected value) of the single objective can be given easily. Therefore, it is more appropriate to choose the ideal point method to construct the fitness function in the cloud-entropy genetic algorithm. The ideal point method is based on the distance between the objective function value and the ideal point to evaluate the advantages and disadvantages of the composition service scheme. The smaller the distance, the better the scheme. The ideal point is composed of the ideal value of each objective function. The ideal value can be specified by the decision maker, and also can be obtained from the single objective optimal value. According to the above analysis, the evaluation function of the cloud manufacturing service composition problem can be constructed: where ( I*, 12*, I3* ) is the ideal point, which is composed of the optimal values of three single objective functions. (Ib I2, I3) is the objective function value of the cloud manufacturing service composition. I is the distance between objective function value of the cloud manufacturing service composition and the ideal point, namely deviation. The quantity level and the important degree of the objective functions I1, I2 and I3 are not the same, so they should be dealt with dimensionless correction and be distinguished with weight coefficients. Thus the evaluation function can be modified as follows: X -I- min I '= U(:M-)2 +£2(IL-^- )2 )2> (15) X -1- I- I2- I- where e1, e2 and e3 are the weight coefficients of the objective functions, and e1 + e2 + e3 = 1. Their values can be determined by the expert evaluation. According to the above analysis, the fitness function of CEGA is constructed as: f(i) = U- ^(^LA.)2 +e2(1-1-f (16) 1 2 h where f(i) is the fitness function of the ith chromosome; Ij, /2 and /3 are the objective function values corresponding to the ith chromosome; and U is a positive and sufficiently large number. 3.3 Selection Operation The roulette method is adopted to perform the selection operation. According to its fitness, each generation has the corresponding probability to be copied to the next generation. Given that the population size is popsize, and the fitness of the individual is f(i), then the selection probability to be copied to the next generation can be calculated as follows. min I = yj ( I -1*)2 + ( 12 -12)2 + ( I3 -1*)2 Pi =- f (i) (14) X f (i) (17) m\+n\ m+ni Private cloud service sets Public cloud service sets Private cloud service sets Public cloud service sets ßl 02 ßm+1 ßl ß2 ßm+1 ßm+n 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 Manufacturing task w 1 Manufacturing task Wi Fig. 4. Example of the encoding method Multi-objective Optimization of Cloud Manufacturing Service Composition with Cloud-Entropy Enhanced Genetic Algorithm 585 =1 Strojniski vestnik - Journal of Mechanical Engineering 62(2016)10, 577-590 3.4 Crossover Operation The crossover probability pc of the population is calculated by Eq. (12), and the expected value Ex, entropy En, and hyper entropy He of the crossover operator are calculated. Produce two parent individuals by the normal cloud model. The operation method called "double crossover points" is adopted; this is randomly selecting two gene segments as crossover points, exchanging gene encodes of the crossover points between the first parent individual and the second parent individual, the unchosen gene encodings remaining the same; thus, two offspring individuals are produced. The crossover operation is shown in Fig. 5. Gene segment I Gene segment 2 Gene segment 3 Parent 1 1000110000 0 0001 0 0 0 1 0 0 0 0 0^1 0 0 1,0 crossover operation. Offspring 1 0 0 0 1 0 I 0 0 0 0 0 0 I I 0 Offspring 2 |000l0000100001 Fig. 5. Crossover operation 3.5 Mutation Operation Calculate the mutation probability pm of the population according to Eq. (13), the expected value Ex, entropy En, and hyper entropy He of the mutation operator. Produce a new individual by the normal cloud model. When pm is bigger than the given threshold, randomly select a gene segment in the chromosome, one of encoded gene in the selected gene segment is set to 1, the others in the same gene segment are set to 0, then a new chromosome is produced. The mutation operation is shown in Fig. 6. CEGA randomly generates an initial population, repeats steps (Sections) 3.2 to 3.5 until the maximum generation equals the setting value 150 (i.e. maxgen=150) or other termination conditions of the algorithm occur, and outputs the optimal results. Gene segment 1 Gene segment 1 Gene segment 3 Parent 000100000101010 The first gene encoding in the gene segment 2 is set to 1 for mutation Offspring 000101000001010 Fig. 6. Mutation operation 4 APPLICATION EXAMPLE A company in Foshan city has built two manufacturing workshops. A private cloud service platform is built inside the enterprise for sharing the equipment, raw materials and other manufacturing resources for the internal manufacturing departments. The manufacturing tasks of the enterprise are synergistically implemented by the internal manufacturing resources (i.e. the enterprise private cloud services) and the external manufacturing resources (i.e. the public cloud services). Take the production of five sets of Automatic Guided Vehicles (AGVs) as an example to illustrate the specific application of the proposed cloud manufacturing service composition optimization algorithm. The manufacturing task of the AGV can be divided into six sub-tasks: car body task wb driving device task w2, auxiliary equipment task w3, power supply system task w4, auxiliary control system task w5 and main control system task w6. All of the sub-tasks are allocated according to the proposed CEGA. The available public cloud service sets for the allocation of the manufacturing tasks w1, w2, w3, w4, and w5 are Qb Q2, Q3, Q4, and Q5, respectively. The numbers of public cloud services contained in the five sets are 3, 3, 4, 2 and 2, respectively. The manufacturing task w6 involves the core technology of the enterprise with a high level of confidentiality, and must be implemented by the enterprise private cloud service set Q6, which contains two private cloud services. In summary, the six manufacturing tasks wb w2, w3, w4, w5, and w6 are allocated to 14 public cloud services and two private cloud services. According to the manufacturing task number, the candidate cloud manufacturing services are arranged in a sequence. The influence factor vectors are obtained according to the definition of service-matching degree. 586 Li, Y.X. - Yao, X.F. - Zhou, J.F. Strojniski vestnik - Journal of Mechanical Engineering 62(2016)10, 577-590 0.6, 0.6] 0.6, 0.4, Capacity factor vector: C = [0.6, 0.2, 0.6, 0.2, 0.4, 0.6, 0.8, 0.6, 0.4, 0.2, 0.2, 0.6, 0.8, 0.2, 0.6, 0.8] Desire factor vector: D = [0.7, 0.6, 0.6, 0.8, 0.7, 0.6, 0.5, 0.8, 0.8, 0.9, 0.7, 0.8, 0.7, 0.8, 0.8, 0.7] Equipment factor vector: E = [0.6, 0.6, 0.4, 0.4, 0.6, 0.6, 0.6, 0.4, 0.6, 0.4, 0.6, 0.8 Position factor vector: P = [1, 0.6, 1, 0.6, 1, 1, 1, 0.6, 1, 1, 1, 0.6, 0.6, 1, 1, 1]. Set a = 0.3, ft = 0.2, y = 0.2, and 8=0.3, and then the service-matching degree vector can be obtained: V= [0.74, 0.44, 0.68, 0.48, 0.68, 0.72, 0.76, 0.60, 0.70, 0.66, 0.58, 0.64, 0.64, 0.64, 0.80, 0.80]. The execution time [hour] of each task is represented by a vector as follows: texe=[73, 70, 68, 75, 70, 60, 70, 85, 90, 88, 52, 54, 48, 60, 63, 58]. The maximum continuous working time [hour] and the maintenance time [hour] are expressed as follows: tcon=[16, 20, 16, 20, 24, 30, 20, 18, 16, 24, 20, 30, 40, 24, 22, 24]; trep= [2, 3, 2, 2, 3, 1.5, 3, 2, 1, 2, 2, 1, 3, 1.5, 2, 1]. The unit time cost [€ per hour] is expressed as follows: y = [37, 61, 47, 28, 43, 57, 47, 67, 31, 59, 45, 41, 46, 43, 49, 51]. The composition harmony degree matrix of the manufacturing task can be obtained according to the definition of the composition harmony degree. W1 W2 W3 W4 W5 W6 W1 ' K h12 h13 h14 hi5 hi6 W2 h21 h22 h23 h24 h25 h26 II K h32 h33 h34 h35 h36 W4 h41 h42 h43 h44 h45 h46 W5 h51 h52 h53 h54 h55 h56 W6 _h61 h62 h63 h64 h65 h66 The matrix is a symmetric one, whose diagonal elements hn, h22, ..., and h66 are 1. h12 represents the composition harmony degree of three candidate cloud manufacturing services for manufacturing task w1 and three for manufacturing task w2. Other elements of the matrix are similar to h12. Their values can be calculated as follows: "0.769 0.667 0.589" 0.588 0.667 0.770 0.667 0.626 0.910 hl2 = h13 = 1.000 0.589 0.668 0.770 0.625 0.834 0.557 0.770 0.909 0.528 0.627 0.716 h14 = 0.835 0.628 0.669 0.771 0.627 0.668 h15 = 0.594 0.770 0.671 0.834 0.670 0.770 h16 = 0.770 0.834 0.909 0.770 0.909 0.909 h23 = 0.667 0.625 0.589 0.527 0.769 0.668 0.590 0.627 0.770 0.592 0.671 0.671 h24 = h26 = h35 = h45 = 0.772 0.591 0.669 0.669 0.589 0.770 0.834 0.910 0.910 0.770 0.910 0.910 0.593 0.770" 0.676 0.670 0.568 0.836 0.777 0.593 0.625 0.589" 0.715 0.556 h25 = h34 = h36 = h46 = 0.774 0.716 0.593 0.626 0.834 0.667 0.717 0.590" 0.673 0.672 0.776 0.633 0.535 0.774 0.910 0.770" 0.771 0.911 0.836 0.837 0.910 0.911 0.770 0.834 0.910 0.833 h56 = 0.910 0.834 0.769 0.910 The cloud-entropy vector of the manufacturing task can be obtained according to the definition of cloud-entropy and Eq. (4): £nC=[1.784, 1.539, 1.658, 1.602, 1.341, 1.622, 1.539, 1.658, 1.946, 1.482, 1.274, 0.764, 0.561, 1.202, 1.307, 1.144]. The delivery time constraint is 480, and the cost constraint is 100000. Specifically, max(tb t2, ..., t6) <480 and £C = £' yi ^ 100000. MATLAB R2015a is used to realize the CEGA programming. Set population size Popsize = 50, maximum generation Maxgen = 150, and U = 100. The weight coefficients of the objective functions are given as e1 = 0.4, e2 = 0.3, and s3 = 0.3, respectively. The ideal point obtained by the single objective Multi-objective Optimization of Cloud Manufacturing Service Composition with Cloud-Entropy Enhanced Genetic Algorithm 587 Strojniski vestnik - Journal of Mechanical Engineering 62(2016)10, 577-590 optimal function is (4.30, 12.768, 9.135). After 48 iterations of the CEGA, the optimal fitness value of the population is 99.934, the service-matching degree is 4, the composition harmony degree is 11.799, the cloud-entropy is 8.708, the delivery time is 375, the cost is 80490, the chromosome encoding of the optimal solution is 1001001000100110, and the distance between the optimal objective function value and the ideal point is 1.101. The chromosome encoding of the optimal solution is shown in Fig. 7, where manufacturing task w1 is allocated to the first cloud service of the public cloud service set Q1; task w2 to the first cloud service of the public cloud service set Q2; task w3 to the first cloud service of the public cloud service set Q3; task w4 to the first cloud service of the public cloud service set Q4; task w5 to the second cloud service of the public cloud service set Q5; and task w6 to the first cloud service of the private cloud service set Q6. The average running time of the algorithm is 11.63 s, and the evolution curves of CEGA are shown in Fig. 8. Fig. 8a) shows the optimal individual fitness value evolution curve, Fig. 8b the service-matching degree evolution curve, Fig. 8c the composition harmony degree evolution curve, Fig. 8d the cloud-entropy evolution curve, Fig. 8e the execution time evolution curve, Fig. 8f the execution cost evolution curve, Fig. 8g the deviation evolution curve and Fig. 8h the three-dimensional scatter diagram of CEGA solution process. The population tends to be stable when it evolves to the forty-eighth generation. Q\ 02 £3 £4 Q5 06 n ' l 0 0 1 0 0 1 0 0 0 1 0 0 1 1 0 Wi w2 w3 w4 w5 w6 Fig. 7. The optimal solution of the AGV manufacturing task Fig. 9 shows the evolution curves of the proposed CEGA and Standard Genetic Algorithm (SGA) under the same conditions. As can be seen from the figure, CEGA converges to the optimal solution of a) d) B 4 ra E (Oqo o 3.8