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Cloud manufacturing (CMfg) is a new service-oriented smart manufacturing paradigm, and it provides a new product development model in which users are enabled to configure, select, and utilize customized manufacturing service on-demand. Because of the massive manufacturing resources, various users with individualized demands, heterogeneous manufacturing system or platform, and different data type or file type, CMfg is fully recognized as a kind of complex manufacturing system in complex environment and has received considerable attention in recent years. In practical scenarios of CMfg, the amount of manufacturing task may be very large, and there are always quite a lot of candidate manufacturing services in cloud pool for corresponding subtasks. These candidate services will be selected and composed together to complete a complex manufacturing task. Obviously, manufacturing service composition plays a very important role in CMfg lifecycle and thus enables complex manufacturing system to be stable, safe, reliable, and efficient and effective. In this paper, a new manufacturing service composition scheme named as Multi-Batch Subtasks Parallel-Hybrid Execution Cloud Service Composition for Cloud Manufacturing (MBSPHE-CSCCM) is proposed, and such composition is one of the most difficult combination optimization problems with NP-hard complexity. To address the problem, a novel optimization method named as Improved Hybrid Differential Evolution and Teaching Based Optimization (IHDETBO) is proposed and introduced in detail. The results obtained by simulation experiments and case study validate the effectiveness and feasibility of the proposed algorithm.

The continuing rise in customer expectation, demand of environmental-friendly production, rapid responsiveness to market changes, and other market competitions poses a critical challenge to manufacturing industry. Under these market pressures, it is very important that manufacturing partners in the industry chain should work together to provide offerings, which contain material products and immaterial services or functionalities, so as to achieve a win-win situation among users, enterprises, environment, and society. So, cloud manufacturing (CMfg) emerges as the time require. The term “cloud manufacturing” was firstly coined by Li et al. [

In the past decades, through the integration of some advanced technology such as Cyber-Physical System (CPS) [

Since the manufacturing services in CMfg are massive, users can acquire a lot of production capability to fulfill their customized demand. Especially for a complex manufacturing task, it is always divided into several subtasks, and for every subtask there are also many manufacturing services that can be selected. Although these candidate services have different performance or QoS, they all satisfy or are within the range of user’s requirements. So, such collaboration is essentially enabled by the composition of manufacturing services, i.e., cloud service composition for cloud manufacturing (CSCCM). CSCCM involves selecting appropriate and optimal manufacturing services from candidate services and assembling them together with logistic. In other words, CSCCM is essentially an interconnected set of multiple specialized manufacturing services to offer the products or functionalities to solve a complex manufacturing task according to user’s requirement. Obviously, such composition is one of the most difficult combination optimization problems with NP-hard complexity. Tao et al. [

Although the aforementioned algorithms and related improved versions can solve NP-hard problem to a certain degree, they cannot address well the mass task in CMfg. In order to achieve a better optimization, adopted are several candidate manufacturing services, when the task amount is very large and there are quite a lot of candidate manufacturing services for corresponding subtasks. Moreover, when the interface is highly standardized, it is possible that multi-services execute parallel and hybrid. The encoding methods and operations of the aforementioned algorithms are just on single gene location, which is not suitable for the scenario of the multi-services selected for one subtask, because to the multi-services, the transportation scheme between subtasks is diversity and should be under consideration when establish the objective function. In addition, the global search ability of the aforementioned algorithms is not ideal for high dimensional and complex objective function in CMfg. So, in this paper, we propose a manufacturing service composition scheme named as Multi-Batch Subtasks Parallel-Hybrid Execution Cloud Service Composition for Cloud Manufacturing (MBSPHE-CSCCM). Meanwhile, a novel optimization method named as

The remainder of the paper is organized as follows. In Section

In our previous work, we have discussed the CMfg architecture [

The architecture of CMfg system [

Generally speaking, the lifecycle of CMfg has several phases just like cloud computing: the definition and publication of CS, the proposal of manufacturing task requirement, the matching of CS, the composition and provision of CS, the determination of manufacturing contract, manufacturing and distribution, and the disposal of manufacturing task [_{1} and SubT_{2} in Figure _{1}=_{2}=_{i,j}, where _{1} will be allocated production task and will deliver their production results to one or more CSs in CSS_{2} after completing their own tasks. For example, in composition scenario shown in Figure _{1,1}, CS_{1,2}, and _{1,1} will be delivered to CS_{2,1} and _{1,2} to CS_{2,1} and CS_{2,2}, and

Schematic of cloud service composition for cloud manufacturing.

MBSPHE-CSCCM is a combinatorial optimization problem with strong NP-hard problem. Furthermore, with the rapid increasing number of candidate CSs and the amount of cloud manufacturing tasks and subtasks, the search space is quite large. It is hard to solve MBSPHE-CSCCM problem with a large search scale by traditional methods. In this paper, the DE algorithm and TLBO algorithm are adopted to design a new method termed as IHDETBO. DE and TLBO are both recently developed meta-heuristic algorithms to enhance and balance the exploration and exploitation capacities. The basic concepts and operations of these two algorithms are detailed in the following sections.

DE was firstly coined by Storn and Price [

Then the population evolves over generations through three types of operations such as mutation, crossover, and selection till one of the termination criterions is satisfied.

In the mutation operation of the

rand/1/bin [

rand/2/bin [

best-to-rand/1/bin [

best-to-rand/2/bin [

rand-to-best/2/bin [

current-to-rand/1/bin [

current-to-pbest/1/bin [

_{1},

_{2},

_{3},

_{4}, and

_{5}are distinct random integers uniformly generated from the set

In the crossover operation after mutation operation of the

A greedy selection operation is used to select individual from each pair of the target vector

TLBO algorithm was firstly proposed by Rao [

In the teacher phase, the algorithm simulates the learning of students from teacher. The teacher (always the best individual of the entire population) will put maximum effort to increase the mean grade of the class from any value to his value, and the learners will gain knowledge according to the quality of teaching delivered by a teacher and the quality of learners present in the class [_{d} is a random number in the range _{F} is the teaching factor which decides the value of the mean to be changed and can be either 1 or 2 and decided randomly as follows:

Based on the

In the learner phase after teacher phase, the algorithm will simulate the learning of the students (individuals) through interacting with each other by discussions, presentations, formal communications, and so on. A learner will develop his knowledge if the other learners are better. So in this phase of the

To solve the MBSPHE-CSCCM problem, a so-called IHDETBO algorithm is proposed by integrating improved DE (named as IDE phase) and the improved teacher phase of TLBO (named as IT phase) to enhance and balance the exploration and exploitation capacities. At first, block encoding and initialization are operated in population initialization. In the IDE phase, block mutation, block crossover and block selection are operated. Besides, factors_{F} will be also improved to make the simulation more in line with the actual. The algorithm is discussed as follows in detail.

To facilitate the discussion of MBSPHE-CSCCM problem, the parameter setting is unified as follows.

_{i}. Generally,

To address the MBSPHE-CSCCM problem, a new encoding method named as block encoding is proposed. A MBSPHE-CSCCM scheme can be encoded as a chromosome by the integer array with the length equal to the number of CSs [

Schematic of encoding [

The initialization is generated randomly and the sum of every rank equals to the amount of the corresponding subtask, so the initialization of every genebit is calculated as follows:

In the IDE phase, there are still three operations: mutation, crossover, and selection mentioned above. Based on the block encoding and initialization, mutation and crossover are both executed rank by rank, which are named as block mutation and block crossover, respectively. Additionally, parameters

Let

In the IHDETBO algorithm, the mutation factor_{d} is improved and calculated adaptively with the aim of generating diversified individuals. At each generation_{d} of each individual

Let_{F} be the set of all successful mutation factors in this generation. The location parameter

According to the existing research results [_{d}, because it is more helpful to diversify_{d} and thus avoid premature convergence which often occurs in greedy mutation strategies if_{d} is highly concentrated around a certain value, so as to enhance the population diversity. Additionally, the Lehmer mean of_{F} makes the adaptation of

Let

In the IHDETBO algorithm, the crossover probability_{d} is also improved and calculated adaptively with the aim of generating better individuals into the next IT phase. At each generation_{d} of each individual

Let_{CR} be the set of all successful crossover probabilities in this generation. The mean _{CR}.

According to the existing research results [_{CR} records recent successful crossover probabilities, and _{d} that has a great probability close to the successful crossover probability values.

After block mutation and block crossover, we can obtain a trial/offspring individual

In IHDETBO algorithm, the teacher phase of TLBO is improved and adopted as IT phase following the IDE phase. Based on the block operations illustrated in Section _{F} will be improved to make the simulation more in line with the actual.

Just as introduced in Section _{d} is a random number in the range _{F} is the teaching factor which can be calculated by (

In the canonical TLBO algorithm, the teaching factor_{F,d} is either 1 or 2. It means that the learners learn nothing from the teacher or learn all the things from the teacher, respectively. Obviously, it is not in line with the actual. In actually teaching-learning phenomenon, the learners may learn in any proportion from the teacher because of the learners’ learning ability, the teacher’s teaching ability, or other reasons, so the teaching factor_{F,d} is not always at its end state for learners but varies in-between also [_{F,d} is calculated as follows:

In this section, the effectiveness of the proposed IHDETBO algorithm is examined by several benchmark functions, and the process of IHDETBO applied to MBSPHE-CSCCM is demonstrated by a case study. These experiments are implemented in a PC with an Intel® Core™ i5-3337U CPU operating at 1.80GHz and 8.00GB of RAM, and operating system is Windows 7 (64 bit). The programming software for the experiments with benchmark functions and that for the case study are Matlab R2016a and Microsoft Visual C++ 6.0, respectively.

To investigate the performance of the proposed IHDETBO algorithm, six different benchmark functions with different characteristics of objective functions and different dimensions and search space are adopted. The results obtained by using the IHDETBO algorithm are also compared with other optimization algorithms such as PSO, DE, and TLBO algorithms with different dimensions and population sizes.

To analyze and compare the performance and accuracy of the IHDETBO algorithm, we adopt six different benchmark functions shown as in Table

Basic functions used in the experiments.

Name | Function | C | Search space | Initial space | Min |
---|---|---|---|---|---|

Sphere | | US | | | 0 |

Rosenbrock | | UN | | | 0 |

Ackley | | MN | | | 0 |

Schwefel 2.26 | | MS | | | 0 |

Griewank | | MN | | | 0 |

Rastrigin | | MN | | | 0 |

We test proposed IHDETBO algorithm with the same parameters setting and compare the test results with PSO and DE algorithms. For PSO algorithm, parameter

The results of comparison test on 6 benchmark functions with different parameters settings.

Benchmark function | algorithm | N | 10 | 20 | 50 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

D | 2 | 5 | 10 | 2 | 5 | 10 | 2 | 5 | 10 | ||

_{1} | IHDETBO | best | 7.58E-154 | 3.56E-68 | 1.11E-36 | 2.52E-135 | 6.14E-54 | 1.27E-27 | 9.72E-120 | 6.39E-47 | 8.65E-23 |

worst | 2.63E-138 | 3.63E-55 | 8.63E-29 | 1.38E-122 | 2.95E-48 | 3.64E-22 | 5.31E-113 | 4.35E-43 | 4.44E-20 | ||

mean | 6.36E-140 | 7.66E-57 | 5.76E-30 | 2.84E-124 | 2.54E-49 | 1.46E-23 | 2.43E-114 | 5.53E-44 | 5.47E-21 | ||

std | 3.68E-139 | 5.07E-56 | 1.53E-29 | 1.93E-123 | 6.60E-49 | 5.19E-23 | 8.54E-114 | 9.57E-44 | 8.16E-21 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

PSO | best | 0.00E+00 | 0.00E+00 | 2.78E+01 | 0.00E+00 | 0.00E+00 | 8.41E-01 | 0.00E+00 | 0.00E+00 | 2.76E-15 | |

worst | 1.65E-43 | 5.00E+00 | 5.34E+03 | 2.03E-48 | 6.62E-30 | 1.62E+02 | 7.32E-55 | 6.56E-53 | 1.60E-03 | ||

mean | 4.17E-45 | 2.42E-01 | 9.88E+02 | 4.67E-50 | 3.42E-31 | 3.98E+01 | 5.41E-56 | 2.18E-54 | 4.60E-05 | ||

std | 2.34E-44 | 7.58E-01 | 9.09E+02 | 2.85E-49 | 1.23E-30 | 4.76E+01 | 1.47E-55 | 1.01E-53 | 2.27E-04 | ||

FE | 1.14E+04 | 1.23E+04 | 1.24E+04 | 2.22E+04 | 2.31E+04 | 2.42E+04 | 5.45E+04 | 5.45E+04 | 5.91E+04 | ||

DE | best | 4.55E-111 | 1.73E-02 | 3.64E+01 | 1.83E-113 | 5.16E-47 | 1.78E-15 | 5.66E-112 | 9.89E-44 | 9.08E-20 | |

worst | 2.68E-01 | 6.28E+02 | 2.42E+03 | 3.01E-104 | 4.33E-06 | 4.66E+01 | 2.65E-104 | 2.60E-40 | 1.11E-17 | ||

mean | 5.40E-03 | 5.57E+01 | 4.51E+02 | 7.63E-106 | 9.90E-08 | 1.51E+00 | 1.07E-105 | 2.41E-41 | 1.56E-18 | ||

std | 3.75E-02 | 1.03E+02 | 5.24E+02 | 4.24E-105 | 6.11E-07 | 6.64E+00 | 4.31E-105 | 4.91E-41 | 1.84E-18 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

TLBO | best | 1.39E-206 | 1.71E-140 | 2.09E-141 | 1.97E-195 | 2.50E-123 | 2.96E-117 | 3.53E-182 | 2.07E-114 | 5.37E-87 | |

worst | 1.68E-189 | 3.79E-131 | 3.74E-130 | 1.10E-177 | 5.87E-116 | 8.28E-110 | 4.21E-174 | 5.35E-109 | 2.22E-84 | ||

mean | 4.12E-191 | 1.08E-132 | 9.72E-132 | 2.20E-179 | 1.05E-117 | 6.04E-111 | 1.57E-175 | 1.35E-110 | 3.58E-85 | ||

std | 0.00E+00 | 5.65E-132 | 5.27E-131 | 0.00E+00 | 8.25E-117 | 1.67E-110 | 0.00E+00 | 7.51E-110 | 5.36E-85 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

| |||||||||||

_{2} | IHDETBO | best | 0.00E+00 | 1.44E-02 | 1.02E+00 | 0.00E+00 | 6.04E-04 | 2.27E+00 | 0.00E+00 | 1.39E-16 | 5.70E-03 |

worst | 3.18E-17 | 4.00E+00 | 7.30E+00 | 0.00E+00 | 5.72E-01 | 4.55E+00 | 0.00E+00 | 2.51E-01 | 4.01E+00 | ||

mean | 6.37E-19 | 5.27E-01 | 4.22E+00 | 0.00E+00 | 2.85E-01 | 3.72E+00 | 0.00E+00 | 3.40E-02 | 2.82E-02 | ||

std | 4.45E-18 | 6.57E-01 | 7.70E-01 | 0.00E+00 | 1.20E-01 | 3.11E-01 | 0.00E+00 | 5.54E-02 | 8.68E-01 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

PSO | best | 0.00E+00 | 7.80E-05 | 1.00E+01 | 0.00E+00 | 0.00E+00 | 5.88E+00 | 0.00E+00 | 0.00E+00 | 7.65E-01 | |

worst | 0.00E+00 | 4.63E+00 | 1.96E+02 | 0.00E+00 | 3.93E+00 | 5.76E+01 | 0.00E+00 | 3.93E+00 | 9.57E+00 | ||

mean | 0.00E+00 | 2.30E+00 | 4.18E+01 | 0.00E+00 | 3.15E-01 | 1.11E+01 | 0.00E+00 | 2.36E-01 | 5.57E+00 | ||

std | 0.00E+00 | 1.58E+00 | 3.48E+01 | 0.00E+00 | 1.07E+00 | 8.77E+00 | 0.00E+00 | 9.34E-01 | 2.22E+00 | ||

FE | 1.11E+04 | 1.24E+04 | 1.24E+04 | 2.16E+04 | 2.31E+04 | 2.42E+04 | 5.32E+04 | 5.49E+04 | 5.98E+04 | ||

DE | best | 0.00E+00 | 2.16E-02 | 6.77E+00 | 0.00E+00 | 1.27E-04 | 2.89E-01 | 0.00E+00 | 7.77E-30 | 1.63E+00 | |

worst | 4.95E+00 | 8.75E+01 | 1.81E+02 | 2.97E-01 | 3.93E+00 | 2.59E+01 | 0.00E+00 | 1.06E+00 | 6.05E+05 | ||

mean | 2.48E-01 | 6.10E+00 | 4.40E+01 | 2.17E-02 | 1.32E+00 | 7.80E+00 | 0.00E+00 | 2.77E-01 | 4.19E+00 | ||

std | 7.36E-01 | 1.34E+01 | 3.47E+01 | 6.03E-02 | 1.10E+00 | 3.39E+00 | 0.00E+00 | 3.21E-01 | 1.24E+00 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

TLBO | best | 5.03E-29 | 1.40E-04 | 5.18E+00 | 5.70E-29 | 2.73E-05 | 5.89E-01 | 9.67E-28 | 1.78E-05 | 1.03E-02 | |

worst | 7.91E-21 | 2.06E+00 | 7.16E+00 | 3.08E-22 | 2.77E-01 | 5.11E+00 | 6.81E-24 | 3.60E-03 | 7.24E-01 | ||

mean | 3.27E-22 | 5.45E-01 | 6.49E+00 | 8.28E-24 | 7.20E-03 | 3.74E+00 | 2.66E-25 | 7.77E-04 | 8.77E-02 | ||

std | 1.31E-21 | 5.11E-01 | 4.53E-01 | 4.32E-23 | 3.86E-02 | 8.08E-01 | 9.64E-25 | 6.35E-04 | 1.23E-01 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

| |||||||||||

_{3} | IHDETBO | best | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 8.30E-14 | 0.00E+00 | 0.00E+00 | 2.76E-11 |

worst | 0.00E+00 | 4.89E-15 | 2.82E-13 | 0.00E+00 | 4.89E-15 | 3.68E-11 | 0.00E+00 | 4.89E-15 | 4.25E-10 | ||

mean | 0.00E+00 | 3.82E-15 | 2.42E-14 | 0.00E+00 | 3.18E-15 | 4.71E-12 | 0.00E+00 | 2.26E-15 | 1.21E-10 | ||

std | 0.00E+00 | 1.63E-15 | 4.86E-14 | 0.00E+00 | 1.77E-15 | 7.58E-12 | 0.00E+00 | 1.56E-15 | 8.58E-11 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

PSO | best | 0.00E+00 | 1.48E-06 | 5.34E+00 | 0.00E+00 | 0.00E+00 | 1.76E+00 | 0.00E+00 | 0.00E+00 | 1.16E+00 | |

worst | 4.89E-15 | 7.50E+00 | 1.74E+01 | 0.00E+00 | 4.17E+00 | 1.25E+01 | 0.00E+00 | 2.32E+00 | 5.09E+00 | ||

mean | 1.47E-15 | 3.17E+00 | 1.06E+01 | 0.00E+00 | 1.02E+00 | 5.38E+00 | 0.00E+00 | 3.10E-01 | 2.88E+00 | ||

std | 6.96E-16 | 2.01E+00 | 2.71E+00 | 0.00E+00 | 2.00E+00 | 2.10E+00 | 0.00E+00 | 6.67E-01 | 9.53E-01 | ||

FE | 1.11E+04 | 1.22E+04 | 1.23E+04 | 2.16E+04 | 2.23E+04 | 2.41E+04 | 5.33E+04 | 5.40E+04 | 5.88E+04 | ||

DE | best | 0.00E+00 | 5.20E-03 | 2.72E+00 | 0.00E+00 | 0.00E+00 | 1.59E-10 | 0.00E+00 | 0.00E+00 | 1.56E-10 | |

worst | 2.58E+00 | 1.41E+01 | 1.49E+01 | 0.00E+00 | 1.65E+00 | 2.58E+00 | 0.00E+00 | 4.89E-15 | 3.60E-09 | ||

mean | 5.87E-02 | 2.66E+00 | 8.67E+00 | 0.00E+00 | 6.58E-02 | 3.30E-01 | 0.00E+00 | 1.47E-15 | 9.13E-10 | ||

std | 3.62E-01 | 3.07E+00 | 2.59E+00 | 0.00E+00 | 3.23E-01 | 6.53E-01 | 0.00E+00 | 6.96E-16 | 6.01E-10 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

TLBO | best | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.33E-15 | |

worst | 4.89E-15 | 4.89E-15 | 8.44E-15 | 0.00E+00 | 4.89E-15 | 8.44E-15 | 0.00E+00 | 4.89E-15 | 4.89E-15 | ||

mean | 1.47E-15 | 4.03E-15 | 5.10E-15 | 0.00E+00 | 3.25E-15 | 5.03E-15 | 0.00E+00 | 3.32E-15 | 4.81E-15 | ||

std | 6.96E-16 | 1.52E-15 | 8.44E-12 | 0.00E+00 | 1.77E-15 | 9.95E-16 | 0.00E+00 | 1.76E-15 | 4.97E-16 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

| |||||||||||

_{4} | IHDETBO | best | 0.00E+00 | 0.00E+00 | 2.27E-13 | 0.00E+00 | 0.00E+00 | 2.73E-11 | 0.00E+00 | 0.00E+00 | 1.39E-09 |

worst | 2.38E+02 | 4.75E+02 | 7.14E+02 | 1.18E+02 | 1.18E+02 | 3.57E+02 | 0.00E+00 | 0.00E+00 | 8.78E-08 | ||

mean | 2.37E+01 | 1.09E+02 | 3.02E+02 | 4.74E+00 | 1.42E+01 | 6.88E+01 | 0.00E+00 | 0.00E+00 | 1.71E-08 | ||

std | 5.31E+01 | 1.13E+02 | 1.84E+02 | 2.32E+01 | 3.85E+01 | 8.25E+01 | 0.00E+00 | 0.00E+00 | 1.65E-08 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

PSO | best | 0.00E+00 | 1.23E-02 | 7.38E+02 | 0.00E+00 | 0.00E+00 | 4.85E+02 | 0.00E+00 | 1.18E+02 | 2.38E+02 | |

worst | 3.57E+02 | 1.08E+03 | 2.54E+03 | 2.38E+02 | 8.69E+02 | 2.26E+03 | 1.18E+02 | 9.52E+02 | 1.92E+03 | ||

mean | 9.68E+01 | 5.72E+02 | 1.69E+03 | 8.29E+01 | 4.43E+02 | 1.39E+03 | 4.50E+01 | 3.88E+02 | 1.19E+03 | ||

std | 9.35E+01 | 2.41E+02 | 4.11E+02 | 7.21E+01 | 2.26E+02 | 3.85E+02 | 5.75E+01 | 1.89E+02 | 3.69E+02 | ||

FE | 1.08E+04 | 1.17E+04 | 1.23E+04 | 2.12E+04 | 2.18E+04 | 2.38E+04 | 5.21E+04 | 5.26E+04 | 5.59E+04 | ||

DE | best | 0.00E+00 | 3.86E-01 | 5.20E+02 | 0.00E+00 | 0.00E+00 | 1.18E+02 | 0.00E+00 | 0.00E+00 | 1.23E-02 | |

worst | 2.74E+02 | 7.90E+02 | 1.82E+03 | 1.40E+02 | 6.25E+02 | 1.03E+03 | 0.00E+00 | 1.25E+02 | 1.26E+03 | ||

mean | 6.52E+01 | 3.94E+02 | 1.15E+03 | 1.80E+01 | 1.94E+02 | 5.98E+02 | 0.00E+00 | 1.32E+01 | 4.76E+02 | ||

std | 6.93E+01 | 1.93E+02 | 2.83E+02 | 4.23E+01 | 1.83E+02 | 2.34E+02 | 0.00E+00 | 3.62E+01 | 3.10E+02 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

TLBO | best | 0.00E+00 | 1.18E+02 | 7.13E+02 | 0.00E+00 | 0.00E+00 | 3.55E+02 | 0.00E+00 | 0.00E+00 | 1.25E+02 | |

worst | 2.39E+02 | 7.15E+02 | 1.58E+03 | 1.18E+02 | 6.51E+02 | 1.28E+03 | 0.00E+00 | 3.55E+02 | 1.04E+03 | ||

mean | 3.08E+01 | 3.22E+02 | 1.28E+03 | 1.18E+01 | 1.93E+02 | 7.33E+02 | 0.00E+00 | 7.88E+01 | 5.35E+02 | ||

std | 5.20E+01 | 1.52E+02 | 2.23E+02 | 3.55E+01 | 1.29E+02 | 2.16E+02 | 0.00E+00 | 9.06E+01 | 1.86E+02 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

| |||||||||||

_{5} | IHDETBO | best | 0.00E+00 | 0.00E+00 | 3.92E-07 | 0.00E+00 | 0.00E+00 | 1.30E-05 | 0.00E+00 | 9.58E-13 | 6.32E-04 |

worst | 7.40E-03 | 1.72E-02 | 3.20E-02 | 0.00E+00 | 1.12E-05 | 2.84E-02 | 0.00E+00 | 1.75E-05 | 2.18E-02 | ||

mean | 1.48E-04 | 2.70E-03 | 7.90E-03 | 0.00E+00 | 6.10E-07 | 7.20E-03 | 0.00E+00 | 8.31E-07 | 8.80E-03 | ||

std | 1.00E-03 | 4.70E-03 | 7.80E-03 | 0.00E+00 | 2.23E-06 | 6.20E-03 | 0.00E+00 | 2.69E-06 | 5.50E-03 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

PSO | best | 0.00E+00 | 7.88E-02 | 2.67E+00 | 0.00E+00 | 3.45E-02 | 1.95E-01 | 0.00E+00 | 7.40E-03 | 8.42E-02 | |

worst | 7.89E-02 | 3.16E+00 | 7.86E+01 | 6.66E-02 | 8.06E-01 | 1.16E+01 | 3.95E-02 | 4.43E-01 | 1.37E+00 | ||

mean | 1.40E-02 | 4.95E-01 | 1.36E+01 | 9.20E-03 | 2.46E-01 | 1.70E+00 | 2.50E-03 | 1.60E-01 | 3.62E-01 | ||

std | 1.69E-02 | 5.05E-01 | 1.22E+01 | 1.37E-02 | 1.50E-01 | 1.81E+00 | 6.20E-03 | 9.92E-02 | 3.47E-01 | ||

FE | 1.09E+04 | 1.22E+04 | 1.23E+04 | 2.12E+04 | 2.20E+00 | 2.40E+04 | 5.22E+04 | 5.30E+04 | 5.89E+04 | ||

DE | best | 0.00E+00 | 3.41E-02 | 7.99E-01 | 0.00E+00 | 7.40E-03 | 9.90E-03 | 0.00E+00 | 2.80E-03 | 1.21E-09 | |

worst | 5.75E-01 | 6.62E+00 | 3.85E+01 | 1.33E-02 | 1.58E-01 | 6.43E-01 | 0.00E+00 | 8.85E-02 | 4.96E-01 | ||

mean | 3.19E-02 | 6.20E-01 | 9.95E+00 | 1.20E-03 | 4.47E-02 | 8.61E-02 | 0.00E+00 | 4.52E-02 | 1.94E-01 | ||

std | 8.11E-02 | 1.17E+00 | 7.67E+00 | 3.00E-03 | 3.19E-02 | 1.00E-01 | 0.00E+00 | 1.98E-02 | 1.50E-01 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

TLBO | best | 0.00E+00 | 2.28E-08 | 0.00E+00 | 0.00E+00 | 2.90E-03 | 0.00E+00 | 0.00E+00 | 7.66E-08 | 0.00E+00 | |

worst | 7.40E-03 | 1.11E-01 | 1.69E-01 | 2.80E-03 | 7.15E-02 | 6.89E-02 | 8.72E-08 | 5.15E-02 | 4.92E-02 | ||

mean | 9.32E-04 | 3.86E-02 | 1.28E-02 | 1.17E-04 | 3.08E-02 | 9.90E-03 | 1.74E-09 | 1.76E-02 | 9.60E-03 | ||

std | 2.20E-03 | 2.87E-02 | 2.81E-02 | 5.42E-04 | 1.50E-02 | 1.74E-02 | 1.22E-08 | 1.08E-02 | 1.37E-02 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

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_{6} | IHDETBO | best | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 1.88E-13 |

worst | 0.00E+00 | 2.98E+00 | 3.98E+00 | 0.00E+00 | 9.95E-01 | 9.95E-01 | 0.00E+00 | 0.00E+00 | 5.38E-11 | ||

mean | 0.00E+00 | 2.79E-01 | 1.21E+00 | 0.00E+00 | 5.97E-02 | 1.99E-02 | 0.00E+00 | 0.00E+00 | 5.02E-12 | ||

std | 0.00E+00 | 5.98E-01 | 1.22E+00 | 0.00E+00 | 2.36E-01 | 1.39E-01 | 0.00E+00 | 0.00E+00 | 8.67E-12 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

PSO | best | 0.00E+00 | 0.00E+00 | 1.27E+01 | 0.00E+00 | 0.00E+00 | 4.44E+00 | 0.00E+00 | 0.00E+00 | 2.00E+00 | |

worst | 1.99E+00 | 3.08E+01 | 5.97E+01 | 9.95E-01 | 2.69E+01 | 4.12E+01 | 9.95E-01 | 1.09E+01 | 3.68E+01 | ||

mean | 4.18E-01 | 7.14E+00 | 3.59E+01 | 2.39E-01 | 5.63E+00 | 2.21E+01 | 3.98E-02 | 3.78E+00 | 1.44E+01 | ||

std | 5.30E-01 | 5.89E+00 | 1.16E+01 | 4.25E-01 | 4.20E+00 | 8.63E+00 | 1.95E-01 | 2.43E+00 | 7.14E+00 | ||

FE | 1.09E+04 | 1.22E+04 | 1.23E+04 | 2.12E+04 | 2.19E+04 | 2.40E+04 | 5.21E+04 | 5.30E+04 | 5.83E+04 | ||

DE | best | 0.00E+00 | 7.53E-02 | 3.25E+00 | 0.00E+00 | 0.00E+00 | 1.17E+00 | 0.00E+00 | 0.00E+00 | 1.22E+01 | |

worst | 1.25E+00 | 1.77E+01 | 4.27E+01 | 0.00E+00 | 2.98E+00 | 2.12E+01 | 0.00E+00 | 1.13E-02 | 3.27E+01 | ||

mean | 3.19E-01 | 3.80E+00 | 1.64E+01 | 0.00E+00 | 5.40E-01 | 5.58E+00 | 0.00E+00 | 2.27E-04 | 2.34E+01 | ||

std | 4.60E-01 | 2.81E+00 | 8.16E+00 | 0.00E+00 | 7.31E-01 | 3.63E+00 | 0.00E+00 | 1.60E-03 | 5.54E+00 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 | ||

TLBO | best | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 0.00E+00 | 2.47E-12 | |

worst | 0.00E+00 | 3.98E+00 | 1.19E+01 | 0.00E+00 | 1.99E+00 | 1.39E+01 | 0.00E+00 | 9.95E-01 | 5.97E+00 | ||

mean | 0.00E+00 | 8.65E-01 | 4.91E+00 | 0.00E+00 | 3.24E-01 | 4.32E+00 | 0.00E+00 | 2.04E-02 | 2.05E+00 | ||

std | 0.00E+00 | 1.27E+00 | 3.02E+00 | 0.00E+00 | 5.10E-01 | 2.81E+00 | 0.00E+00 | 1.39E-01 | 1.53E+00 | ||

FE | 1.00E+04 | 1.00E+04 | 1.00E+04 | 2.00E+04 | 2.00E+04 | 2.00E+04 | 5.01E+04 | 5.01E+04 | 5.01E+04 |

Every experiment is operated 50 times independently. The results of comparison test on 6 different benchmark functions are shown as Table

Objective function landscape of the 6 benchmark functions for

According to the landscape shown in Figure _{1} is a unimodal separable function. It is a very simple benchmark function, which is the easiest to find the global minimum among the six functions. It requires nearly no global search capability and pays special attention on local convergence speed of an algorithm. As shown in Table _{2} is a unimodal non-separable function. Although it is unimodality, its shape is spiral, so it is prone to oscillation that makes it difficult to identify the search direction. Due to the feature, it is difficult to find global minimum, and this benchmark function is always used to evaluate the global search capability of an algorithm. As shown in Table _{3} is a multimodal non-separable function. Although it is multimodality and there are many local minimums, most of them exist in a long and narrow place around the global minimum. Thanks to this feature, these local minimums have no deceptive. So, it is also very easy to find the global minimum, and the global search capability of an algorithm has little effect on the optimization result. As shown in Table _{4} is a multimodal separable function and has a very strong deception. Around the global minimum, there are many local minimums, whose gradients are very similar to that of global minimum, and the optimization algorithm may be mistaken for finding the global minimum. So, it can well evaluate the diversity of population and the global search capability of an algorithm. As shown in Table _{5} is a typical non-linear multimodal non-separable function and has a wide search space. The variables in every dimension are closely related to and interact with each other, and there are a lot of local minimums. So, it is usually considered as a complex multimodal problem which is difficult to deal with by optimization algorithm. As shown in Table _{5}, the sixth one_{6} is a typical non-linear multimodal non-separable function, too. In the^{D} local minimums, and the shapes of these irregular peaks are uneven and jump up and down. So, the effect of traditional gradient-based algorithm is often not ideal, and it is also difficult to find global minimum. As shown in Table

In summary, the classical DE algorithm has very strong global search capability, but its convergence speed is slow. As to classical TLBO algorithm, every individual tries its best to approach the teacher individual in teacher phase, and then in learner phase positive learning and reverse learning are carried out when excellent partner and poor partner are selected, respectively. So, the local search capability is very strong and the convergence speed is very high, which we can obtain through_{1} and_{3}, but the performance is mediocre for complex deceptive benchmark functions such as_{2},_{4},_{5}, and_{6}. The algorithm proposed in this paper is divided into two phases, i.e., IDE and IT. In the IDE phase, the mutation factor_{d} and crossover probability_{d} are both improved. Especially, the mutation factor_{d} that generated with a Cauchy distribution is very important to keep the diversity of population and improve the global search capability. The teacher phase of classical TLBO algorithm has very strong local search capability and leads to a very high local convergence speed; the improvement in the IT phase not only enhances the local search capability, but also avoids losing the possibility of finding better solutions due to overreliance on the teacher individual, so as to better balance the exploration and exploitation capacities. According to the experimental results, the algorithm proposed in this paper performs better to the high-dimensional non-linear multimodal benchmark function, which is always considered as mathematical model of complex engineering problems such as cloud service composition for CMfg.

CMfg is a complex manufacturing system. Taking the car manufacturing as an example, automobile industry is a large and complex manufacturing system involving more than 200 industry fields such as design, material, electronic equipment, and so on. For every automaker, nearly 70% spare parts are outsourced. In this paper, we take the tire manufacturing as a case study, and it refers to raw material production, tire production, hub production, wheel assembly, vehicle assembly, and auto dealer. So, we can decompose the task into 5 subtasks: raw material production is subtask 1, tire production and hub production is subtasks 2.1 and 2.2 which can be executed parallel and regarded as subtask 2, wheel assembly is subtask 3, vehicle assembly is subtask 4, and auto dealer is subtask 5.

The case data is from [

: List of candidate CSs.

Subtask 1 | Subtask 2 | Subtask 3 | Subtask 4 | Subtask 5 | |||||
---|---|---|---|---|---|---|---|---|---|

CS | t | CS | t | CS | t | CS | t | CS | t |

1 | 0.80 | 1 | 0.0873 | 1 | 0.0078 | 1 | 0.3040 | 1 | 0.3333 |

2 | 0.70 | 2 | 0.0775 | 2 | 0.0071 | 2 | 0.2670 | ||

3 | 0.63 | 3 | 0.0685 | 3 | 0.0058 | 3 | 0.2812 | ||

4 | 0.61 | 4 | 0.0901 | 4 | 0.0065 | ||||

5 | 0.57 | 5 | 0.0823 | 5 | 0.0069 | ||||

6 | 0.64 | 6 | 0.0734 | 6 | 0.0069 | ||||

7 | 0.71 | 7 | 0.0060 | ||||||

8 | 0.76 | 8 | 0.0063 | ||||||

9 | 0.55 |

Objective function is the goal of MBSPHE-CSCCM. Normally, it is significant to optimize the QoS according to customer’s preferences. For the sake of discussion, we take the production time as the optimization objective. So, the objective function is defined as follows:_{i} is the production time of the

Examine row (

Examine row

Examine column

In this experiment, the parameters are set as follows: the population size

The production time of every scheme (individual) in the last generation.

No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

T | 457.318 | 452.676 | 448.705 | 444.982 | 452.278 | 453.831 | 486.805 | 453.236 | 476.361 |

| |||||||||

No. | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |

T | 483.416 | 450.803 | 445.757 | 449.945 | 487.402 | 450.2 | 486.736 | 449.795 | 451.612 |

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No. | 19 | | 21 | 22 | 23 | 24 | 25 | 26 | 27 |

T | 453.816 | | 453.446 | 449.327 | 488.205 | 447.775 | 484.68 | 486.12 | 484.042 |

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No. | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 |

T | 485.717 | 471.496 | 484.962 | 450.663 | 453.67 | 447.113 | 449.442 | 448.972 | 452.468 |

| |||||||||

No. | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 |

T | 453.126 | 446.577 | 470.006 | 454.908 | 447.644 | 451.225 | 449.972 | 457.097 | 450.997 |

| |||||||||

No. | 46 | 47 | 48 | 49 | 50 | ||||

T | 482.804 | 478.697 | 458.643 | 454.673 | 453.376 |

The subtask amount of every CS.

Subtask 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

Amount | 326 | 464 | 435 | 504 | 546 | 420 | 368 | 462 | 475 |

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Subtask 2 | 1 | 2 | 3 | 4 | 5 | 6 | |||

Amount | 281 | 955 | 606 | 1026 | 810 | 322 | |||

| |||||||||

Subtask 3 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |

Amount | 634 | 382 | 755 | 495 | 716 | 250 | 494 | 274 | |

| |||||||||

Subtask 4 | 1 | 2 | 3 | ||||||

Amount | 553 | 307 | 140 | ||||||

| |||||||||

Subtask 5 | 1 | ||||||||

Amount | 1000 |

Figure

Schematic of the best scheme.

With the intense competition in the global market and increasingly serious energy and environmental issues, the integration and sharing of manufacturing resources have been becoming more and more important in manufacturing industry. As one of the new manufacturing paradigms, CMfg has been proposed to address to these problems and has gradually been in focus. In practice, CMfg is a large-scale networked distributed manufacturing. The manufacturing resources which always scatter all over the world have the characteristics of massive, heterogeneous, complexity, and coarse granularity. Besides, the transportation among them is very complex because of today advanced logistic. Generally speaking, CMfg is a typical complex system in complex environment, and the manufacturing resources are encapsulated as CS. In complex system, because the total amount of task may be very large, the problem of service composition also becomes very complex. In this paper, we begin with a discussion of the state-of-the-art CMfg and then introduce the manufacturing scheme named as MBSPHE-CSCCM, in which a mass task can be transformed into multi-batch subtasks which will be parallel-hybrid executed. To address the service composition problem for MBSPHE-CSCCM, a novel optimization method IHDETBO for MBSPHE-CSCCM is proposed. This method can be divided into two phases: the first phase is IDE phase, based on basic concept and operation of DE, factors_{F} will be also improved to make the simulation more in line with the actual. In addition, to adapt the special condition of CMfg, block operation including block encoding and initialization, block mutation, block crossover, block selection, and block teaching operation are also proposed. Finally, with the simulation experiments and a case study, we demonstrate the advantage of the proposed method. MBSPHE-CSCCM plays a very important role in CMfg. Besides, there are also many other problems of CMfg that need to be studied, such as task decomposition, the evaluation of CS QoS, CS selection based on performance matching, and so on, which deserves our further consideration.

The experimental data and case study data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work was partly supported by the National Natural Science Foundation of China (Grants nos. 61701443, 61876168, and 61403342) and Zhejiang Provincial Natural Science Foundation of China (LY18F030020).