Task Allocation Optimization in Collaborative Customized Product Development Based on Adaptive Genetic Algorithm

1 Introduction

With the fast development of market economy and the ever-increasing updating speed of products, customer demands are developing constantly into the direction of diversification and individuation, which challenges enterprises with extremely fierce competitions [10]. To pursue their favorable positions and development goals in the market, enterprises are keen to further shorten the product development cycle, reduce R&D cost, and improve production efficiency to obtain competitive advantages in terms of time, quality, and cost. All these require companies to come up with an innovative product design approach. Collaborative customized product development, serving as an innovative and potential design mode, combines the advantages of traditional design patterns and advanced design techniques. Under the premise of maximizing the economic benefits of enterprises and with the characteristics of modular design and parts standard, this mode ensures that enterprises can adapt to the market and to customer-oriented requirements more flexibly, and task allocation is one of the most important parts of the collaborative customized product development process. Reasonable task allocation can optimize the allocation of various development resources and make full use of them, leading to a smooth process of collaborative customized product development.

In terms of task allocation, there are many methods introduced by different scholars. Dianxun et al. [1] introduced a new kind of generalized particle model for the parallel optimization of enterprise resources and task allocation problem. Wunhwa and Chinshien [15] introduced a hybrid method combining tabu search algorithm with the noising method to solve the task allocation problems. Fernandez and Lamari [2] studied and discussed the processor number for continuous communication task allocation problem and introduced two kinds of accurate polynomial time algorithms. Min-Hyuk et al. [8] proposed a distributed task allocation algorithm for a team of robots with constraints on energy resources and operates in an unknown dynamic environment, with the objective of maximizing the task completion ratio while minimizing resource usage. Yin et al. [17] presented a multiobjective task allocation algorithm based on particle swarm optimization (PSO) in the presence of system constraints to achieve throughput maximization, reliability maximization, and cost minimization in a distributed computing system. Yung-Cheng et al. [18] proposed a task allocation algorithm for any parallel programs on a given machine configuration by traversing a state–space tree that enumerates all the possible task assignments and applying a pruning rule on each traversed state. Son et al. [11] proposed an efficient workflow task allocation method based on the locality principle in a distributed workflow system that used the concept of graph partitioning to improve the performance of workflow processing by minimizing remote processing costs. Tripathi et al. [13] presented a multiagent-based approach for the part allocation problems in flexible manufacturing systems to cope with the dynamic environment where four agents (communicator, machine, part, and material handling device) were involved in carrying out the tasks of allocating parts on different machines. Zhang et al. [19] designed the PSO algorithm for task optimization allocation in the suppliers’ participation in collaborative product development. Jing et al. [4] constructed a task allocation bi-level programming model for suppliers’ involvement in product collaborative development. In a comprehensive consideration of product quality, cost, information, and other factors of suppliers, Hou et al. [3] constructed a design task allocation optimization model for interfirm product collaborative development. Most of the above-mentioned literatures constructed task allocation models and introduced corresponding algorithms based on the analysis of the goals of task allocation, whereas the number of researches and discussions related to the relationship between personnel and tasks to optimize the task allocation process is relatively small. However, in the current mode, where customers and suppliers collaboratively participate in customized product development, the fitness of suppliers to the development tasks and the coordination efficiency between suppliers and other factors greatly influence customized product task allocation. Therefore, fitness and coordination efficiency in the customized product development model are very important in task allocation optimization research.

Based on the analysis of related research results of domestic and international task allocation, this article introduces the definitions and calculation methods of task fitness and task coordination efficiency. Based on these, a multiobjective optimization mathematical model of customized product task allocation is constructed. Finally, an adaptive genetic algorithm (AGA) for solving the model is proposed.

The rest of this article is organized as follows. The process and task allocation strategy of collaborative customized product development is analyzed in Section 2. The task allocation mathematics model in collaborative customized product development is established in Section 3. The multiobjective optimization algorithm for task allocation in collaborative customized product development is proposed in Section 4. In Section 5, a 5-MW wind turbine R&D project example is introduced to verify the feasibility and the efficiency of the task allocation algorithm. Finally, Section 6 concludes the paper.

2 Analysis of Collaborative Customized Product Development Process and Task Allocation Strategy

2.1 Analysis of Collaborative Customized Product Development Process

With the increasing degree of product customization, the scope and degree of collaboration among enterprises, suppliers, and the customers is also increasing. An increasing number of enterprises, suppliers, and customers participate in the customized product development design process of core enterprises, relying on customized product collaborative design platform and making full use of all kinds of customized product collaborative tools such as custom products integrated visualization, customized process information communication collaboration, information integration and conflict resolution technology, sharing server, customized system knowledge base, etc. to analyze and map customer needs and perform scientific decomposition and reasonable allocation for customized product parts design tasks, ultimately completing the customized product design [16], which is shown in Figure 1.

Figure 1

Collaborative Customized Product Development Process.

Figure 1 shows that the relationship among suppliers, customers, and enterprises who participate in the collaborative customized product development chain is no longer the simple cooperative relationship of the material supply type or the supply-and-demand relations type. They are fully involved in the whole product development and designing phase. The collaborative relationship between them changes due to different task decomposition and allocation results.

3 Establishment of Task Allocation Mathematics Model in Collaborative Customized Product Development

3.1 Description of the Problem

Suppose a product customization development project can be decomposed into n design subtasks, namely T = {T₁, … , T_n}, and it needs to select corresponding suppliers from l sets of suppliers with the enterprise’s development team and customers to finish the subtasks collaboratively. The l sets can be represented as P₁, … , P_i, … , P_l, and the numbers of the suppliers contained in each set are k₁, … , k_i, … , k_l, respectively, and the suppliers in set i can be represented as the set P_i = {P_i1, … , P_iki}. The n design subtasks are allocated to the most suitable suppliers selected from the suppliers, the enterprise’s own development team, and the customers to finish collaboratively. The allocation relationship can be shown by the following mapping diagram in Figure 2.

Figure 2

The Mapping Relationship Diagram of Product Customization Development Task Allocation.

4 Multiobjective Optimization Algorithm of Task Allocation in Collaborative Customized Product Development

Task allocation in collaborative customized product development is a multiobjective combinatorial optimization NP-hard problem. It is difficult to obtain the optimal results quickly by traditional methods. Genetic algorithm is a kind of search optimization algorithm simulating the process of biological evolution. It has a strong global searching capability, but with a poor partial searching capability, and it is easy to fall into local optimum and lead to the premature phenomenon [6]. In view of the limitation of the nonlinear multiobjective combinatorial optimization characteristic of collaborative customized product development mathematical model, AGA is chosen to solve the task allocation model of collaborative customized product development.

The specific descriptions of the AGA operation process follow.

4.1 Coding and Decoding

Here, the binary coding method is adopted. The length of each chromosome is m + n. Each chromosome is divided into n gene segments, and each gene segment represents a task. All suppliers that can finish customization task i are ranged in a sequence according to serial number sequence of supplier sets. Assume that there are m_i suppliers, the number of optional allocated objects for customization task i is m_i + 1, and the first represents the enterprise itself. The sum of all suppliers that can complete n customized tasks is m, namely In chromosome coding, a gene value of 0 means that the corresponding task of the gene segment is not allocated to the supplier or the enterprise itself. A gene value of 1 means the task that is assigned to this supplier or enterprise itself. In addition, the chromosome can be decoded according to the chromosome coding method.

A feasible chromosome coding schemes is shown in Figure 3. In this coding scheme, task 1 represents allocation to the first supplier of supplier set 1. Its gene value is 1, and the values of the rest of the genes are 0. For the same reason, task n is allocated to the second supplier of supplier set m.

Figure 3

A feasible Chromosome Coding Scheme.

5 Case Study

Take a customized development design project of 5-MW variable-speed, constant-frequency wind turbine generator in a wind power generation company as an example to apply the product customization collaborative development task allocation optimization algorithm proposed above.

The collaborative development project of 5-MW wind turbine can be divided into 10 subtasks, namely, A, spindle design; B, yaw system design; C, gear box design; D, transmission chain system design; E, electrical system design; F, generator set system design; G, control cabinet system design; H, cabin design; I, pitch system design; G, wheel design. According to the task allocation algorithm proposed in this article, the 10 subtasks are allocated.

Tasks A, B, C, D, E, F, G, H, I, and J can be allocated to suppliers set P₁, P₂, P₃, P₄, P₅, P₆, P₇, P₈, P₉, P₁₀, respectively. The numbers of suppliers contained in each set are 4, 2, 5, 3, 3, 3, 2, 3, 2, and 2, respectively. Among these, task E can also be designed by the enterprise itself. Let the enterprise itself be the first one in set P₅. The first supplier in P₁ can simultaneously participate in tasks A and C; thus, the supplier is also included in set P₃ as its first supplier. The first supplier in P₄ can simultaneously participate in tasks D and E; thus, the supplier is also included in set P₅ as its second supplier. The first supplier in P₆ can simultaneously participate in tasks F and G; thus, the supplier is also included in set P₇ as its first supplier. Ten tasks (A–J) are allocated to 29 suppliers and the enterprise itself.

Here, all the suppliers and enterprise itself are arranged in a sequence according to the serial number of design tasks. According to the definition of task fitness, the geographical factor vector formed by d(i, j) can be obtained as follows:

d = [2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1].

The ability factor vector formed by b_ij is

b = [0.2, 0.4, 0.2, 0.4, 0.6, 0.8, 0.4, 0.6, 0.8, 0.6, 0.2, 0.6, 0.4, 0.6, 0.8, 0.4, 0.6, 0.4, 0.4, 0.6, 0.8, 0.4, 0.6, 0.2, 0.6, 0.8, 0.8, 0.6, 0.4, 0.6].

The equipment factor vector formed by p(i, j) is

p = [2, 3, 2, 1, 2, 1, 1, 2, 2, 3, 1, 1, 2, 2, 3, 1, 2, 2, 2, 1, 3, 2, 3, 1, 2, 1, 3, 1, 1, 2].

The interest factor vector formed by c_ij is

c = [0.6, 0.7, 0.6, 0.8, 0.6, 0.5, 0.8, 0.6, 0.5, 0.3, 0.7, 0.6, 0.6, 0.8, 0.8, 0.6, 0.7, 0.6, 0.5, 0.3, 0.6, 0.4, 0.5, 0.6, 0.8, 0.7, 0.2, 0.3, 0.5, 0.6].

Setting α = 0.2, β = 0.4. δ = 0.2, ε = 0.2, the fitness vector can be obtained as follows:

F = [1, 1.1, 1, 0.72, 0.96, 1.02, 0.92, 0.96, 1.02, 1.1, 0.62, 0.96, 0.88, 1.2, 1.48, 0.68, 1.18, 1.08, 1.06, 0.9, 1.24, 0.84, 1.34, 0.6, 1.2, 0.86, 1.36, 0.7, 0.66, 0.96].

The task execution time of 29 suppliers and the enterprise itself can be expressed with vector as follows:

t = [215, 210, 200, 220, 160, 140, 360, 345, 350, 355, 360, 200, 180, 210, 262, 270, 268, 156, 220, 216, 210, 180, 196, 160, 146, 180, 160, 172, 130, 120].

The cost per unit time can be expressed with vector as follows:

e = [2.1, 3.3, 2.6, 1.4, 2.2, 1.9, 3, 2.8, 2.9, 3.6, 3.2, 2.4, 3.1, 2.6, 3, 3.2, 3.2, 2.8, 1.8, 1.6, 2.2, 2.2, 2.4, 2.3, 2.3, 1.9, 3.2, 2.6, 2.3, 2.4].

The relative quality can be expressed with vector as follows:

q = [0.5, 0.6, 0.7, 0.8, 0.5, 0.6, 0.3, 0.4, 0.6, 0.8, 0.7, 0.65, 0.72, 0.56, 0.8, 0.7, 0.64, 0.53, 0.6, 0.42, 0.46, 0.6, 0.8, 0.6, 0.4, 0.2, 0.6, 0.4, 0.5, 0.8].

According to the definition of task coordination efficiency, the task coordination efficiency matrix can be obtained:

The matrix is a symmetric matrix, and the diagonal elements are zero. For example, s₁₂ represents the coordination efficiency between four candidate suppliers of task A and 2 candidate suppliers of task B, and it is a 49×2 matrix as follows:

The rest of the elements are similar. Although there are matrix elements, because of space limitations, only s₁₂ is listed above. The rest of the data is listed in the task coordination efficiency matrix as follows:

The delivery time constraint is 2100, the cost constraint is 5500, and the quality constraint is 6.5, namely,

∑t ≤ 2100; ∑c ≤ 5500; ∑q ≥ 6.5.

According to the literatures [5], the population size directly affects the convergence of the algorithm and computational efficiency. If the population size is too small, it is easy to converge to a local optimal solution. If the population size is too large, the calculation speed will be reduced. The general population size is often set to 10–200, according to the actual situation. The crossover probability controls the use frequency of the crossover operation. A greater crossover probability can enable future generations to fully cross, whereas a small crossover probability may cause the evolutionary speed to relatively slow down. The generally recommended value of the crossover probability is set to 0.4–0.99. The mutation probability controls the mutation operation. If the mutation probability is too small, it is easy to lead to premature convergence. If the mutation probability becomes larger, it will enable the solution that jumped out from the local extreme point to obtain the global optimal solution. The mutation probability is set to 0.0001–0.1. Here, set the initial population size as 50, the maximum number of iteration as 500, M = 100, P_{c max} = 0.45, P_{c min} = 0.25, P_{m max} = 0.004, and P_{m min} = 0.002; weights of the two objective functions are w₁ = 0.5 and w₂ = 0.5, respectively, and the ideal point consists of two single-goal optimal function values (12.00, 34.19). Use Matlab R2010a for programming calculation. Obtain the chromosome coding of the optimum scheme 1000 10 01000 001 1000 100 01 010 10 10, with the best fitness value of 99.9145, distance between the corresponding optimal objective function value point and ideal point of 0.0755, and the following chromosome coding: task A is assigned to the first supplier in supplier set P₁, task B is assigned to the first supplier in supplier set P₂, task C is assigned to the second supplier in supplier set P₃, task D is assigned to the third supplier in supplier set P₄, task E is assigned to the enterprise itself, task F is assigned to the first supplier in supplier set P₆, task G is assigned to the second supplier in supplier set P₇, task H is assigned to the second supplier in supplier set P₈, task I is assigned to the first supplier in supplier set P₉, and task J is assigned to the first supplier in supplier set P₁₀.

Because of the relative fuzzy grasp on the customization demands of the electrical system of the owners, task E should be completed with the owner’s collaboration. To sum up, the final optimal allocation results of all design tasks of 5-MW wind turbine product are shown in Figure 4.

Figure 4

The Final Optimal Allocation Results of Design Tasks of 5-MW Wind Turbine Products.

Under the circumstances that the population size and the maximum number of iterations are equal, AGA, PSO, and SGA are used for solving the problem, respectively. The parameters of PSO were set as follows according to the literatures [14]: set the initial inertia weight as 0.9 and the acceleration coefficient as c₁ = c₂ = 2. The results are shown in Figure 5. Run independently 50 times, and the best statistical results are shown in Table 2.

Figure 5

The Operation Results of AGA, PSO, and SGA.

Figure 5 and Table 2 show that AGA converges to the optimal solution after 131 generations, PSO converges to the optimal solution after 153 generations, and SGA converges to the optimal solution after 302 generations. When run on the computer with a dual-core I5-430M CPU, basic frequency of 2.27 GHZ, and 1 GB of memory, the time obtained is 17.61 s for AGA, 21.33 s for PSO, and 35.43 s for SGA.

Thus, it can be seen that AGA converges faster than PSO and SGA, has a greater stability, and has a shorter the running time. Moreover, the optimal value found by AGA is better than those by PSO and SGA. When solving task assignment problems, AGA is superior to PSO and SGA.

When the crossover probability, mutation probability, and other parameters remain the same, the population size was set to 50, 100, and 200. The results are shown in Table 3.

Figures 6–8 and Table 3 show that the larger the population size, the quicker the AGA algorithm converges and the shorter the time needed to find the optimal solution. The number of iterations needed to achieve the optimal solution also decreases.

Figure 6

The Convergence Curve when the Population Size is Set to 50.

Figure 7

The Convergence Curve when the Population Size is Set to 100.

Figure 8

The Convergence Curve when the Population Size is Set to 200.

When the population size, mutation probability, and other parameters remain the same, the maximum and minimum crossover probability was set to (0.4, 0.2), (0.6, 0.4), and (0.8, 0.6). The results are shown in Table 4.

Figures 9–11 and Table 4 show that with the crossover probability increases, the convergence rate increases and the global optimization capability increases. In addition, it can obtain the optimal solution in a shorter time.

Figure 9

The Convergence Curve when the Crossover Probability is Set to (0.4, 0.2).

Figure 10

The Convergence Curve when the Crossover Probability is Set to (0.6, 0.4).

Figure 11

The Convergence Curve when the Crossover Probability is Set to (0.8, 0.6). The Results are Shown in Table 4.

When the population size, crossover probability, and other parameters remain the same, the maximum and minimum mutation probability was set to (0.004, 0.002), (0.006, 0.004), and (0.008, 0.006). The results are shown in Table 5.

Figures 12–14 and Table 5 show that with the mutation probability increases, the convergence enhances and the local searching ability increases. The time required to achieve the optimal solution decreases. It can approximate the optimal value faster.

Figure 12

The Convergence Curve when the Mutation Probability is Set to (0.004, 0.002).

Figure 13

The Convergence Curve when the Mutation Probability is Set to (0.006, 0.004).

Figure 14

The Convergence Curve when the Mutation Probability is Set to (0.008, 0.006).

6 Conclusion

Problem of task allocation in collaborative customized product development was studied based on artificial intelligence technology. Theoretical guidance was provided for optimizing the allocation of development resources, which shortens the product development cycle and improves the efficiency of product collaborative design. The main contributions of this article as the following:

1. The definitions and calculation methods of task fitness and task coordination efficiency were given, and a multiobjective optimization mathematical model of collaborative customized product development task allocation was constructed.

2. The AGA for solving the model was introduced, and a new solution for collaborative customized product development task allocation optimization problems was provided.

3. A 5-MW wind turbine product development project of a wind power generation company was used as an example. The results verified the feasibility and the effectiveness of AGAs in solving task allocation optimization problems compared with methods such as SGA.

Task allocation in a collaborative customized product development process is a complex problem. There are many factors that influence task allocation, and there are relatively more algorithms. In this article, only two dimensions of fitness and coordination efficiency of cooperative tasks are studied. The factors considered are relatively few, and they need to be further studied and expounded. Further enriching and improving the objective function and the constraints and its algorithm of task allocation will be the next research focus.