J. Cent. South Univ. (2012) 19: 527−536 DOI: 10.1007/s11771−012−1036−z
Multidisciplinary design optimization for air-condition production system based on multi-agent technique YANG Hai-dong(杨海东)1, E Jia-qiang(鄂加强)2, QU Ting(屈挺)1 1. Department of Mechatronics Engineering, Guangdong University of Technology, Guangzhou 510006, China; 2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China © Central South University Press and Springer-Verlag Berlin Heidelberg 2012 Abstract: In order to guarantee the overall production performance of the multiple departments in an air-condition production industry, multidisciplinary design optimization model for production system is established based on the multi-agent technology. Local operation models for departments of plan, marketing, sales, purchasing, as well as production and warehouse are formulated into individual agents, and their respective local objectives are collectively formulated into a multi-objective optimization problem. Considering the coupling effects among the correlated agents, the optimization process is carried out based on self-adaptive chaos immune optimization algorithm with mutative scale. The numerical results indicate that the proposed multi-agent optimization model truly reflects the actual situations of the air-condition production system. The proposed multi-agent based multidisciplinary design optimization method can help companies enhance their income ratio and profit by about 33% and 36%, respectively, and reduce the total cost by about 1.8%. Key words: multi-agent system; production operation; multidisciplinary optimization; self-adaptive chaos optimization; immune optimization algorithm
1 Introduction Intensified competition among enterprises has, to a large extent, led to the expansion of production scale as well as applications of new production equipments and control systems. It not only makes the enterprises discrete, uncertain, dynamic and complex, but also makes the enterprise manufacturing process decentralized and heterogeneous, which has brought certain difficulties for the production operation. Thus, the enterprise production modeling and simulation techniques have gradually attracted the attention of enterprise operators and academic researchers [1]. The simulation blocks in traditional simulation method [2] lack initiative and autonomy and the department level blocks also lack responsibility for the whole model system in the processing of air-condition enterprises operation system. However, in practice, each part of the air-condition enterprise is intelligent, and they can analyze the internal and external information and make decisions accordingly. Such cooperation capability of departments is based on the collaboration of each department, as well as the comprehensive analysis of their own information and decision-making. When the
traditional simulation methods are applied to intelligent air-condition enterprises, they only consider operation process, the logistics and information flow of the enterprise, and do not take the changes of market and the cash flow impacting on business operations into account. Hence, the traditional simulation methods are certainly not suitable for applications in task allocation, decomposition, production planning and scheduling, as well as resource planning in the production process of the air-condition enterprises. Since distributed artificial intelligent agents can run independently under certain environments, they have their own attributes, behaviors, goals and knowledge, as well as their characteristics in initiative, intelligence, responsiveness, interaction, etc. Therefore, the multi-agent technique is attractive simulation tool for the enterprise production systems [3−7]. In the modern management of production systems, it is necessary to take information like logistics, information flow and fund flow, into account. The organization of enterprise becomes more and more complex, and the operation process becomes more and more complicated. Therefore, it is necessary for the optimization modeling of enterprise production system to be systematic and general. With the rapid improvement
Foundation item: Project(60973132) supported by the National Natural Science Foundation of China; Project(2010B050400005) supported by the Science and Research Program of Guangdong Province, China Received date: 2010−11−29; Accepted date: 2011−04−18 Corresponding author: YANG Hai-dong, Professor, PhD; Tel: +86−13926036043; E-mail:
[email protected]
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of computer performance, the increasing complexity of the enterprise production system and higher demands for the properties of products, a new method for modeling and optimization of enterprise production operation system (POS) is proposed based on the multidisciplinary design optimization (MDO) [8−10] recently.
2 MDO for POS in air-condition enterprise 2.1 POS model for air-condition enterprise The production operation process of modern air-condition enterprises emphasizes the collaboration between internal functional departments and external environments. Each department is responsible for making its own decision according to different information, and the production operation tasks will be completed through the collaboration of all related departments. As depicted in Fig. 1, the order fulfillment is taken as the essential objective in the production operation process. The production plan is made mainly based on the sales forecast. The production plan department is responsible for coordinating the production resources and arranging the production activities in aircondition enterprises. The inventory department is responsible for managing raw materials and ultimate products in air-condition enterprises. The procurement department organizes procurement based on business needs of the air-condition enterprise, but the actual procurement is determined by the market fluctuation.
Fig. 1 Model of air-condition enterprise production operation
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The production department carries out ordered products according to the production plans. 2.2 Simulation model based on multi-agent As shown in Fig. 2, by combining the model of air-condition enterprise production operation system shown in Fig. 1 and the multi-agent technology, knowledge on enterprise production operation can be fed to the production plan agent, marketing agent and procurement agent. The necessary external environment for the production planning agent, sales agent and procurement agent is created by the production server, inventory server, sales server and financial server. Each individual functional department mentioned above should possess certain properties and characteristics of realizing the operation of air-condition enterprise department and can respond accordingly to different decisions made by production plan agent, marketing agent and procurement agent. High-level strategies for the operations of production planning agent, sales agent and procurement agent are achieved by reasoning and decision-making based on necessary information in the simulation system. 1) The production planning agent makes the production plan based on the demand information forecast by the sales agent, under the consideration of the current raw materials and production capability levels of enterprise and other information. 2) The sales agent forecasts the demands of
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Fig. 2 Simulation model of enterprise production operation based on multi-agent technique
air-conditioners based on the historical demand data and the market trends. When receiving the actual demands of air-conditioners, it notifies the warehouses to deliver air-conditioners. 3) The procurement agent firstly evaluates the suppliers with the fuzzy analytic hierarchy process (AHP) method, selecting those of good performance and negotiating the order details. After receiving the supplied raw materials, the procurement agent conducts a quality test and then records the performance of the suppliers to the knowledge base for future evaluation. 4) The inventory server records the changes of raw material and ultimate product inventory. It responds to the queries of the production planning agent about current raw material and the queries of the sales agent about current ultimate product. 5) The production server arranges the raw materials and production capacities for production according to the production plan. During the production process, it records the real-time production capacity information of the enterprise. After the complement of production, the occupied production capacity is set free, and the air-conditioners are sent to warehouses. All the material transaction processes will be recorded. 6) The finance server records the income and cost information of the enterprise, estimates the profits to facilitate the decision-making for the managers. 7) The market server provides external environment for the operation of the system: 1) Describing market conditions of raw materials, and providing the raw material demands according to the market changes; 2) Describing the actual air-conditioner demand information. 2.3 MDO for air-condition POS Multidisciplinary design optimization (MDO) is a
methodology to design complex system and sub-system through exploring and using the interactional synergistic mechanism in system. The main idea of MDO for the production operation system (POS) is to integrate the multidisciplinary knowledge through the whole process of the complex system design. The air-condition enterprise POS is designed and optimized based on the multi-agent technique and utilization of effective design, optimization strategies and distributed computer network system. The optimum design results of the air-condition enterprise POS are obtained by making use of synergistic effect generated by interaction among subjects (sub-systems). The MDO framework of the air-conditioner enterprise POS is shown in Fig. 3. The MDO is carried out on three levels of the air-condition enterprise POS: system level, interaction level (information flow, logistics and cash flow) and department level (production capacity management, sales management, production planning management, production management, finance management, inventory management and procurement management). The objective function of global optimization for air-condition enterprise POS is to minimize the overall production cost, and to maximize the profits of the POS. Meanwhile, it distributes indicators to the interaction level under the constrained conditions that the indicators of the system level are same to those of the component level. It takes the minimization on the difference between indicators of distribution of optimization design for the component level and that of the system level as the objective function of the component level optimization design, and it distributes indicators to its own departments under the constrained conditions of the component level. By adjusting the geometric structure size of component, it causes constrained condition of each
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Fig. 3 Grading structure of multidisciplinary optimization design
subject in the department level to be met. Through the above three-level optimization, coordination is achieved among the departments and enterprise. In other words, the complex coupling relationships among the departments and enterprise are decomposed through the consistency constraints, and the comprehensive optimum design scheme would be found through it. In the above process, if an upper-level system contains too many lower-level systems, one or more intermediate levels could be added if necessary. For example, a unit level optimization can be added between the interaction level and department level. 2.4 MDO model of air-condition enterprise POS Based on the above-mentioned MDO framework, the process of the multidisciplinary design optimization on air-condition enterprise production operation system is designed and depicted in Fig. 4, including the production planning agent, sales agent, procurement agent, production server, inventory server, market server and financial server of the POS. The problem of the MDO on POS can be expressed as a mathematical programming optimization problem: min f(X, Y, Z)
(1)
s.t. gi(X, Y, Z)≤0 (i=1, 2, …, n) where f(X, Y, Z) is the objective function. f(X, Y, Z)=W1f1(X, Y, Z)/f10(X, Y, Z)+ W2f2(X, Y, Z)/f20(X, Y, Z)+W3f3(X, Y, Z)/ f30(X, Y, Z)+W4 f4(X, Y, Z)f40(X, Y, Z)+ W5f5(X, Y, Z)/f50(X, Y, Z)+W6f6(X, Y, Z)/ f60(X, Y, Z)+W7 f7(X, Y, Z)/f70(X, Y, Z) where f1(X, Y, Z) is the objective function of production planning agent, f2(X, Y, Z) is the objective function of sales agent, f3(X, Y, Z) is the objective function of procurement agent, f4(X, Y, Z) is the objective function of production server, f5(X, Y, Z) is the objective function
Fig. 4 MDO process of air-condition enterprise production operation system
of inventory server, f6(X, Y, Z) is the objective function of market server, f7(X, Y, Z) is the objective function of financial server; f10(X, Y, Z) to f70(X, Y, Z) are the initial values before MDO of production planning agent, sales agent, procurement agent, production server, inventory server, market server, financial server respectively; W1, W2, W3, W4, W5, W6 and W7 are the weighted coefficients of the objective functions of the production planning agent, the sales agent, the procurement agent, the production server, the inventory server, the market server and the financial server in the total objective planning, respectively, and W1+W2+W3+W4+W5+W6+W7=1; X=(X1, X2, …, Xi, …, XI)T, is the information flow variable; Y=(Y1, Y2, …, Yj, …, YJ)T is the logistics variable；Z=(Z1, Z2, …, Zk, …, ZK)T is the cash flow variable; gi(X, Y, Z) is the constrained condition.
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2.5
Self-adaptive chaos immune optimization algorithm with mutative scale 2.5.1 Selection of chaos model It has been proven in Ref. [11] that the one-dimensional self-mapping described in Eq. (2) has infinite folds. It has infinite fixed points and zero points in [−1, 1], and has more obvious chaos characteristics than the logistic model: xn 1 sin( 2 / xn ), n 0, 1, 2, 1 xn 1, xn 0
(2)
2.5.2 Parallel chaos immune clustering algorithm In the artificial immune algorithm, matching algorithm or evolution algorithm is used to accomplish data training and immune memory. Evolution algorithm has better performance than matching algorithm. The parallel chaos immune clustering algorithm in this work can be described as follows. Step 1: Input the antigen {g} and normalize it. Choose Eq. (1) as a chaos model, and randomly generate N initial antibodies {b} in interval (0, 1). Step 2: Operate on each antigen gi as follows: 1) Use Eq. (3) to calculate the appetency aij between antibody bi and antigen gi: aij
n
(bik g jk )2
(3)
k 1
2) Select m pieces of antibodies with the highest appetency as the network cells. 3) Operate cloning on the m pieces of selected network cells. The higher the appetency, the larger the cloning times, Nc. 4) Use equation C=C−α(C−X) to carry out mutation operation for the cloned cells, where C is the clonal antibody cell, X is the clonal antigen cell, and α is the mutation rate. 5) Re-calculate the appetency of C after mutation. 6) Select the best appetency, ξ, as the partial memory cell dataset Mp. 7) Use Eq. (4) to calculate the similarity sij between antibody bi and antibody bj and abandon the individual whose similarity sij is greater than the threshold value ss in Mp:
Suppose the better individuals are X=(X1, X2, …, Xk), the search interval of the chaos variable can be narrowed, and it can be described as ai X i (bi ai ) bi X i (bi ai )
(5)
where φ∈(0, 0.5), is the narrowing factor. To guarantee that the new interval is not out of bounds, the following steps are needed: if ai bi, then bi =bi. After reverted in the new interval [ ai , bi ], Xi is changed to Yi, which can be determined by Yi
X i ai bi ai
(6)
Use the linear combination of Yi and Xi, n+1 as a new chaos variable for a new search:
X i, n 1 (1 i )Yi i X i , n 1
(7)
where 0
