A Novel Back Propagation Neural Network Optimized by Rough Set and Particle Swarm Algorithm for Remanufacturing Service Provider Classification and Selection

Aiming at the problem that the high classification feature dimensionality of the back propagation neural network (BPNN) leads to slow convergence speed and the initial weight and threshold sensitivity of the BPNN lead to the problem of easy convergence to the local optimum. A novel BPNN optimized by rough set and particle swarm algorithm (RS-PSO-BPNN) for remanufacturing service provider classification and selection is proposed. First, the attribute reduction method of rough set theory is used to preprocess the classification features of remanufacturing service providers, redundant attributes are deleted from the decision table, and the input feature dimension is reduced; then the PSO algorithm is used to optimize the network Initial weight and threshold. Finally, the proposed method is used for the selection and optimization of remanufacturing service providers. The results show that the proposed RS-PSO-BPNN has higher classification accuracy and efficiency for the problem, which provides scientific decision supports for remanufacturing service provider selection.


Introduction
Remanufacturing is one of the effective strategies to improve the product life cycle and achieve sustainable production [1,2]. After the remanufacturing was proposed, it has attracted the attention of many countries all over the world and has developed rapidly [3]. The practice gives products of equal even better quality to conventional manufacturing for reduction up to 60% energy, 70% materials, 50% cost, 80% air pollution [4]. The remanufacturing industry represented by the United States, Japan and Europe has a history of more than 50 years and has formed a very mature remanufacturing industrial chain. China's '14th Five-Year' Circular Economy Development Plan also proposes to promote the high-quality development of the remanufacturing industry.
Different from traditional manufacturing, the remanufacturing process generally includes waste product recycling, cleaning, testing, disassembly, remanufacturing design, remanufacturing, re-sales and other activities, and each step is highly professional. Remanufacturers publish their remanufacturing capabilities, such as cleaning, disassembly, etc., to the remanufacturing service platform in the form of services. And remanufacturing demanders find suitable remanufacturers on the remanufacturing service platform according to their needs [5]. During the remanufacturing process, high-quality remanufacturing service providers are an important prerequisite for achieving green, efficient, and low-cost remanufacturing. Therefore, how to choose remanufacturing service providers scientifically and effectively is an important issue to remanufacturing demanders.
At present, there are more researches on traditional manufacturing supplier selection. The researches of supplier selection are mainly concentrated on the selection evaluation index system and evaluation method. Related researches on supplier evaluation index system include the 23 indexes of supplier selection [6], the three main principles [7] and so on. Supplier evaluation methods are mainly AHP [8], fuzzy c-means (FCM) [9], BPNN [10] etc. Yin analyzed the relationship of remanufacturing service and Quality of Service (QoS), as well as the characteristics of the existing common evaluation index of manufacturing service [11]. The current research mainly focuses on the selection of traditional manufacturing suppliers, and there are few researches on remanufacturing service providers.
Due to the big difference between remanufacturing and traditional manufacturing, the evaluation indicators and methods are also different. There are few studies on the selection of remanufacturing service providers. Therefore, this paper proposes a remanufacturing service provider classification and selection method based on RS-PSO-BPNN. Rough set (RS) is used to discover the core evaluation indexes of the remanufacturing service providers. The back propagation neural network (BPNN) is used to construct a remanufacturing service provider classification model so as to reduce the complexity in the traditional supplier selection procedures. Because the parameters of BPNN have a significant influence on results, and particle swarm optimization (PSO) is capable of quickly finding optimal solutions, PSO and BPNN have been integrated so that the convergence rate is improved and precision is relatively enhanced.

The remanufacturing service provider selection model based on RS-PSO-BPNN
The algorithm flow based on RS-PSO-BPNN for remanufacturing service provider selection is shown in Figure 1.  In this model, firstly, the rough set method is used to determine the evaluation indexes of the remanufacturing service provider, and the BPNN network structure is determined according to the indexes. Then, the initial weights and thresholds of BPNN are determined through the PSO algorithm. Finally, the neural network will be trained with sample data. When the training achieve the precision, we can use this BPNN to classify the remanufacturing service provider.

Construction of Evaluation Index System
Remanufacturing service provider evaluation index system is an important part of remanufacturing service provider selection. Whether index selection is appropriate, affects the remanufacturing service provider selection. Combined with remanufacturing industry enterprise and related research results. a two-level remanufacturing service provider evaluation index system is established, which includes 5 first-level indexes and 15 second-level indexes. The first level indexes are remanufacturing quality, remanufacturing price, company strength, greenness and service level. The second level indexes are remanufacturing grade, remanufacturing qualification ratio, remanufacturing price level, remanufacturing cost, asset capacity, technical level, enterprise credit, overall management level, qualification certification, Energy consumption, carbon emission, material utilization, timeliness of Service, service professional, service attitude, shown in Figure 2.

Reduction of evaluation indicators
Rough set is an effective method of data set reduction [12]. Rough set theory is proposed by Pawlak in 1982 [13]. Reducing the evaluation indicators of remanufacturing service providers through rough sets mainly includes the following steps [14].
Where [ ] R x represents equivalence class whose equivalence relation R contains element X.
Upper approximation set: Analyzing the set composed of all objects in U that definitely or possibility belong to the set X according to existed knowledge R, Where [ ] R x represents equivalence class whose equivalence relation R contains element X. The relationship between knowledge reduction and core: the intersection of ( )

Red P and reduction
set is equal to the core of P , namely: In one aspect, the core is the basic of the calculation of reduction. In another aspect, the core is the most important part of the knowledge base which cannot be deleted when knowledge reduction is conducted. Table. Decision table is a special kind of knowledge representation system. Setting

Classification and Selection based on improved BPNN
PSO is used to optimize BPNN's initial weight and thresholds. Use the weights and thresholds of BPNN as individuals of PSO, and use BPNN output error as fitness function value. When the iteration reaches the set number of times or the output error reaches the specified accuracy, BPNN gets the optimal weights and thresholds. PSO regards each individual as a particulate flying in a certain speed at the search space in D-dimensional search space. The speed is adjusted by its own experience and the , also known as best p . All particles in the population experienced the best index of the position is expressed by symbol g, which is also known as best g .The speed of partials is represented as ( ) 1 2 , , , For each generation, section Ddimensional (1 d D ≤ ≤ ) changes according to the equation (4, 5) [15].
Where w is Inertia weight, 1 c and 2 c are Constant acceleration, 1 rand and 2 rand are random functions in the range 0-1.The speed of particle Vi is limited by a maximum speed. If the current acceleration of speed makes particle faster than the maximum speed of the dimension, the speed for the dimension is limited to the maximum speed max V .

Data Discretization.
The values of decision table should be discrete data when rough set is used to process decision tables. In intelligent information processing, continuous data should be pre-treated and discretized, and converted to rough set theory identified data, from which useful information and knowledge is extracted. The above data is discretized, which is shown in Table 2.

Rule Extraction.
In the decision table, a total of 91 decision rules are obtained and one of the rule is shown as: C1(2) AND C2(2) AND C3(0) AND C4(0) AND C5(2) AND C7(1) AND C9(1) AND C13(1) => D1(2). The reduction attributes and decision rules obtained through the rough set will be used for determining the structure of BPNN.

PSO-BPNN Training and Testing
3.3.1. Determine the particle swarm dimension. Due to the individual particle swarm is made up of BPNN's weights and thresholds. Each weight or threshold is one dimension of the particle swarm, the BPNN structure should be decided first. According to the previous rough set reduction properties, the number of input layer node can be set as 9, the number of output layer node is 1 and hidden layer can be set according to inspired formula [16]: Where, i is the number of nodes in the hidden layer; n is the number of nodes in the input layer; m is the number of nodes in the output layer; a is a constant and 1 10 a < < .Here a is taken as 6 .Number of nodes in the hidden layer is calculated as 10.BPNN is identified as 9-10-1. So PSO dimension is D n *i i i * m m 111 = + + + =     Figure 6. The circle represents the real value, the cross represents the traditional BPNN test value, and the asterisk represents the PSO-BPNN test value. The classification accuracy of BPNN reaches 85.7%, and the classification accuracy of PSO-BPNN reaches 98.3%. The results show that PSO-BPNN has a higher classification accuracy, and the accuracy is greatly improved. At the same time, it also proves the effectiveness of the RS-PSO-BPNN method for the classification of remanufacturing service providers. Decision makers can choose better remanufacturing service providers based on the results

Conclusion
A remanufacturing service provider classification and selection method based on the rough set, particle swarm and BPNN is proposed in this paper. First of all, the evaluation index system of remanufacturing service suppliers is established according to the remanufacturing service process. Then, the rough set method is used to reduce the index system, and 9 core evaluation indexes are obtained, which reduces the difficulty of subsequent classification selection. Finally, in view of the slow convergence of BPNN training, the initial weight and threshold of BPNN are optimized by PSO, which effectively improves the training speed and classification accuracy of BPNN. The optimized BPNN can be trained in 69 iterations and the classification accuracy of the RS-PSO-BPNN method reaches 98.3%, which can provide effective decision support for the selection of remanufacturing service providers.