A Novel Forecasting Model Based on Support

International Journal of Information Technology & Decision Making Vol. 13 (2014) c World Scienti¯c Publishing Company ° DOI: 10.1142/S0219622014500849

A Novel Forecasting Model Based on Support Vector Regression and Bat Meta-Heuristic (Bat–SVR): Case Study in Printed Circuit Board Industry

Int. J. Info. Tech. Dec. Mak. Downloaded from www.worldscientific.com by UNIVERSIDADE DE BRASILIA on 11/25/14. For personal use only.

Amirmohammad Tavakkoli Department of Information Technology Engineering Faculty of Technology and Engineering, University of Qom, Qom, Iran [email protected]

Jalal Rezaeenour* and Esmaeil Hadavandi† Department of Industrial Engineering Faculty of Technology and Engineering, University of Qom, Qom, Iran *[email protected] †[email protected] Published 17 November 2014 Sales forecasting is very bene¯cial to most businesses. A successful business needs accurate sales forecasting to understand the market and sales trends. This paper presents a novel sales forecasting model by integrating support vector regression (SVR) and bat algorithm (BA). Since the accuracy of SVR forecasting mainly depends on SVR parameters, we use BA for tuning these parameters because Bat is a newly introduced algorithm and has many parameters. In order to ¯nd the best set of BA parameters Taguchi method was utilized. We validated our model on four known UCI datasets. Then we applied our model in printed circuit board (PCB) sales forecasting case study. We compared the accuracy of the proposed model with Genetic algorithm (GA)–SVR, particle swarm optimization (PSO)–SVR, and classic-SVR. The experimental results show that the proposed model outperforms the others. To ensure the robustness of our proposed model, sensitivity analysis was also done using our model to ¯nd out the e®ects of dependent variables values on sales time series. Keywords: Forecasting; support vector regression; Bat meta-heuristic; data mining.

1. Introduction and Literature Review In commercial decision making, planning and controlling are critical. Forecasting, as a basis of planning and controlling, attempts to calculate and predict the future trends and is vital for the planning and operation of an industry. Managers use the information provided by forecasting to make the strategic decisions and comprehend many kinds of plans.1,2 Over the past years, sales forecasting has been a very helpful tool for companies in a highly competitive and dynamic business environment. An accurate sales

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A. Tavakkoli, J. Rezaeenour & E. Hadavandi

forecasting can help a company to improve its business. It increases the e®ectiveness of business programs such as inventory management, advertisement, supply chain management and so on.3 Sales forecasting o®ers quantitative information that is useful for company competitive strategy. Decreasing uncertainly and providing inputs for the future decisions are the goals of the sales forecasting systems. Inaccurate sales forecast could make wrong business decisions.4,5 Researchers have listed six important applications of sales forecasting as follows: personnel planning, marketing planning, ¯nancial planning, sales quota planning, production, and inventory planning.6 Sales forecasting is a key factor to integrate management. It can be very helpful for the management to apply the marketing management approach.7 Sales forecasting is one of the necessary tools for marketing planning. E®ective deployment of resources highly depends on sales forecasting data. It a®ects almost every other forecasting of business operations. Sales forecasting is used in determining various conditions of management decisions and operations.7 Sales forecasting is also very useful in marketing management support systems (MMSS). MMSS were de¯ned as follows \Any device combining (A) information technology, (B) analytical capabilities, (C) marketing data, and (D) marketing knowledge, made available to one or more marketing decision maker(s) to improve the quality of marketing management".8 Accurate sales forecasting improves the outcome of business, because it helps in the function of a company, such as sales and marketing, production and ¯nance to develop the programs more e®ectively.9 In real cases, sales data contain seasonal patterns and/or trend patterns. The failure to account for these patterns may result in poor forecasts. Therefore, it is very important to justify these patterns. Nevertheless, how to improve the quality of forecasts is still an outstanding question.10 A sales forecasting model forecasts the future sales based on the past sales information. Since sales data often is nonlinear and noisy, researchers have used arti¯cial intelligence models instead of the traditional methods.11 It is well known that arti¯cial intelligence models are more °exible and can estimate nonlinear relationship.12–16 Many researches combined various arti¯cial intelligence (AI) techniques such as genetic algorithm (GA), fuzzy logic, arti¯cial neural networks (ANN) and so onto build hybrid intelligent models for forecasting the problem17–19 and build decision support systems.11,20 Hadavandi et al.52 integrate genetic fuzzy system and data clustering to build the hybrid sales forecasting problem. They grouped data records into clusters and built independent model for each cluster. They tested their system on real case and concluding results were better than the previous works.9 A study combined self-organizing map (SOM) fuzzy rule and built a forecasting model. They used SOM for classifying the independent variables of sales. The comparison of their model with other approaches was shown in a simulation.21


A Novel Bat Inspired Support Vector Regression

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Thomassey and Fiordaliso presented a hybrid model based on clustering and decision trees and evaluated the performance of their model on French textile distributor case.22 Chang et al. utilized a hybrid model to forecast the future sales. Their hybrid model was based on k-means and fuzzy neural network. They classi¯ed the data into clusters and their results showed improvements compared to the other approaches.23 Recently many researches tend to use support vector regression (SVR)24 for forecasting problems.25,26 SVR is a version of support vector machines (SVM) for regression. Since the parameters of SVR mainly a®ect the performance of SVR and there is no scienti¯c method for setting the parameters of SVR, di®erent researches have used various approaches for setting these parameters.27,28 Most of the mentioned researches set the parameters of SVR manually and some use nature-inspired general algorithms such as GA for setting these parameters.29 For example, in one research, GA has been used to set SVR parameters and the proposed model (GA–SVR) was used to predict cars sales.30 Hong et al. utilize chaotic genetic algorithm (CGA) for parameter determination of SVR model. CGA is a combination of chaotic optimization algorithm with GA. In another research, they used the same model for forecasting the cyclic electric load.31 SVR with GA is superior to the other competitive forecasting models (Autoregressive Integrated Moving Average (ARIMA) and Arti¯cial Neural Network (ANN)). However, it has some drawbacks for ¯nding the global optimum and often gets trapped in local optimums.32,33 Bat algorithm (BA) developed by Yang,34 is a very promising algorithm which uses a good combination of other meta-heuristics. Experiences showed that it is much superior to particle swarm optimization (PSO) and GA and simulated annealing.34 With the best of our knowledge, there is not any research in literature that uses BA for tuning the parameters of SVR. So there is a research gap for using BA in setting SVR parameters and evaluate its results. We take these clues to reach a conclusion and develop a new hybrid intelligent model (Bat–SVR) by a combination of BA and SVR. BA is used for setting the parameters of SVR. The comparison is done among the proposed Bat–SVR method and the existing methods such as GA–SVR, PSO–SVR, Scatter-SVR and classicSVR in two steps. At ¯rst, we use four well-known UCI35 datasets for forecasting problems: \Abalone",36 \Auto mpg",37 \airfoil self-noise",38 and \Energy e±ciency".39 Then we test the capability of the proposed method by applying it to a sales forecasting case study called \printed circuit board (PCB) industry in Taiwan" which has been frequently used by the other authors as a case.40 In order to determine the e®ects of some variables on sales and to ensure the robustness of the proposed model, a sensitivity analysis is performed using our forecasting model. 2. Methodology The forecasting accuracy of SVR model depends on the values of SVR hyper parameters ðC ; "Þ and kernel parameters ðd; Þ. For example, if C is very large, then the

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A. Tavakkoli, J. Rezaeenour & E. Hadavandi

only objective will be minimize the empirical risk. Larger " will cause fewer numbers of support vectors. There is no general method for setting a set of SVR parameters. As mentioned in Sec. 1, in order to set SVR parameters more accurately, our model utilizes the bene¯ts of BA. Therefore, Secs. 2.1 and 2.2 brie°y review SVR and BA concepts and the Sec. 2.3 introduced new Bat–SVR model.


2.1. Support vector regression One of the important machine learning methods is SVM. In statistics perspective SVM tries to minimize the structural risk.41 Two categories of SVM applications have been introduced: support vector classi¯cation (SVC) and SVR.42 When SVM has been used in regression case, it is named SVR.24 Consider training data elements: S ¼ fðX 1 ; Y 1 Þ; ðX 2 ; Y 2 Þ; . . . ; ðX n ; Y n Þg;

ð2:1Þ

where S