Research Article  Open Access
Linhui Li, Haiyang Huang, Jing Lian, Baozhen Yao, Yafu Zhou, Jing Chang, Ning’an Zheng, "Research of Ant Colony Optimized Adaptive Control Strategy for Hybrid Electric Vehicle", Mathematical Problems in Engineering, vol. 2014, Article ID 239130, 10 pages, 2014. https://doi.org/10.1155/2014/239130
Research of Ant Colony Optimized Adaptive Control Strategy for Hybrid Electric Vehicle
Abstract
Energy management control strategy of hybrid electric vehicle has a great influence on the vehicle fuel consumption with electric motors adding to the traditional vehicle power system. As vehicle real driving cycles seem to be uncertain, the dynamic driving cycles will have an impact on control strategy’s energysaving effect. In order to better adapt the dynamic driving cycles, control strategy should have the ability to recognize the realtime driving cycle and adaptively adjust to the corresponding offline optimal control parameters. In this paper, four types of representative driving cycles are constructed based on the actual vehicle operating data, and a fuzzy driving cycle recognition algorithm is proposed for online recognizing the type of actual driving cycle. Then, based on the equivalent fuel consumption minimization strategy, an ant colony optimization algorithm is utilized to search the optimal control parameters “charge and discharge equivalent factors” for each type of representative driving cycle. At last, the simulation experiments are conducted to verify the accuracy of the proposed fuzzy recognition algorithm and the validity of the designed control strategy optimization method.
1. Introduction
Combined with the feature of traditional gasoline vehicle and pure electric vehicle, hybrid electric vehicle (HEV) improves the fuel economy and emission performance while sustaining enough travel distance, and it has become an important development direction of automotive industry [1]. If the energy management control strategy of HEV can realize the reasonable distribution between the vehiclemounted multiple energy power sources, the fuel economy and emission would be improved, the lifetime of power battery would be extended, and the vehicle maintenance cost would be minimized under the requirement for vehicle dynamic performance [2, 3].
Early energy management control strategy of HEV includes rulebased strategies and optimizationbased strategies [4]. Most of them are usually based on the fixed control parameters that could not adapt the dynamic driving cycles [5–7]. The actual energy saving effect seems to be unsatisfactory. Later, researchers find that the fuel consumption and emissions are sensitive to the driving cycle variation, and they start to study driving cycle recognition and adaptive control strategies in two aspects. One is using global position system (GPS), car navigation system, car to car communication, and other approaches to acquire the future road and traffic information such as average vehicle speed, road grade, and turning radius and then obtain the approximate global optimal energy distribution principles through the dynamic programming or other optimization algorithms [8]. But this kind of method needs a complex hardware implementation, and the global optimization needs large calculating quantity which may lead to a poor realtime performance. There is difficulty in its popularization and application. Another aspect of research is utilizing pattern recognition technology to identify the current type of driving cycle, according to the vehicle state parameters in the past period of time, such as average speed, idle time, and maximum acceleration [9]. It is relatively easy to implement, and this research method is selected to develop the adaptive control strategy in this paper.
At present, the research on driving cycle recognition mainly contains neural network, support vector machine (SVM) and other predictive methods. Engström and Victor [10] proposed a statistical pattern recognition framework to analyze the collected vehicle operating data and utilized feedforward neural network to classify the actual driving cycle into four types which are highway, arterial road, suburban, and urban, respectively. But the neural networkbased method required a large number of suitable training samples to obtain a relatively accurate recognition result. Watanabe and Katsura [11] proposed an SVM driving cycle recognition method; it was suitable for the twoclass classification problem, but it was more difficult to solve the multiclass classification problems. Gong et al. [12] proposed an iterative Markov chain approach for generating velocity profiles, which represent the specific driving pattern well based on the comparison of the phase plot to the typical real driving cycle. In this paper, a fuzzy driving cycle recognition algorithm is proposed to lay the foundation for the control strategy’s adaptive adjustment.
The optimal control parameters in different types of driving cycles need to be determined after realizing the driving cycle recognition. The control parameters in present researches are mainly selected discretely according to the engineering experience, and then a relatively optimal solution is obtained through the simulating calculation; the parameter optimization result has the potential to be improved. Generally the optimization algorithm would be used to solve this kind of parameter optimization problem. As HEV is a strongly nonlinear complicated system, it takes a large amount of time for calculating the objective function according to the vehicle model; the optimization algorithm should have a fast convergence speed. Therefore, intelligent optimization algorithms such as genetic algorithm [13, 14], particle swarm optimization [15, 16], and simulated annealing algorithm [17] are introduced to solve such parameter optimization problem. In recent years, swarm intelligence algorithm did well in solving travelling salesman problem (TSP) and other NPcomplete problems [18–21], and it also has some applications in the field of optimal control research [22]. In this paper, utilizing the feature of automatic gain and accumulating the knowledge about searchspace, we introduce an ant optimization algorithm to solve the HEV optimal control parameters in each type of driving cycle.
The rest of the paper is structured as follows. In Section 2, four types of representative driving cycles are constructed based on the actual vehicle operating data and a fuzzy driving cycle recognition algorithm is proposed for online recognizing the type of actual driving cycle. Section 3 introduces basic equivalent fuel consumption minimization strategy and studies the offline control parameter optimization in different driving cycles based on the ant colony optimization method. Section 4 presents the simulation experiment results of the designed adaptive control strategy. Section 5 concludes the presented work.
2. Driving Cycle Classification and Recognition
To achieve the objective of making control strategy being able to adaptively adjust according to different types of driving cycles, the driving cycle classification and recognition should be implemented in advance. In this section, driving cycles are classified into four types and representative cycle for each type is built to reflect the geography and traffic features in different regions. Then, a fuzzy clustering center matrix and the corresponding relative membership degree function are defined to realize the driving cycle recognition.
2.1. Construction of Representative Driving Cycles
The classification and construction of four types of driving cycles are based on the independently developed remote data acquisition and monitoring system [23]; it has been operating for nearly five years, as shown in Figure 1. The original vehicle data are gathered from the hybrid electric buses on the Dalian Energy Efficient and New Energy Vehicle Demonstration Project. A large number of reliable vehicle realtime operating data are collected from the Controller Area Network (CAN) bus through vehicle mounted terminal. The data can be divided into four types according to the city structure features; they are stopngo to represent the traffic jam cycles in the downtown, urban to represent the low speed flow in urban areas, suburban to represent the medium speed flow, and rural to represent the high speed flow in rural areas.
The steps for constructing four types of representative driving cycles are as follows. First, the microtrips are divided from the original vehicle speed data (microtrips are defined as a small driving trip segment from a vehicle idle point to the next idle point), and the database of the microtrips can be obtained from the original speed statistic database. Second, the characteristic parameters of each separate microtrip are calculated; the principal components and the corresponding contribution rate of these characteristic parameters can be obtained by the principal component analysis. Thus the cluster analysis technique is able to classify the microtrips into four cluster centers easily by theses principal components, and the microtrips which are nearest to the cluster center are chosen to construct the representative driving cycles. At last, four types of representative driving cycles are obtained by the linear combination of these selected microtrips. The results of the constructed four representative cycles are shown in Figure 2.
2.2. Fuzzy Recognition of Driving Cycle
The driving cycle recognition is based on the statistic characteristic parameters of actual driving cycle [24]; the commonly used cycle characteristic parameters are as follows: cycle average speed, average driving speed, maximum speed, mean acceleration, mean deceleration, maximum acceleration, maximum deceleration, idle time, the percentage of idle time, number of stops, and so on. In this paper, average cycle speed , average driving speed , average deceleration , average acceleration , and percentage of idle time are selected as the characteristic parameters for fuzzy recognition of driving cycle.
The sample driving cycle segment characteristic vector need to be recognized is expressed as . Together with four groups of parameters of the typical driving cycle constructed in Section 2.1, the characteristic vector is assembled as a matrix to be identified:
As characteristic vector elements , , are different in physical dimensions, the matrix to be recognized should be normalized; the elements to be identified in the normalized matrix are expressed as , which are calculated as follows:
Five index characteristic values of the four representative driving cycles make up the clustering center of the driving cycle class. After normalization it can be expressed as standard fuzzy clustering center matrix in the fuzzy recognition:
As characteristic parameters have different impact in the process of driving cycle fuzzy recognition, different weights of characteristic parameters need to be considered. So a characteristic indicator weight vector is defined as which should satisfy the constraint conditions of . In this paper, the characteristic indicator weight vector is selected as .
After the initialization above, the relative membership degree of sample to the category is calculated as follows:
So the sample driving cycle segment is recognized as the driving cycle type which has the maximum relative membership degree .
3. Control Parameter Optimization Based on Ant Colony Algorithm
3.1. Basic Equivalent Fuel Consumption Minimization Strategy
The basic energy management control strategy to be optimized in this paper is ECMS. Its main idea is to multiply the battery electricity consumption by an equivalent factor and transfer this electric energy to an equivalent vehicle instantaneous fuel consumption. In every computing interval , the total equivalent fuel consumption to be calculated is the sum of drive motor’s electric equivalent fuel consumption and actual engine fuel consumption, which is shown as follows: where is the total equivalent fuel consumption mass flow, in kg/s, and is the actual engine fuel consumption mass flow which can be calculated as follows: where is the engine output power, is the engine working efficiency, and is the fuel low caloric value, in J/kg.
is battery’s electric equivalent fuel consumption mass flow; as the actual power consumption of battery is electricity, it should be converted to the equivalent fuel consumption through the following equations: where is the motor output power, when motor works as a generator it was a negative value; is the battery discharge efficiency; is the battery charge efficiency; is the motor drive efficiency; is the motor generating efficiency; is the discharge equivalent factor; is the charge equivalent factor.
In (5) the calculated battery equivalent fuel consumption is not related to the current battery State of Charge (SOC); the strategy cannot ensure the battery SOC maintaining around a nominal value and get an acceptable battery efficiency to preserve battery life. Therefore the motor equivalent fuel consumption needs to be penalized with a nonlinear function to control the fluctuation range of SOC and ensure the battery charge balance. Firstly, SOC value in every simple time needs to be normalized as follows:
where and are the battery SOC working range. To maintain the SOC balance, if the SOC is in a lower stage, penalty function should enlarge the motor equivalent fuel consumption to increase the cost of battery discharge and decrease the battery charge cost. Therefore the penalty function of SOC is selected as Sshape high order polynomials:
Finally, the basic equivalent fuel consumption minimization control strategy can be simplified to an optimization problem in each instantaneous sample time:
s.t. where is the driver’s instantaneous power demand; is the drivetrain’s working efficiency; motor output power and engine output power should be within a certain range constrained by the constraint of current operating speed and battery SOC. The electric motor output power is selected as a control variable. Thus, the which satisfy the constraint conditions and make the objective function minimum can be solved to determine the motor and the engine working point.
3.2. Parameter Optimization Problem
In the above ECMS methods, selection of discharge equivalent factor and charge equivalent factor will directly affect the vehicle’s utilization of electric energy and eventually have an impact on vehicle fuel economy. For example, in a congested urban driving cycle, a smaller equivalent factor will make vehicles tend to consume electric energy and reduce the engine working at a low speed with lower efficiency and higher emission. Therefore, according to the driving cycle recognition result, the optimal charge and discharge equivalent factors need to be determined under each type of driving cycle. It means that parameters of the basic control strategy need to be optimized to adaptively adjust for a better fuel economy without losing power performance.
Currently, the widely used control parameter calculation method is realized by setting a number of disperse experimental values and then adjusting the parameter with trial and error method. And this calculation method always relies on the engineering experience. Although this method is practical, it cannot achieve the best efficiency of the power system. Therefore, it is necessary to introduce an optimization method to optimize HEV control parameters.
However, classic optimization methods generally require the objective function to be continuous and differentiable, and the sawtooth phenomenon leading to a slow convergence may occur while approaching the optimal solution. HEV is a complicated nonlinear system; in its control parameter optimization problem, it is difficult to find the optimal solution rapidly by using these classic optimization methods. Thus, this paper proposed an ant colony HEV control parameter optimization method to optimize the charge and discharge equivalent factor in each type of driving cycle, respectively. It has features of parallelism and positive feedback, and it can make full use of the vehicle model information.
This HEV control parameter optimization problem is to search the best solution for the objective function which minimizes the overall fuel energy consumption in every representative driving cycles constructed in Section 2. But as the charge and discharge equivalent factors are varied in the parameter optimization, the electric energy consumption under different parameters should be assessed according to a unified standard. Therefore we use the battery average efficiency , motor average efficiency , and transmission system average efficiency to convert the battery energy consumption to the oil consumption; it can be expressed as follows:
Then the objective function, total equivalent fuel energy consumption can be expressed as where is the control parameters “charge and discharge equivalent factors” to be optimized under each type of driving cycle; generally its value range is from 2 to 3.5. This optimization problem should satisfy the constraint of driving cycle’s realtime speed requirement. The objective function value is the integration of total equivalent fuel consumption mass flow in (5) at every sample moment of the driving cycle to be optimized. Rules for ant colony parameter optimization are as follows.
(1) Ant Initialization. Randomly distribute the given number of ants in a certain position of the variable definition domain ; each ant is positioned as follows: where rand is a random number between .
The initial pheromone quantity of each ant’s position can be expressed as where is the objective function value of ant .
(2) Ant Travelling Rules. After all the ants accomplish a searching process, one of them will find an optimal position in the current loop which will be the transfer guide for the rest ants’ travelling in the next loop. So the ants transfer can be divided into two parts, one is the global search for the ants that have not found the optimal solutions moving towards the optimal solution X(Best), its transfer probability and step length is related to the amount of pheromone and relative positions of and X(Best); the transfer probability is calculated as follows:
When ant moves to a large quantity of pheromone information position, it may find a better optimized solution. Thus the transfer step length of ant is defined in (16) when it is moving to the best position X(Best): where , .
Another part of ants transfer is local search of the Best ant. It randomly searches for a better solution in a small determined neighborhood. The search radius decreases with the increase of iterations to find a more accurate solution in the later search period. The rules for local search are shown as follows: where is the current number of iterations and is the maximum iteration number.
(3) Pheromone Update Rules. When the global and local search are finished, the pheromone information of every ants’ position needs to be updated as follows: where is the pheromone volatilization coefficient and , is calculated in (14).
(4) Solve Procedure of Parameter Optimization. The HEV control parameter optimization solving procedure is as follows.(a)Determine the maximum iteration numbers , the ant colony size , and the value range of control parameter .(b)Initialize current ant colony position and the corresponding pheromone quantity according to (14)(15).(c)Determine the ant at the optimal position according to the object function.(d)The ants that did not find the optimal solutions conduct the global search to update ants’ position according to (16)(17).(e)The ant at the optimal position does the local search and updates optimal position according to (18).(f)Update the pheromone information with (19).(g)If the termination condition is satisfied which means , then finish the loop and output the optimal solution; otherwise go to step (c).
4. Simulation and Analysis
The ant colony control parameter optimization algorithm is realized by a Matlab mlanguage program. The relevant parameter settings are as follows: maximum iteration numbers , ant colony size , control variables charge, and discharge equivalent factors value range , , .
The optimized object is a parallel hybrid electric bus in this paper; its basic power component’s technical parameters are shown in Table 1.

The objective function Equation (12) is evaluated through a Matlab/Simulink model. According to the features of hybrid powertrain and ECMS control method, the vehicle fuel consumption simulation calculating model is constructed, as shown in Figure 3.
The input of this simulation model is the four representative driving cycles constructed in Section 2, respectively, and the control parameters charge and discharge equivalent parameters are adjusted by the ant colony optimization algorithm. While the algorithm’s termination condition is satisfied, the objective fuel consumption calculated by the model will be minimized under the corresponding driving cycle. The parameter optimization process is shown in Figure 4.
With the control parameters varied in the iteration, the objective function equivalent oil consumption convergence procedure in four different types of driving cycles are shown in Figure 5. In this procedure, the ant algorithm adjusts the power distribution between engine and motor by changing the value of charge and discharge equivalent factors, so as to release and recover the electric energy more reasonable and effective, and to optimize the engine working range while making the objective function converge to the optimal value. The final optimal value of charge and discharge equivalent factors under each driving cycle is shown in Table 2.

In order to achieve the purpose of making basic ECMS have the ability of adaptive adjustment with driving cycle and greatly improving the vehicle performance, an adaptive scheme of optimized ECMS is designed in this paper as shown in Figure 6.
The optimal control parameters and driving cycle recognition part are added into the hybrid electric bus Simulink strategy model (as shown in Figure 3) to test the control strategy’s performance. The driving cycle tested in the process of simulation is the Dalian cycle (as shown in Figure 7(a)). It is constructed based on a realtime operating database which was collected from the hybrid electric buses in Dalian for four years by the remote vehiclemounted data acquisition system for new energy vehicle. The total cycle time is 1235 s and it can reflect the actual geographical and traffic features of the Dalian area.
(a) Driving cycle of Dalian
(b) Cycle recognition result
While Dalian driving cycle is inputted to the HEV Simulink model, the strategy module could receive vehicle speed information from the driving cycle module. The codes in the strategy module’s Matlab mfile which realized the driving cycle recognition algorithm proposed in Section 2 calculate the relative membership degree . Thus the driving cycle type of microtrips in the recognition period can be identified, and the optimal equivalent factors can be updated in the strategy module realizing the adaptive ECMS scheme as shown in Figure 6. The recognition period is set to be 10 s in this paper. Recognition results are shown in Figure 7(b). Types 1, 2, 3, and 4 represent stopngo, urban, suburban and rural, respectively. From the recognition results, we can see that the driving cycle type can be identified well; speed and other characteristic parameter values are in accordance with the corresponding recognized representative cycle. The real driving conditions in the Dalian area can be reflected.
Basic ECMS control method is simulated as a contrast to the optimized adaptive control strategy. This paper is mainly studying the effect of charge and discharge equivalent factors on the fuel economy, and the vehicle fuel economy performance results are determined by the energy power distribution between engine and motor, so the battery power curve in the whole cycle is the best way to express the energy distribution and the utilization of electric power. The contrast of the battery power curve between basic ECMS and optimized adaptive strategy is shown in Figure 8. From the result we can see that for the adaptive control strategy battery charge and discharge are fewer under middle high speed than those frequent battery charge and discharge in the basic ECMS. It is because that the charge equivalent factor is smaller. The discharge equivalent factor is larger in the middle high speed urban and suburban driving cycles under the optimized adaptive ECMS, and the cost to charge and discharge is large for the objective function of ECMS. As a result, the vehicle tends to use more engines to power the vehicle and reduce the battery charge and discharge. On the other hand, the adaptive control strategy tends to discharge more at a lower speed and charge more at a higher speed; it is also the consequence of the equivalent factor’s adjustment under rural and stopngo driving cycles.
The fuel consumption and SOC variation curves are shown in Figure 9; it shows that the adaptive control strategy proposed in this paper has a better fuel economy with a bit lower final SOC; the engine oil consumption is 14% lower than the basic ECMS.
5. Conclusion
In this paper, control strategy of HEV is further researched on the basis of remote data acquisition and monitoring system. Then an adaptive control strategy based on the ant colony parameter optimization for HEV is proposed. It can adaptively adjust the control parameters according to the real driving cycle, and it is effective in improving vehicle fuel economy of hybrid electric vehicle. The main work of this paper includes: four representative driving cycles are constructed according to the vehicle operating data for the past five years; a fuzzy driving cycle recognition algorithm based on a relative membership degree function is proposed; for online recognizing the type of actual driving cycle; for each type of driving cycle, the optimal control parameters corresponding to each type of driving cycle are determined by using an ant colony optimization method which can effectively shorten the control parameter’s adjustment time in the HEV road test; the validity and accuracy of the algorithm are verified by the simulation experiments at last. The results show that according to the online driving cycle recognition, vehicle controller is adjusted to the corresponding optimal control parameters, which realized the control strategy adaptive adjust with the variation of actural driving cycles, and the proposed control method improves vehicle fuel consumption effectively.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This project is supported by the National Natural Science Foundation of China (Grant nos. 51107006, 61203171, and 61473057) and China Postdoctoral Science Foundation (Grant nos. 2012M510799 and 2013T60278).
References
 R. Dosthosseini, A. Z. Kouzani, and F. Sheikholeslam, “Direct method for optimal power management in hybrid electric vehicles,” International Journal of Automotive Technology, vol. 12, no. 6, pp. 943–950, 2011. View at: Publisher Site  Google Scholar
 S. Brown, D. Pyke, and P. Steenhof, “Electric vehicles: the role and importance of standards in an emerging market,” Energy Policy, vol. 38, no. 7, pp. 3797–3806, 2010. View at: Publisher Site  Google Scholar
 J. Lian, H. Han, L. H. Li, Y. F. Zhou, and J. Feng, “Research on optimal control method of hybrid electric vehicle,” SimulationTransactions of the Society for Modeling and Simulation International, vol. 89, no. 9, pp. 1137–1146, 2013. View at: Google Scholar
 K. Çağatay Bayindir, M. A. Gözüküçük, and A. Teke, “A comprehensive overview of hybrid electric vehicle: powertrain configurations, powertrain control techniques and electronic control units,” Energy Conversion and Management, vol. 52, pp. 1305–1313, 2011. View at: Google Scholar
 N. Sadegh, B. Khan, and J. Meisel, “Optimization of the fuel consumption of a parallel hybrid electric vehicle, advanced intelligent mechatronics,” in Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 128–133, 2005. View at: Publisher Site  Google Scholar
 J.P. Gao, G.M. Zhu, E. G. Strangas, and F.C. Sun, “Equivalent fuel consumption optimal control of a series hybrid electric vehicle,” Proceedings of the Institution of Mechanical Engineers D: Journal of Automobile Engineering, vol. 223, no. 8, pp. 1003–1018, 2009. View at: Publisher Site  Google Scholar
 D. Wang, X. Lin, and Y. Zhang, “Fuzzy logic control for a parallel hybrid hydraulic excavator using genetic algorithm,” Automation in Construction, vol. 20, no. 5, pp. 581–587, 2011. View at: Publisher Site  Google Scholar
 N. Cui, J. Fan, C. Zhang, and J. Wu, “Research on predictive control based energy management strategy for Hybrid Electric Vehicle,” in Proceeding of the 3rd IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG '12), pp. 642–646, Aalborg, Denmark, June 2012. View at: Publisher Site  Google Scholar
 A. Ravey, B. Blunier, S. Lukic, and A. Miraoui, “Control strategy of fuel cell hybrid electric vehicle based on driving cycle recognition,” in Proceedings of the IEEE Transportation Electrification Conference and Expo (ITEC '12), pp. 1–5, June 2012. View at: Publisher Site  Google Scholar
 J. Engström and T. Victor, “System and method for realtime recognition of driving patterns,” U.S. Patent 6,879,969, 2005. View at: Google Scholar
 T. Watanabe and S. Katsura, “Online recognition of driving road condition using support vector machine,” in Proceedings of the IEEE International Conference on Industrial Technology (ICIT '11), pp. 405–410, March 2011. View at: Publisher Site  Google Scholar
 Q. Gong, S. MidlamMohler, V. Marano, and G. Rizzoni, “An iterative markov chain approach for generating vehicle drive cycles,” SAE International Journal of Engines, vol. 4, no. 1, pp. 1035–1045, 2011. View at: Publisher Site  Google Scholar
 H. S. Hamut, I. Dincer, and G. F. Naterer, “Analysis and optimization of hybrid electric vehicle thermal management systems,” Journal of Power Sources, vol. 247, pp. 643–654, 2014. View at: Publisher Site  Google Scholar
 B. Yu, Z. Z. Yang, and J. B. Yao, “Genetic algorithm for bus frequency optimization,” Journal of Transportation Engineering, vol. 136, no. 6, pp. 576–583, 2010. View at: Publisher Site  Google Scholar
 S. Caux, D. WanderleyHonda, D. Hissel, and M. Fadel, “Online energy management for HEV based on particle swarm optimization,” in Proceedings of the IEEE Vehicle Power and Propulsion Conference (VPPC '10), pp. 1–7, September 2010. View at: Publisher Site  Google Scholar
 J. Wu, C. H. Zhang, and N. X. Cui, “PSO algorithmbased parameter optimization for HEV powertrain and its control strategy,” International Journal of Automotive Technology, vol. 9, no. 1, pp. 53–59, 2008. View at: Publisher Site  Google Scholar
 Y. Deng, K. Chen, and J. E, “Parameters optimization for HEV based on simulated annealing particle swarm algorithm,” Automotive Engineering, vol. 34, no. 7, pp. 580–584, 2012. View at: Google Scholar
 B. Yao, C. Yang, J. Hu, J. Yao, and J. Sun, “An improved ant colony optimization for flexible job shop scheduling problems,” Advanced Science Letters, vol. 4, no. 67, pp. 2127–2131, 2011. View at: Publisher Site  Google Scholar
 B. Z. Yao, P. Hu, M. H. Zhang, and S. Wang, “Artificial bee colony algorithm with scanning strategy for the periodic vehicle routing problem,” Simulation, vol. 89, no. 6, pp. 762–770, 2013. View at: Publisher Site  Google Scholar
 B. Z. Yao, P. Hu, X. H. Lu, J. J. Gao, and M. H. Zhang, “Transit network design based on travel time reliability,” Transportation Research C, vol. 43, pp. 233–248, 2014. View at: Publisher Site  Google Scholar
 B. Yu, Z. Z. Yang, and B. Z. Yao, “A hybrid algorithm for vehicle routing problem with time windows,” Expert Systems with Applications, vol. 38, no. 1, pp. 435–441, 2011. View at: Publisher Site  Google Scholar
 J. van Ast, R. Babuška, and B. de Schutter, “Ant Colony Optimization for optimal control,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '08), pp. 2040–2046, June 2008. View at: Publisher Site  Google Scholar
 J. Lian, Y. Zhou, T. Ma, X. Shen, and J. Li, “Research on data monitoring system of Hybrid Electric Vehicle,” Sensor Letters, vol. 9, no. 5, pp. 2012–2016, 2011. View at: Publisher Site  Google Scholar
 D. Savvidis, H. Li, G. Andrews, and C. Ioakimidis, “Analysis of various driving parameters and emissions for passenger cars driven with and without stops at intersections under different test cycles,” Diesel Engine, vol. 2011, pp. 8–19, 2011. View at: Google Scholar
Copyright
Copyright © 2014 Linhui Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.