The AVS/RS Modeling and Path Planning

Transcription

1 Journal of Applied Science and Engineering, Vol. 18, No. 3, pp (2015) DOI: /jase The AVS/RS Modeling and Path Planning Tang Meng 1 * and Xue-Fei Liu 2 1 Shenzhen Energy Corporation, Shenzhen, P.R. China 2 Wuhan Railway Bureau, Wuhan, P.R. China Abstract This paper focused on the theme of AVS/RS with multi-rgv and multi-lift scheduling optimization. Firstly, we establish the corresponding mathematical model. Then, an encoding and decoding method is designed, which contains RGV task allocation and elevator selection information. Dynamic range vision and discrete adaptive step are introduced to accelerate the convergence speed and optimization direction. The mechanism of survival of the fittest groups appropriate is introduced to update the population so as to enhance the diversity of the population. Finally, we complete simulation based on the concrete living example of AVS/RS in a provincial verification center. The results obtained by the proposed algorithm are compared with another two optimization algorithm. Analysis shows that the proposed algorithm has the characteristics of fast convergence and could get the best solution. Key Words: AVS/RS, DAFSA, Scheduling, Multi-RGV, Multi-Elevator 1. Introduction In 2001, Malmborg s team at Rensselaer Poly real technic Institute in U.S. proposed the autonomous vehicle storage and retrieval system (AVS/RS), which is more flexible and efficient with respect to throughput capacity in the transfer of unit loads in high density storage areas than the traditional automated stereoscopic warehouse (AS/RS) [1]. The AVS/RS mainly includes RGV system, elevator system, aisle and shelf, which are shown in Figure 1. For the AVS/RS scheduling, Luo [1] proposed an improved QPSO to improve the performance of RGVs in AVS/RS, but not involving in the scheduling of elevator. Wu [2] proposed a deadlock control modeling method based on Petri nets and directed graph to avoid the cycledeadlock of RGVs system, but there only exists one elevator. Y. Ekren and Fukunari [3] considered the AVS/RS analytical model as a semi-open queuing network (SOQN), *Corresponding author @qq.com which consists of customers, a secondary resource and servers. However, the modeling of AVS/RS with multiple RGVs and multiple elevators has received limited attention at present. In this paper, we present a new AVS/RS compound operation scheduling mathematical model, which contains multiple RGVs and multiple elevators that has greatly increased the complexity of AVS/RS scheduling. A discrete artificial fish swarm algorithm (DAFSA) is proposed to solve mathematical model of the system. 2. The Model of AVS/RS with Mulit-RGV and Mulit-Elevator 2.1 Problem Description There are three kinds of assignments: outbound operation, inbound operation and compound operation. This paper mainly discussed the third condition, which is the most complex condition. RGV adopts compound operation can greatly improve the efficiency of the system, that means the outbound operation and inbound opera-

2 246 Tang Meng and Xue-Fei Liu Figure 1. The main parts of the AVS/RS. tion going interleaving, we show a diagram for compound operation of RGV in Figure 2. All tasks are firstly divided into several groups according to the number of available RGVs and RGVs carry out the cycle compound operation [4 7]. There are three stages in a RGV compound operation: (i) RGV runs from the current position to the starting point of the outbound task. (ii) RGV runs from the starting point of the outbound task to the I/O point. (iii) RGV runs from the I/O point to the ending point of the inbound task. After completing the task allocation, the system needs to give path planning in every stage for each RGV. For the across layer task, due to the horizontal path is determined by the selected elevator, RGV path planning should consider the elevator scheduling. 2.2 The Conversion of Problem Owing to most of the tasks in the system are cross layer task, so in a RGV compound operation, every stage includes two parts of running distance: (i) The horizontal running distance is consisted of the distance of RGV runs from the current position to the elevator point and the distance of RGV runs from the elevator point to the destination point. (ii) The vertical running distance is the empty running distance of elevator plus the actual running distance of the elevator. This paper proposed a RGVs compound operation scheduling model, which involved multiple elevators. Figure 3 shows the AVS/RS scheduling model. Stage 1 is the task assignment phase, stage 2~stage 4 are the RGVs actual operating phase. In a RGV compound operation, there are at least two actual operating phases involving the selection of the elevator. In other words, there would appear the condition there is no need for RGV to use the elevator in some stages (no-cross layer task). So, we add a virtual elevator in the system, if one RGV selecting this elevator that means the RGV can reach it s destination without using elevator in this stage. 2.3 The AVS/RS Scheduling Modeling There are M inbound tasks and M outbound tasks arriving in the system, the number of RGV is N, the number of elevator is F-1. The all tasks are divided into M group, which consists of M/N = P batches. Every group Figure 2. The RGV compound assignment plane sketch. Figure 3. The AVS/RS scheduling model schematic diagram.

3 The AVS/RS Modeling and Path Planning 247 includes a inbound task and an outbound task. Each cycle operation (batch) has N task group. One RGV choose different elevators in the same stage has different running distance [8]. (1) (2) (3) (4) Formula (1) is the objective function. D sbihk,,, is the 1 distance of RGV b took group i from the current position to the position of elevator f. D sbihk,,, is the distance 2 of RGV b traveling from the elevator point to the destination point of the task. Formula (2) is the vertical running distance of RGV b, which contains the actual running distance of elevator fr s, b, f and empty running distance of elevator f from the current moment to reaching the RGV layer W s, b, f. Formula (3) is the elevator f occupied time by the group i in stage s. Formula (4) means each RGV only occupying one elevator in one stage. 3. Discrete Artificial Fish Swarm Algorithm 3.1 The Basic Artificial Fish Swarm Algorithm (AFSA) In basic artificial fish swarm algorithm (AFSF), artificial fish model is structured firstly, then they search the food by simulating three kinds of fish behavior pattern as follows: swarming, following and preying. The state of the artificial fish is defined as X =(x 1, x 2, x n ), x i is the optimization variable, the dimension of the vector X is n. The food concentration of the artificial fish in current location is defined as Y = f(x), Y is the fitness function. Visual is the vision field of the artificial fish, Step is largest moving step length, is the congestion degree factor. Although the AFSA has strong global search ability, the effect of congestion degree makes the individuals not be able to rally near the optimal value, that resulting in slowing the late convergence speed and easily falling into the local extreme value point. 3.2 The Discrete Artificial Fish Swarm Algorithm (DAFSA) There are various improved the artificial fish algorithm [7,9 11]. Duan [7] proposed the PSO-FSA to improve convergence speed and searching precision of the AFSA. Sun [9] proposed an AFSA adding the fish jumping behavior, Xu [10] proposed an adaptive meta- cognitive artificial fish swarm algorithm to speed up the convergence in the later period of the basic AFSA. Different from those studies, we used the discrete adaptive step length and dynamic visual field to accelerate the convergence speed and optimization direction. Meanwhile, we proposed evolution mechanism and the communication behavior in AFSA Discrete Adaptive Step and Dynamic Visual Before each iteration, every AF must determine the vision field of the current generation firstly. Visual field is generally determined according to the solution of precision and the size of the space, we used dynamic visual field to improve the whole the adaptability of the individuals in the iterative process. Improvement of individual dynamic visual field is shown in formula. (5) Visual max and Visual min are upper and lower of the visual, m is the total number of iterations, t is the current generation number. The current state of the AF is X i, the next state of the AF is X i,next, X j is the moving direction of X i, it s next move can be defined as follow: (6)

4 248 Tang Meng and Xue-Fei Liu X ip and X jp represent the value of No.p in location information of X i and X j Evolution Mechanism and Communication Behavior The evolution mechanism: the AF which fitness function value ranked in late P size *G (P size is total number of individuals, G is the update rate) are eliminated, and the same amount of new individuals are generated. The communication behavior: AF X i moves one step to the history optimal position H best in the bulletin that made next step consider the optimal position of whole fish swarm, which enhancing the information exchange and sharing between individuals. 4. The DAFSA for AVS/RS Scheduling According to the characteristics of the AVS/RS scheduling, encoding and decoding, fitness function, the process of the proposed algorithm are given in this section. 4.1 Encoding and Decoding According to the characteristics of the AVS/RS scheduling model, We adopt floating point encoding method: integer part represents RGV s task allocation or elevator number selected by RGV in each stage, decimal fraction part represents service sequence of tasks choosing the same RGV or elevator. The state vector X i represents a AF, the dimension of AF is 4M that includes the scheduling information of RGVs and elevators, different AF represents a feasible scheduling solution. For example, let a AF state is X i =(x 1, x 2, x M x M +1, x M+2... x 2M x 2M+1, x 2M+2...x 3M x 3M+1, x 3M+2...x 4M ) = (1.1, 2.1, , 1.2, , 2.1, 1.1), each character elements are a random value in [1, 1 + N]. The first three character element represents the information of RGV s task allocation, such as the third element 2.2 means the task 3 rd serviced by No. 2 RGV. 4.2 Fitness Function In this paper, the optimization of objective function is the maximum running distance of all the tasks, the fitness function is: (7) L max is the maximum running distance of a scheduling scheme represented by a AF. 4.3 Procedure of DAFSA for AVS/RS Scheduling (1) Setting the AF swarm scale P size, the maximum iteration numbers m, initialing information of the AF, included the position, Visual min and Visual max. (2) Calculating the fitness function of each AF and recording the optimal value of AF state to the bulletin board, adjusting step and Visual. (3) Assessing the behaviors of N AF, and selecting the optimal behavior, including swarming behavior, following behavior and communication behavior. If the moving state is superior to the current position, update the state of AF. Otherwise, move a step randomly. (4) Eliminate the AF which fitness function value are ranked in late P size *G, then generate new individuals in the same number. (5) Determining whether it is reach the maximum iteration m. If do, output the optimal solution, if not, come back to step 3). 5. The Application of DAFSA in AVS/RS Taking a AVS/RS in warehouse of a provincial power company for example, the system contains 4 RGVs, 4 elevators, 6 shelves.the length of shelf is 11 m, the height of shelf is 15 m, the number of bay per aisle is 13. Each aisle has S/R locations on both sides. 5.1 Parameter Setting In order to verify the effectiveness of the proposed DAFAF to solve this problem, we randomly generate a compound operations containing 4 outbound tasks and 4 inbound tasks. Comparing the proposed DAFSA with basic ABC, QPSO [1] by the simulation of the above instance, the swarm scale N = 500, the maximum iteration

5 The AVS/RS Modeling and Path Planning 249 numbers m = 160, the dimension n = 16, the three algorithms runs independently 30 times, other parameters are: ABC: P 1 =0.5,P 2 = 0.3, Limit = 15. QPSO: =0.8,C 1 =C 2 =2,r 1,r 2, (0, 1). DAFSA: Trynumber = 8, = 0.75, G = 0.15, Visual min = 2, Visual min =4. The 8 unit loads is given as follow: D = [(2, 7, 23), (7, 3, 18); (9, 13, 8), (5, 11, 16); (1, 8, 15), (3, 4, 6); (9, 3, 15), (6, 2, 18)]. The task 1, 3, 5, 7 are the outbound tasks, In this paper, a new model of AVS/RS scheduling is proposed, and a discrete AFSA was introduced to solve the mathematical model. An encoding and decoding method was designed, which contains RGV task allocation and elevator selection information Dynamic range vision and discrete adaptive step are introduced to accelerate the convergence speed and optimization direction. The mechanism of survival of the fittest groups appropriate is introduced to update the population so as to enhance the diversity of the population. However, in the actual operation, the delaying, the collision and other factors should the task 2, 4, 6, 8 are the inbound tasks. The task 8 th means the load located in 18 th floor, 2 rank, No Comparison Analysis (1) Comparison of convergence rate: the convergence process curve of three algorithms are shown in Figure 4, and we can find that ABC and QPSO has poor performance on the speed of convergence. The DAFSA can achieve convergence rapidly than the others. It denoted that DAFSA has better global astringency ability. (2) Comparison of the optimal results: the average of the optimal results by the three algorithms with 8 unit loads are shown in Table 1. Under the same condition, the QPSO has the shortcomings at speed of convergence and optimal solution. Therefore, the DAFSA is better than the QPSO and ABC in solving such problem. The discrete adaptive step and dynamic visual can increase the rate of convergence in the later period of the optimization. The RGV s threedimensional path trajectory by the DAFSA is shown in Figure 5. Figure 4. The convergence of three algorithms. Table 1. The comparison results of the three algorithms with 8 unit loads Algorithm QPSO ABC DAFSA Average convergence iteration The optimal solution/s The average solution/s The standard deviation of solution s/% Conclusions Figure 5. The RGV s three-dimensional path trajectory.

6 250 Tang Meng and Xue-Fei Liu be considered. In our future work we will focus on the cycle-deadlock control of RGVs. Acknowledgement The authors would like to thank the editor and reviewers for providing detailed comments, which have significantly improved the quality of this paper. References [1] Luo, J., Wu, C.-Q. and Li, B., Modeling and Optimization of RGV System Based on Improved QPSO, Computer Integrated Manufacturing Systems, Vol. 17, No. 2, pp (2011). [2] Wu, C.-Q., He, S.-J. and Luo, J., Cycle-deadlock Control of RGVs in Autonomous Vehicle Storage and Retrieval Systems, Computer Integrated Manufacturing Systems, Vol. 14, No. 9, pp (2008). [3] Fukunari, M. and Almborg, C. J., A Network Queuing Approach for Evaluation of Performance Measures in Autonomous Vehicle Storage and Retrieval Systems, European Journal of Operational Research, Vol. 193, No. 2, (2009). doi: /j.ejor [4] Naderi, B., Ahmadi, A. and Javid, F., Permutation Flow-shops with Transportation Times: Mathematical Models and Solution Methods, International Journal of Advanced Manufacturing Technology, Vol. 46, pp (2010). doi: /s [5] Wang, S.-Y., Wang, L. and Xu, Y., Estimation of Distribution Algorithm for Solving Hybrid Flow-shop Scheduling Problem with Identical Parallel Machine, Computer Integrated Manufacturing Systems, Vol. 12, No. 6, pp (2013). doi: /s y [6] Wang, X. and Tang, L., A Tabu Search Heuristic for the Hybrid Flow-shop Scheduling with Finite Intermediate Buffers, Computers & Operations Research, Vol. 36, No. 3, pp (2008). doi: /j.cor [7] Duan, Q.-C., et al., Simulation Analysis of the Fish Swarm Algorithm Optimized by PSO, Control and Decision, Vol. 28, No. 9, pp (2013). [8] Gao, J., Chen, R. and Wu, D., An Efficient Tabu Search Algorithm for the Distributed Permutation Flow-shop Scheduling Problem, International Journal of Production Research, Vol. 51, No. 3, pp (2013). doi: / [9] Sun, D.-H. and Song, X.-X., Scheduling Model of Motorcycle Parallel Conveyor Belt Flow Shop and its Solution, Computer Integrated Manufacturing Systems, Vol. 17, No. 2, pp (2011). [10] Xu, H. R. and Li, R., An Adaptive Meta-cognitive Artificial Fish School Algorithm, International Forum on Information Technology and Applications, pp (2009). doi: /IFITA [11] Yang, C. G., Tu, X. Y. and Chen, J., Algorithm of Marriage in Honey Optimization Based on the Wolf Pack Search, International Conference on Intelligent Pervasive Computing, pp (2007). doi: /IPC Manuscript Received: May 8, 2014 Accepted: Apr. 20, 2015