Parallel Simulation-based Optimization on Block

International Journal of Information Systems for Logistics and Management Vol. 4, No. 2 (2009) 1-8

http://www.knu.edu.tw/academe/englishweb/web/ijislmweb/index.html

Parallel Simulation-based Optimization on Block Planning and Dynamic Truck Configuration of Container Terminals Haoyuan Li and Dingwei Wang The Institute of Systems Engineering, Northeastern University, ShenYang 110004, China Received 10 January 2009; received in revised form 19 March 2009; accepted 5 May 2009

ABSTRACT Simulation is an effective means when solving the design and operation problems in modern container terminals. Applying object-oriented discrete event system simulation method, and analyzing the technological process of loading and unloading as well as the operational management in modern container terminals, a simulation model was constructed to describe the whole operation system of container terminals, in which container ships, anchorages, berths, quay cranes, gantry cranes, internal container trucks, external container trucks and yard gates were all included. In order to solve the block planning and dynamic container truck configuration problem of container terminals, a simulation-based optimization (SBO) method was proposed. The MPI-based parallel computing technology was introduced to the solving process and the computing time of SBO was reduced effectively. Keywords: simulation-based optimization, block planning, dynamic truck configuration, parallel computing.

1. INTRODUCTION Container truck transportation is an important link in the operating system of container terminals, which connects the quay cranes and gantry cranes. Only the truck configuration fits the work of quay cranes and gantry cranes at the same time, the efficiency of container terminals can be ensured. The volume of handling tasks in container terminals is quite different in different periods, so the number of container trucks should be configured dynamically. Block planning is also quite important in the operational process of container terminals. Only the block planning fits the work of container trucks, the container trucks can accept the loading and unloading operation quickly at the gantry cranes and ensure the efficiency of container terminals. At present the researches on horizontal transport

vehicles of container terminals mainly focus on the AGV (automated guided vehicle) which is used in automatic or semi-automatic ports. Domestic ports are mostly nonautomated ports. Considering the cost of labors and the flexibility of manipulation, most domestic ports use the container trucks as the horizontal transport vehicles. However, the block planning and truck configuration problem in non-automated port involves many factors and large uncertainties, the researches on that are relatively deficient, especially the models and methods for the truck quantity configuration problems. Bish et al. (2001) did a research on truck distribution problem in non-automated ports, and gave a heuristic algorithm. Koo (2004) proposed a two-stage heuristic tabu search algorithm, the objective of which was the minimum number of truck configuration and the determination of the optimal path for each truck. Based on mathematical programming, the above

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International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 4, No. 2 (2009)

researches focus on the analysis and solution of problems which have limited and fixed restrictive conditions. However, the container terminal operating system is a typically multi-link complex dynamic random system, and the links restrict each others mutually. Subjected to the influence of many random factors, a great error may result from the analytical method. In recent years, the computer simulation technology is used in the planning and management of container terminals more and more. Yang and Ding (2003) built a dynamic multilevel queuing network for Waigaoqiao Container Terminals of Shanghai and gave the optimal equipment allocation. Zhang and Huo (2006) built a simulation model of ship handling and transportation by using Witness simulation software, and analyzed the effect of the quantity and the speed of the container trucks. However, the simulation model is just a testing and confirming platform, it is unable to provide the assistant decision-making function. In recent years, the simulation-based optimization method which developed on the basis of simulation redeems the defect effectively. In this paper, we use the simulation-based GA algorithm to solve the block planning and dynamic truck configuration problem of container terminals, and introduce the parallel computing technology which is realized by MPI to the solving process. The experimental results show that we can get the satisfactory solution of the block planning and dynamic truck configuration problem by SBO, and the high computational cost problem of SBO is effectively solved. 2. SIMULATION-BASED OPTIMIZATION 2.1 Summary Simulation-based optimization (SBO) is an optimization method which is combined of simulation technology and optimization algorithm. Using the evaluation from the simulation model, the optimization algorithm can improve the solution and the output response continually, and finally find the best input variables and the best output. At present, the simulation-based optimization method mainly uses GA (Ding et al., 2004), SA (Duh and Brown, 2007) and PSO (He et al., 2007) as the optimization algorithm. It is mainly applied in complex engineering system (Tveit and Fogelholm, 2006), supply chain and logistics system (Schwartz et al., 2006), manufacturing system (Arakawa et al., 2003), and socioeconomic system (Ermolieva, 2005). In the container terminal applications, Yu et al. (2007) realized the optimal planning on the gate system on container yard by simulation-based optimization. Cai and Zhang (2006) built a simulation and optimization model which aimed at the problem of berth and quay crane scheduling. The main reason which leads to the restrictions on

Optimization Module Solution

Evaluation

Simulation Module Simulation

Verification

The Actual System Fig. 1. Principle of SBO algorithm

application and development of the simulation-based optimization is that the computational cost is too high. To solve the problem, some scholars abroad carried out some researches and have made some progress. Lee et al. (2006) proposed a SAA(Sample Average Approximation) method which could reduce the computational cost. Bachelet and Yon (2007) proposed a Model Enhancement method and applied it to vehicle routing problem successfully. In this paper, we use the parallel cluster computing technology to reduce the high computing costs of SBO. 2.2 Basic Principle The principle of simulation-based optimization algorithm is shown in Fig. 1. First, establish the simulation model of the practical system. The optimization algorithm generates initial decision variables and sends them into the simulation model. Then the simulation model gives the output which takes the place of fitness value back to the optimization model. According to the evaluation from simulation model, optimization algorithm improves the decision variables and repeats the above process until the termination condition is met. Then we can get the optimization parameters of the system. 3. ESTABLISHMENT OF SIMULATION MODEL 3.1 Operational Process of Container Terminals Generally, the operating system of modern container terminals is composed of loading and unloading operation, yard operation, gate operation and horizontal transportation. As the interface between ship operation and gate operation, the container yard divide the whole operational process into two parts, berth-yard operational mode and gate-yard operational mode, as shown in Fig. 2. 3.2 Layout of Container Terminals In this paper, the simulation model is set up according to the actual layout of a domestic container port, as shown in Fig. 3. There are four berths on the waterside of the terminal. Each berth is assigned two quay cranes

H. Li and D. Wang: Parallel Simulation-based Optimization on Block Planning and Dynamic Truck Configuration

Arrival of container ships

Unloading of ships

Loading of ships Departure of container ships

Loading of trucks Handling operation of quay cranes

Examination of containers Departure of container ships

Placement of containers Horizontal transportation of internal trucks

Handling operation of yard gates

Procedure transaction

Lifting of containers

Lifting or placement of containers

Position assignment

Examination of containers Arrival of container ships

Unloading of trucks

3

Horizontal transportation of external trucks

Handling operation of gantry cranes

Lifting or placement of containers

Fig. 2. The process of container terminals

3.3 Character of Simulation Model

Command Building Fig. 3. The layout of container terminals

for loading and unloading operation and each quay crane has a certain number of internal container trucks for horizontal transportation. There are 36 blocks in the container yard and each block can contain 50 × 6 × 4 TEU containers. Each block is assigned one gantry cranes for loading and unloading operation. All blocks are separated by the transverse operating lines and the longitudinal transport lines. The transverse operating lines are one-way traffic lanes and the loading and unloading operations are carried out on them. The longitudinal transport lines are two-way traffic lanes and they are for the traffic of the container trucks in the yard. All trucks that are moving on the lines in the yard are not allowed to overtake each other. The yard gate is composed of three entrance routes and three exit routes, which is for the external container trucks’ procedure transaction and position assignment.

(1) The object of this study is multi-ship operational process. The simulation model can describe a series of processes and events that are included in the operational process of container terminals from the arrival of container ships to the end of loading and unloading operation. The operational process from the arrival of the external container trucks to the leavetaking is also described. (2) Each entity (each container, each handling equipment, each truck, etc) is the object of this model. The model can give the description of each detail of the whole operational process in container terminals and reflect the changing process of each entity’s state. (3) Activity scanning is adopted as the simulation strategy to promote the progress of simulation time. Second is set as the simulation step. (4) Digital simulation mode is adopted in our simulation model. Considering the running cost of simulation program, our simulation model doesn’t involve the graphic simulation mode. (5) Set eight hours as a work period, different amount of trucks are assigned to the quay cranes at different period. (6) The outputs of the simulation model are evaluations which the container terminals’ managers pay more attention to, including the number of ships that arrived, the number of ships that received services, the number of external trucks that arrived, the number of external trucks that received services, throughput in the simulation time, utilization of the berths, utilization of the quay cranes, average berthing time of

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International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 4, No. 2 (2009)

container ships, the average waiting time of internal container trucks, average staying time of external trucks, average efficiency of loading and unloading.

and elitism strategy is adopted in our algorithm. We use the one-point crossover with a probability pc = 0.8 and bit mutation with the mutation probability pm = 0.05.

4. DESIGN OF SIMULATION-BASED GA

4.1.4 Termination conditions When the iteration is more than 100, the algorithm terminate.

4.1 Parameter Design of Block Planning 4.1.1 Coding scheme

4.2 Parameter Design of Truck Configuration For the block planning problem in this study, we select the binary encoding method to express the decision-making vector: xb = (x1, x2, x3, …, x36)

(1)

There into:

xi =

1, Block i is designated as a import block 0, Block i is designated as a exp ort block

4.2.1 Coding scheme For the dynamic truck configuration problem in this study, we select the binary encoding method to express the decision-making vector. Every four binary codes represent the amount of trucks assigned to each quay crane in an 8-hour work period: xt = (x1, x2, x3, …, x24)

(4)

There into: i = 1, 2, …, 36

(2) x1, x2, x3, x4:

4.1.2 Calculation of fitness According to the characteristic of the container terminal operating system, if the average efficiency of loading and unloading or the utilization of the quay cranes that is got from the simulation program is higher, the fitness of the solution is higher. Considering the convenience of container terminal management and scheduling, we design a structured coefficient that can represents the orderliness degree of the blocks. Higher the structured coefficient is, higher the fitness value is. As the output of the simulation program for the solution i, the average efficiency of loading and unloading is expressed as Efi, the utilization of the quay cranes is expressed as Qfi, structured coefficient Sti is obtained by the following rules: Sti is initialized to 0. For the 6 × 6 blocks, if there are n rows in which all of blocks are import block or export block, Sti plus n. For the 6 × 6 blocks, if there are n lines in which all of blocks are import block or export block, Sti plus n. Do the normalization of Efi , Qfi and Sti , and give them 0.4, 0.4, 0.2 weight coefficient, respectively. Then we can get the fitness value of solution i:

transcoded from 0-1 code to integer code, the integer is the amount of trucks in the first 8-hour period;

x21, x22, x23, x24: transcoded from 0-1 code to integer code, the integer is the amount of trucks in the sixth 8-hour period; 4.2.2 Calculation of fitness According to the characteristic of the container terminal operating system, if the average efficiency of loading and unloading or the utilization of the quay cranes that is got from the simulation program is higher, the fitness of the solution is higher. Considering the wastes of container truck resources, lower the average waiting time of internal container trucks is, higher the fitness of the solution is. As the output of the simulation program for the solution i, the average efficiency of loading and unloading is expressed as Efi, the average waiting time of internal container trucks is expressed as Wfi. Do the normalization of Efi and Wfi, and give them 0.6 and 0.4 weight coefficient, respectively. Then we can get the fitness value of solution i: Fitt(i) = 0.6 * Efi + 0.4 * (1 – Wfi)

(5)

4.2.3 Genetic operators Fitb(i) = 0.4 × Efi + 0.4 × Qfi + 0.2 × Sti

(3)

4.1.3 Genetic operators Fitness proportionate selection with roulette wheel

Fitness proportionate selection with roulette wheel and elitism strategy is adopted in our algorithm. We use the one-point crossover with a probability pc = 0.8 and bit mutation with the mutation probability pm = 0.05.

H. Li and D. Wang: Parallel Simulation-based Optimization on Block Planning and Dynamic Truck Configuration

Start Host computer generates initial population Host computer distributes the population

Guest computer 1 calculate the fitness

Guest computer 2 calculate the fitness

...

Guest computer n calculate the fitness

5

vious difference between simulation-based GA and simple GA is that the evaluation of each solution spends too long. Because the computing time for evaluation of each solution is roughly the same, simulation-based master-slave parallel genetic algorithm is the most direct and the most efficient way. The process of master-slave parallel GA is shown in Fig. 4. 5. EXPERIMENT AND ANALYSIS

Host computer collects the fitness Selection Crossover Mutation Generate new population Meet the termination condition? Give the results Complete

Fig. 4. The process of master-slave parallel GA

5.1 Design of the Simulation Parameters The simulation program and algorithm program are complied by VC++6.0. The simulation time length of the actual system is set to one day (86400 seconds) for block planning and two days (172800 seconds) for truck configuration. The stochastic parameters of the simulation program are set as follows: (1) The arrival intervals (second) of container ships follow the negative exponential distribution with a parameter λ = 0.3535; (2) Operation mode of container ships:

4.2.4 Termination conditions When the iteration is more than 100, the algorithm terminate. 4.3 Parallel Computing In simulation-based optimization algorithm, the fitness value of each solution is got from the simulation program whose running time is thousands of computing mathematical function, so the high cost of SBO algorithm is unacceptable. Considering the inherent parallelism of Genetic Algorithm, parallel computing is an effective way to solve the problem. Cluster technology that rises in recent years is a new high-performance computing technology. Compared with the traditional high-performance computer technology, cluster technology can use servers of various grades as nodes. The cost of cluster system is very low and high computational speed can be achieved. MPI (Message Passing Interface) is a very famous massage passing standard for parallel computing environment. MPICH is a full realization of MPI1.2 standards and it is also a parallel and distributed environment that has the most extensive application. 4.4 Algorithm Process Currently parallel genetic algorithm can be roughly divided into three categories: global type—master-slave model, independent type—coarse-grained model, and decentralized type—fine-grained model. The most ob-

A=

loading 0 < r < 0.2 unloading 0.2 ≤ r < 0.4 loading and unloading 0.4 ≤ r < 1

r is a uniformly distributed random number between 0 and 1; (3) Loadage of container ships (TEU):

B=

500 0 < r < 0.2 1000 0.2 ≤ r < 0.7 1500 0.7 ≤ r < 1

r is a uniformly distributed random number between 0 and 1; (4) The arrival intervals (second) of external container trucks follow the negative exponential distribution with a parameter λ = 0.45; (5) Handling efficiency (TEU/hour) of quay cranes follows the normal distribution N (34.6, 2.69); (6) Operating time (second) of gantry cranes follows the normal distribution N (90, 2.69). 5.2 Performance Analysis Table 1 shows the computing time of block planning in different mode. And Table 2 shows the computing time of truck configuration in different mode. As shown in Table1 and Table 2, by introducing the parallel cluster computing technology into the SBO algorithm, the cost of calculation and the computing time

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International Journal of the Information Systems for Logistics and Management (IJISLM), Vol. 4, No. 2 (2009)

Table 1. The computing time of block planning in different running mode

Table 2. The computing time of truck configuration in different running mode

Running mode

Running mode

Computing time

The running of simulation program

12 seconds

Computing time

The running of simulation program

38 seconds

The running of single computing system

307500 seconds (85.4 hours)

The running of single computing system

199510 seconds (55.4 hours)

The running of 5 computers parallel computing system

67415 seconds (18.75 hours)

The running of 5 computers parallel computing system

47415 seconds (13.17 hours)

The running of 10 computers parallel computing system

33705 seconds (9.35 hours)

The running of 10 computers parallel computing system

25705 seconds (7.14 hours)

Table 3. Comparison of the evaluations between the optimal solution and some actual planning for block planning

Throughput in the simulation Utilization of the quay

111100 110000 110000 111100 111000 111010

111000 111000 111000 111000 111000 111000

000111 000111 000111 000111 000111 000111

000000 000000 000000 111111 111111 111111

111111 111111 111111 000000 000000 000000

5173 (TEU)

4599 (TEU)

4345 (TEU)

4321 (TEU)

4188( TEU)

86%

84%

78%

82%

75%

Average berthing time of container ships

77458 (second) 76116 (second) 74768 (second) 71652 (second) 81407 (second)

Average efficiency of loading and unloading

48 (TEU/hour) 48 (TEU/hour) 40 (TEU/hour) 46 (TEU/hour) 39 (TEU/hour)

5.3 Simulation Results of Block Planning The evolutionary process of simulation-based GA for block planning is shown in Fig. 5. When the iteration is more than 37, the best fitness value is stabilized. The simulation-based GA has a good convergence and can solve the block planning problem of container terminals effectively. After calculation, the optimal solution from simulation-based GA is xb = (1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0) For convenience, the decision-making vector xb is

0.8 0.8 Fitness

are reduced significantly. Because the computing time of each simulation case is basically the same, the host computer doesn’t need to wait for some guest computer that has relatively slow computing speed. The master-slave parallel computing method is an effective way to improve the computational efficiency. Clearly seen from the tables, the computing time of single computing system is approximately N times more than that of parallel computing system which is combined of N computers. The efficiency of parallel computing is particularly high.

0.8 0.8 0.8

1

9 17 25 33 41 49 57 65 73 81 89 97 Iteration

Fig. 5. The relative curve of fitness and iteration in simulation-based GA for block planning

converted to a 6 rank phalanx):

Xb* =

1 1 1 1 1 1

1 1 1 1 1 1

1 0 0 1 1 1

1 0 0 1 0 0

0 0 0 0 0 1

0 0 0 0 0 0

Putting the actual block planning into the simula-

H. Li and D. Wang: Parallel Simulation-based Optimization on Block Planning and Dynamic Truck Configuration

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Table 4. Comparison of the evaluations between the optimal solution and some actual planning for truck configuration

Truck configuration

Throughput in the simulation time

Utilization of the berths

Utilization of the quay cranes

Average efficiency of loading and unloading

Average Average waiting berthing time of internal time of container trucks container ships

{9, 8, 8, 8, 8, 13} {5, 5, 5, 5, 5, 5} {8, 8, 8, 8, 8,, 8} {10, 10, 10, 10, 10, 10} {13, 13, 13, 13, 13, 13} {15, 15, 15, 15, 15, 15}

13257 (TEU) 10719 (TEU) 13323 (TEU) 13397 (TEU) 12207 (TEU) 12856 (TEU)

91% 92% 91% 91% 91% 92%

90% 80% 90% 91% 86% 92%

68 (TEU/hour) 53 (TEU/hour) 68 (TEU/hour) 68 (TEU/hour) 62 (TEU/hour) 65 (TEU/hour)

70635 (second) 82132 (second) 79816 (second) 59976 (second) 70620 (second) 90366 (second) 70619 (second) 102982 (second) 70614 (second) 126747 (second) 70533 (second) 134391 (second)

0.7

Fitness

0.6 0.5 0.4 0.3 0.2 0.1

1

15

29

43 57 Iteration

71

85

99

Fig. 6. The relative curve of fitness and iteration in simulation-based GA for truck configuration

tion program, we compared the output evaluation with that of the optimal solution from simulation-based GA. The results are shown in Table 3. In the comparison of the four evaluations which the container terminals’ managers pay more attention to, simulation-based optimization algorithm achieves the better result. 5.4 Simulation Results of Truck Configuration The evolutionary process of simulation-based GA for truck configuration is shown in Fig. 6. When the iteration is more than 52, the best fitness value is stabilized. The simulation-based GA has a good convergence and can solve the dynamic truck configuration problem of container terminals effectively. After calculation, the optimal solution from simulation-based GA is xt = (1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1) For convenience, the decision-making vector xt is transcoded from 0-1 code to integer code: xt* = {9, 8, 8, 8, 8, 13} 9 is the amount of trucks in the first 8-hour period,

8 is the amount of trucks in the second 8-hour period, similarly, 8 trucks are used in the third, fourth and fifth 8-hour period, and 13 is the amount of trucks in the sixth 8-hour period. Putting the optimal solution into the simulation program, we compare the output evaluation with that of some actual truck configurations from simulation-based GA. The results are shown in Table 4. In the case that the throughput, utilization of quay cranes, and average efficiency of loading and unloading have little difference, the result of simulation-based optimization reduces the average waiting time of internal trucks and increases the efficiency of the internal trucks greatly. Simulation-based optimization algorithm achieves the better result. 6. CONCLUSIONS In this paper, we use the simulation-based GA algorithm to solve the block planning and dynamic container truck configuration problem of container terminals, and introduce the parallel computing technology which is realized by MPI to the solving process. The experimental results show that we can get the satisfactory solution of the block planning and dynamic truck configuration problem by SBO, and the high computational cost problem of SBO is effectively solved. REFERENCES Arakawa, M., Fuyuki, M. and Inoue, I. (2003) An optimizationoriented method for simulation-based job shop scheduling incorporating capacity adjustment function. International Journal of Production Economics, 85(3), 359-369. Bachelet, B. and Yon, L. (2007) Model enhancement: Improving theoretical optimization with simulation. Simulation Modelling Practice and Theory, 15(6), 703-715. Bish, E. K., Leong, T. Y. and Li, C. L. (2001) Analysis of a new vehicle scheduling and location problem. Naval Research Logistic, 48(5), 363-385. Cai, Y. and Zhang, Y. W. (2006) Simulation optimization for

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