Modeling and Optimization Algorithm of FMS Logistics System Based on Petri Nets and PSO - Advanced Research on Computer Education, Simulation and Modeling - page 364

The objective function
With the purpose of achieving the shortest time, considering the uniform of multiple
AGV tasks, so set the maximal AGV task time as the objective function while itera-
tion, then make the overall operating efficiency optimal [8].Objective function as
follows [9]:

N J

s.t. , min F = max( ∑ A + B , m = 1 2 … J ) A , B ≥ 0 ∑

=

n m = N

fit mnij mnjk

mnij mnjk

n = 1 m 1

The delivery time of task n contains two parts: the time that AGV reaching the cur-
rent position of the task from the current position, and the time that from the current
position of the task to the target location. A mnij means the task n moving time from its
current location i to location j by AGV m; B mnjk means time from current position of
the task j to the task target location k . System initialization can set the initial AGV
position in the warehouse, after executing a mission it stops at the target location k ,
AGV continue to execute the next task, the new task's AGV starting position is last
task's target location, Viz. i n+1 = k n .
The algorithm's objective function is calculated as follows: in each group of task
queue, first process velocity - displacement calculation according to the encoding of
the particle, and then decoding the new position of particles that calculated by the
method which proposed in 3.3. After decoding, according to each AGV number that
corresponding to the task order to determining start and end of each task, then cumu-
lative running time of the corresponding AGV, which is the total running time of the
AGV. Then compare the total run time of all the AGV, in order to get the shortest
running time of FMS and for each AGV run time uniform, select a maximum time as
the objective function of the iteration.

4 Simulation and Analysis

The actual system is a small FMS consist of four machine tools, an automated ware-
house, two AGV, and a buffered station. To facilitate for analysis, simulate on multi-
procedure processing of 6 work piece, the simulation result is shown in Table 2:

Table 2. Optimization results in the different PSO parameters

ω /c 1 /c 2 iterations AGV1 AGV2 Time/s

1.2/2/2 50 1260 1480 1542

0.9/2/2 50 1402 1400 1474

0.6/2/2 50 1442 1318 1506

0.3/2/2 50 1282 1510 1558

It can be seen from the simulation result, when c1 = 2, c2 = 2 and ω = 0.9, the op-
timization result is better, so finally select this set parameters as the PSO parameters
to simulate. To demonstrate the strongpoints of this algorithm, comparing with opti-
mization result of the genetic algorithm(GA). The result is shown in Table 3.