COMPUTATIONAL METHODS IN ENGINEERING AND SCIENCE
EPMESC X, Aug. 21-23, 2006, Sanya, Hainan,China
©2006 Tsinghua University Press & Springer
Path Optimization of Large-Scale Automated Three-Dimensional
Garage Based on Ant Colony Algorithm
Jianjun Meng1*, Zeqing Yang1, Zhenrui Peng2
1
2
Institute of Mech-Electronic Technology, Lanzhou Jiaotong University, Lanzhou, 730070 China
National Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, 310027 China
Email: [email protected], [email protected]
Abstract To settle the contradiction among convergence speed and precocity and stagnation in ant colony algorithm,
a new-type intellectual ant colony algorithm was developed, and then applied to the path optimization of the
large-scale automated three-dimensional garage. The improved algorithm can shorten the time of taking and parking
vehicles in the garage and raise the tasking efficiency. The experiment results show that the improved algorithm has
higher convergence speed and stability, and it can get ideal searching result.
Key words: Ant Colony Algorithm, Three-Dimensional Garage, task, path, optimization
INTRODUCTION
Automated three-dimensional garage, which is based on modern logistics technique and automation technique, has
played an important role in solving the parking problem in the cities. However, there exist some requirements for
garages, including safety and quickness of taking and parking vehicles, and maintenance of continuity in garages task.
So it would be desirable to optimize the path of taking and parking vehicles to improve the efficiency of garage task.
And the optimization is also important for theory research and engineering application.
Many approaches have been proposed to solve the complex combined optimisation problems based on creature
evolution since the middle of 1950’s, including gene algorithm, genetic algorithm and ant colony algorithm. Ant
colony algorithm (ACA), one of random optimization algorithms, has been rapidly developed and applied to many
combination problems to obtain better feasible solution.
In this work, a new-type intelligent ant colony algorithm (NIACA) is developed based on the comparison of basic
ACA and max-min ant colony algorithm (MMACA), and its application in path optimization of the large-scale
automated three-dimensional garage demonstrates the effectiveness of the NIACA.
ANT COLONY ALGORITHM
1.The principle of ant colony algorithm ACA belongs to one of simulated evolutional algorithms by imitating the
behaviour of real ant colony [1-2]. Real ants can find the shortest path from nest to food source by a kind of
pheromone, Because of the similarity between searching manner of ants and TSP (Travelling Salesman Problem) [3],
M. Dorigo presented the ACA to solve the combination optimization problem by simulating the indirect
communication behaviour of real ants.
When ants move, they will deposit pheromone on the passed path, and the others can detect the existence and
concentration of pheromone to adjust their directions. Ants prefer to move towards paths with a high amount of
pheromone. The behaviours of many ants behave the phenomena of positive feedback—the more ants in a path, the
more probable for the others to select this path. Meanwhile, ants have the ability to adopt the environment variation.
For example, ants can find a new shortest path when obstacles appear on the old shortest path.
2.The basic model of ant colony algorithm The search manners of many ACA models are essentially based on the
pheromone level. We first analyze the basic ACA model and then give the comparison of MMACA with basic ACA.
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TSP is the most common application background for ACA [4-5]. Ant k in city at time itchoose the next city based on
the probability
where J k (i ) is the set of cities that remain to be visited by ant k positioned on city i; is the pheromone of the path
connected city i and city j at time t; ηij is the heuristic information associated with city i and city j, which is determined
based on the requirement of practical problem and in this work ηij is set with 1 dij and dij is the distance between city
i and city j; and α, β are the parameters that determine the importance of τij (t ) and ηij , respectively.
ρ , Pheromone decay parameter, is introduced in ACA to weaken the influence of initial state, for the beginning state
is set randomly and the initial pheromone also has great randomness.
where
is the amount sum of pheromone between city i and j city when ants locating at city i visit
city j from time t to time (t + n) .
ACA has been applied to the path optimization problems. However, there exist some problems such as great
computation and unsatisfactory search results. While searching the best path, ants only use the local information to
adjust the pheromone. When all ants completed a tour, pheromone will be adjusted again using the global updating rule.
Because of its positive feedback mechanism, the computed speed is greatly accelerated and it is especially suitable for
small combination problem. However, when the scale increases, the algorithm efficiency drops greatly and stagnation
often occurs so to result in the trap of local optimization. MMACA was then presented to solve these problems.
3. Max-min ant colony algorithm The followings give the comparison of MMACA and ACA.
1) Updating manner of pheromone Only the best ant that constructed the shortest tour is allowed to deposit pheromone.
The updating rule of this ant is given by
Where Δτijbest = 1 f ( s best ), f ( s best ) indicates that this solution is the best one of current iteration or the global one.
2) Range limitation of pheromone The range limitation is implemented when the pheromone exceeds [τ min , τ max ] . If
τij > τ max , τ ij is set with τ max , while if τij < τ min , τ ij , is set with τ min . Reference [6] points out that τ max converges
at τij (1 − ρ ) f ( s opt ) and τ min has the relationship as following:
From above analysis, we can find that ACA and MMACA are essentially accordant. On the one hand, both of them
enhance positive feedback to improve the search efficiency. On the other hand, some techniques are carried out to
reduce the possibility of getting in local optimization snap.
Another disadvantage of ACA is that many parameters are just empirically set, and the number of ant colony is
frequently adjusted based on the experimental results. So, when ACA is applied to a practical problem, some attempts
are carried out in advance in order to adjust parameters based on the experimental results, and then search can be done
again. The above process leads to the difficulties for the application of ACA. Furthermore, the performance is rapidly
dropped especially for large-scale optimization problems. We propose a new-type intellectual ACA to solve these
problems.
NEW-TYPE INTELLECTUAL ANT COLONY ALGORITHM
The proposed intellectual ACA is different in spirit from the other ACAs in that it adopts a novel dynamic pheromone
updating rule, uses a particular variation scheme to optimize each searched result, and introduces artificial
interference.
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1. The novel dynamic pheromone updating rule Pheromone, which is the communication medium for ants, can
guide search directions of ants. Local pheromone updating is utilized in many ACAs. However, we found that its effect
is unsatisfactory after carrying out many experiments. More time is required because each move of ants must update
pheromone, and the pheromone level in the optimized path are greater than that of other path outside the optimized
path due to the local pheromone updating, especially for the upper search. So the computation time can be greatly
reduced and the repeated search can be avoided if pheromone is only deposited in the global optimized path and the
last optimized search path without lose of excellent performance. Based on the extent of distribution uniformity in
optimized solution, we proposed a new state transition rule given by (5) while the pheromone is still updated according
to (3).
where Dij is the distance from destination to initial point and is inverse-ratio with Qij . The shorter the distance from
destination to initial point is, the greater the probability of selecting this destination is. This rule can direct ant to move
towards point with shorter path. Vij is the visited time of (i, j ) and is inverse-ratio with Qij , too. The more the visited
time of any destination is, the smaller the probability of selecting this destination is. This can direct ant search new path
to avoid the problem of local optimization. And the trade-off between convergence acceleration and prevention
stagnation can be obtained. This new-type dynamic pheromone updating rule has more excellent performance in
convergence speed and stability compared to the common ACAs, for each ant has contribution to search during search
process.
2. Inverse variation The severe disadvantage of ACA is to demand great search time. For this problem, many
improved schemes have been proposed. For example, a new individual is produced using crossover operator in genetic
algorithm. Namely, two individuals are randomly selected from parent population and a new individual is produced by
randomly exchanging some gene section of the two ones. However, this method often destroys the conditions with
which individuals may be the feasible solution. In this work, parent crossover operator is discarded and single-parent
exchange operator and inversion operator are designed to produce new individuals that are applied to by inverse
variation method to change the variation conditions.
Single-parent exchange operator can produce a new individual by randomly exchanging a pair of gene of parent one,
and the exchanging number and position are stochastic.
is just an example. The variation
operator means that two positions are randomly selected in an individual with that the individual are divided into three
parts, then the mid-part still maintains invariability except the order is reversed. For example,
(where is inversion point),
[8], a new bit string, will be produced after an inverse variation
operation. Another example is given as following:
. The single-parent crossover and
variation operator maintain the possibility that individual becomes feasible solution and the search ability can be
improved in solution space. For any individual, the single-parent crossover operator can produce a new individual by
some gene exchanging operations. The variation operator can transmit effective gene section of individual to its
offspring, and the important gene can be more compact and be rarely divided by crossover operator, and the
computation speed is greater due to the two operators.
The produced individual also needs mutation operation. Let agnate chromosome be
. If the
mutated variable is , then
, where function
returns a value between (0, a ) and converges at 0
with increment of t. And Δ (t , a ) has a relationship as followings: Δ (t , a ) = a (1 − t T ) , where a is a random
b
number between (0,1); T is the largest algebra and b is just a parameter. This function makes that search uniformly
distributes in solution space at the beginning of iteration and distributes in the local space to avoid destruction of
excellent individuals produced at the upper iteration. After mutation operation, the length of chromosome varies along
with change of path. A deletion or insertion must be done at the chromosome tail to match the corresponding path. The
be a passed path by one ant, if the
inserted weight is a stochastic real number. Let
is met and the time-consuming after path inversion is
condition of
shorter than the one before inversion, a new path will replace the old one, otherwise the old path is still saved. This
process is repeated for population until some terminated conditions are met.
The mutation number is stochastic but there is a rule that the number is increased along with the increment of path
length. The performance of iteration will be improved and the time will be greatly reduced owing to this mutation
operation.
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3. Artificial interference The basic ACA easily runs into local optimization if there exists repeated path. When the
information from garage gate to vacant vehicle position is ultimately equal, ants will search these paths with equal
probability. Then oscillation may occur in some paths. So, we introduce artificial interference to delete some paths that
will block the vehicle entrance. All optimized paths are dynamic due to the dynamic change of vehicle position.
OPTIMIZATION PROBLEM OF LARGE-SCALE AUTOMATED THREE-DIMENSIONAL GARAGE
1. System structure of automated three-dimensional garage The garage task system consists of monitoring server
and PLC (Programmable Logic Controller). And the task mainly involves two processes—card-number identification
and movement of stacker. When entering the garage, users must take out a card that is scanned by the server. The
server identifies the card-number and automatically sends the task instruction to PLC system. Then the PLC system
moves stacker into the appointed position by the decision instruction. When parking vehicle, driver is guided by
indicator light. The parking indicator light will be lightening when the vehicle parks the correct position. The garage
gate will be automatically closed after completing the parking task. Many signal detections, including over-length
detection, position detection, urgent parking detection and etc, are implemented for correctly moving stacker. If
stacker doesn’t reach the correct position or the vehicle length exceeds the limitation, the stacker wouldn’t do any
operation. If the urgent parking instruction is detected, any operation won’t be carried out. Moreover, control software
can select some protected operations. For example, time protection can ensure the safety of equipment and vehicle
when system can’t detect any signal due to the hardware malfunction. The path of stacker getting in or out garage has
decisive influence on task efficiency.
2.The mode of getting in or out of garage based on NIACA We apply NIACA to the optimization problem of
large-scale automated three-dimensional garage. Stacker, which can move vertically and horizontally, takes charge of
moving vehicles between vacant position and gate. The three-dimensional garage structure is illustrated in Fig.1.
X-axis denotes the parking position and y-axis denotes the storey number of parking position. The garage is divided
into n parts. In each part, a stacker is mainly responsible for the task of this part. If one stacker fails to work, adjacent
stacker will take over the work of the one with malfunction. The time from gate to the i-th position is obtained as
following:
where L and H are the length and height of parking position, respectively. There is a relationship ν x = 3ν y and
( xi , yi ) is the coordinate of the i-th position.
Figure 1: The three-dimensional garage structure
The following are some statements in algorithm.
(1) All ants set out from source point (garage gate) with equal speed in all directions, and finally reach the destination
(vacant parking position).
(2) After reaching destination, ants return immediately, and randomly select path according to pheromone until they
reach the source point, and then set out again. This process is repeated until some terminated conditions are met.
(3) Ants have memory and visit any point only one time.
The algorithm steps are given as following:
Step1: Initializing pheromone, ants begin to search from gate. Each ant transfers to the next position with probability
given by (1).
Step2: One search is completed when ant reaches vacant parking position. When all ants completed a search, the new
dynamic pheromone-updating rule will be carried out. The number of ant colony m and the length passed by each ant
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are recorded.
Step3: During the optimized process, gene exchange and inverse variation operation are carried out to maintain the
diversity of population. If new path is shorter than old one, then the new one will replace the old path, otherwise still
reserve it.
Step4: If pheromone is equal in adjacent regions, artificial interference is introduced, and the path with smaller energy
consuming is selected. The state of parking position is detected at any moment during the process. When the state of
parking position changes, optimized path will be gained by dynamic adjustment.
Step5: The algorithm is terminated if some conditions are met. i.e. the optimized number reaches the set time or latest
iteration performance maintain nearly invariable.
Step6: Outputting the result.
EXPERIMENTAL RESULTS
We have experimented with three ACAs for the optimization problem of taking and parking vehicles in garage, and
Table.1 reported the performance comparison of three ACAs. The 6-storey garage is divided into four sections. In each
part, a stacker takes charge of the task. We implement the basic ACA, MMACA and NIACA to this problem,
respectively. The parameters were set as following: ρ = 0.4, α = 1, β = 5 , and ant number is equal with the number of
vacant positions. Each algorithm ran 30 times with 300 iterations.
Table 1 indicates that the new-type intellectual ACA outperforms the two other ACAs, and the time-consuming of
NIACA is least. Fig. 2 and Fig. 3 illustrate the simulated result at 50 iterations and 100 iterations, respectively. The
path is dynamically changed due to artificial interference.
Table 1 The performance comparison of three ACAs
Figure 2: The parking position after 50 iterating
Figure 3: The parking position after 100 iterating
Fig.4 shows the time-consuming performance of ACA with and without artificial interference. The method of artificial
interference is illustrated as follows: one ant is randomly selected, and its eyeable region and adjacent region are both
set with D0 . When a vehicle appears in the D0 , the ant can pass this region (this principle is similar to the one of the
eddy current sensor, adopted in the anticollision device of robot. The principle of eddy current is that when conductor
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moves in the nonuniform magnetic field or is in alternating magnetic field, the conductor will produce induced current,
called eddy current, with which existence of the object and its distance can be detected). This strategy leads to the
dynamic adjustment of the selected path, and the feasible path that blocks the entrance task will be discarded and the
optimized path with fewer energy consuming will be saved.
CONCLUSIONS
A new-type intellectual ant colony algorithm is proposed based on the comparison of basic ACA and Max-min ACA.
The computation complexity is reduced and good performance is obtained, for only smaller iterations are demanded
due to adoption of dynamic updating pheromone, inverse variation and artificial interference. Its application in the
large-scale automated three-dimensional garage shows that the proposed method is effective. The time for taking and
parking vehicles in garage is greatly reduced and the efficiency is greatly improved. Meanwhile, this algorithm has
good robustness and can be carried out in parallel mode. The research results show that the prospect of this algorithm
in optimization problems is promising.
Acknowledgements
The support of the ‘Qing Lan’ Talent Engineering Founds of Lanzhou Jiaotong University is gratefully acknowledged.
In the mean time,the authors also express their sincere thanks to Dr. Qiangwei Li, who read the manuscript carefully
and gave valuable advice.
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