Deriving Situation-Adaptive Strategy for Stacking Containers in an Automated Container Terminal
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PUSAN NATIONAL UNIVERSITY
Deriving Situation-Adaptive Strategy for Stacking
Containers in an Automated Container Terminal
Taekwang Kim, Jeongmin Kim, and Kwang Ryel Ryu
Pusan National University
Dept. of Electrical and Computer Engineering
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Outline
• Automated Container terminal
• Stacking Policy
• Background and Previous Works
• Approach to Deriving Situation-Adaptive Strategy
• Case Study
• Experimental Results
• Conclusion
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Automated Container Terminal
2
Enlarged view of a block part
tiers
Seaside
StackingYard
LandsideExternalTrucks
AGVs
QC
Seaside ASC
Seaside HP
Landside HP
Landside ASC
Quay
Quay Crane (QC)
Hinterland
Enlarged view of a block part
Stacking Yard
External Truck(ET)
Automated Stacking Crane
(ASC)
Automated Guided Vehicle(AGV)
Seaside Handover Point
(HP)
LandsideHandover Point
(HP)
Stack
Operations in Stacking Yard
• Crane interference occurs frequently because of the opposite
directions of container flow
• Determination of stacking position is one of the most important
operational problems in container terminals
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Seaside HP
Landside HP
Loading Carry-in(Export)
Carry-outRehandling
Transshipment
Discharging(Import)
Repositioning
Stacking Policy
• Stacking policy takes account of various criteria to determine optimal
stacking positions in the stacking yards
• A good position should allow efficient operation not only at the time of
stacking but also at the time of retrieval
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Stacking Policy
container 1. Request for a stacking location
3. An optimal stacking position
4. Stack
Stacking yard
2. Evaluate candidate positions
• Stacking policy based on single criterion [Duinkerken M. B., 2001]
[Dekker, R., 2006]
Background and Previous Works
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Distance to the Handover Point
Category of a container (destination, weight, type)
Container type
(e.g. normal, reefer, dangerous goods)
Maximum stack height
Constraints
Background and Previous Works
• Stacking policy based on multiple criteria [Park, T., 2010a] [Park, T.,
2010b]
• Multiple criteria are taken into account simultaneously by a scoring function
of a weighted sum
x a candidate position
Ci i-th criterion
wi weight for the i-th criterion
• The position with the best score is selected
• Stacking policy is represented as a vector of the weight values
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( ) ( )i ii
s x w C x
Background and Previous Works
• Stacking policy based on multiple criteria
• A policy consists of a set of rules for various container types
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Background and Previous Works
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• Stacking policy based on multiple criteria
Example: s7 (R7) for repositioning export containers
s7(x) = w34DI(x) + w35DO(x) + w36H(x) + w37E(x) + w38T(x) + w39G(x) + w40S(x)
DI(x)The distance in number of bays from the current location of the target container to the candidate location x
DO(x) The distance from x to a seaside HP of the block
H(x) The height of the stack at x
E(x)Indicates whether or not the candidate location is an empty ground slot
T(x)Indicates whether or not the container at the top of the stack at xis a repositioned container
G(x)The estimated likelihood of causing rehandling if the target container is eventually put on x
S(x)The amount of reduction in empty ground slots after putting the target container on x
• Deriving a robust stacking policy using a Noise-Tolerant Genetic
Algorithm (NTGA) [Jang, H., 2012]
• An evaluation of a candidate strategy demands an extensive simulation of
container handling in a block
• A strategy good for one scenario may not be so for a different scenario
• NTGA is provided with a pool of scenarios for evaluation
• A candidate strategy is initially evaluated by using a random couple of
scenarios in the pool
• If the candidate later turns out to be critical, then it is evaluated more
thoroughly using more random scenarios in the pool
• Final strategy thus obtained is the one with the best average
performance on various situations
Background and Previous Works
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Motivation
• Limitations of the previous works
• The strategy performs well on the average in a variety of situations
• The performance in a certain situation can be worse than that of the
strategy custom-designed for that particular situation
• What we want is a set of strategies that can take good care of a
variety of situations (or virtually any situation)
• How will that be possible?
• There exists not just a few discrete situations but an infinite number of
continuously varying situations
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Basic Idea
• We can derive a small number of representative strategies each for a
particular situation
• Given a new situation, we can apply the representative strategies
probabilistically according to their relevancies to the current situation
• Strategies are stochastically applied in such a way that a strategy for a
situation closer to the current situation is applied with a higher probability
• As a situation can be represented by a set of features, the Euclidian
distance between any two situations is easily calculated
• The application probability of each strategy depends on the distance to the
current situation from the situation that the strategy is specialized for
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Representation of a Situation
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• Suppose there are m indicators to specify a situation
• Then a situation e can be represented as a hyper-rectangle in an m-
dimensional space:
e = ([a1 , b1 ], [a2 , b2 ], . . . , [am , bm ])
where [aj , bj ] with aj , bj R represents that the j-th indicator takes the
value within the specified interval
Example: One-dimensional case
When the occupancy rate of the target storage block is the only
indicator of a situation
elow = [0 , 0.4 ] situation with occupancy rate 40%
ehigh = [0.6 , 1.0] situation with occupancy rate 60%
Distance Measure
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• The distance d(ei , ej ) between two situations ei and ej is defined as
Example: Distance in 2-D space
• Two indicators used:
– Occupancy rate
– Crane workload
• d(e1 , e2 ) is the distance between the
two nearest vertices
• The closeness (similarity) c(ei , ej ) between two situations ei and ej is
defined as 1 / d(ei , ej )
2/1
1
2
],[],[
)(min),(
,,
,,
m
k kk
baybax
ji yxd
kjkjk
kikik
ee
e1
e2
a1,1 b1,1 a2,1 b2,1
a2,2
b2,2
a1,2
b1,2
d(e1 , e2 )
Crane Workload
Occ
upan
cy R
ate
Scoring by Multiple Representative Strategies
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• Let si be the scoring function specialized to situation ei
• Then the score sc (x) of a candidate stacking position x in the current
situation ec can be obtained by
where c(ec , ei ) is the closeness between ec and ei
• sc (x) can be viewed as the expected score of position x when each
scoring function si for ei is applied probabilistically in proportion to its
respective closeness c(ec , ei ) to ec
m
i ic
m
i iic
cc
xscxs
1
1
),(
)(),()(
ee
ee
Case Study
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• The workload of the seaside crane is our only indicator of a situation
• The workload of the upcoming horizon can be estimated from the job
schedule
• We focus on stacking strategies for
el = [0 , vl ], when the crane workload is low
eh = [vh , ∞], when the crane workload is high
• Based on these two, we should be able to deal with any intermediate
situation in-between the two situations
Case Study
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• How can we derive those representative strategies?
• We need simulation scenarios to derive strategies
• For an accurate evaluation of a candidate strategy, it should be tested for a
long enough period of container ‘in’s and ‘out’s at a block
(About 2 weeks of yard operations per scenario in our experiment)
• Can we derive each strategy separately?
• Log data from real container terminals show continuously changing
situations
• Simulation scenarios with constant crane workload may be generated only
artificially
• But, what are good values of vl and vh ?
Case Study
• Our solution:
• Use scenarios of continuously varying situations
• Search for the two strategies simultaneously
• Also search for good values of vl and vh
• Evaluation of a candidate pair of strategies:
• The two strategies are probabilistically applied during the simulation of a
scenario of container handlings in various situations
• Average AGV delay and ET waiting time are measured for each simulation
min (w1 DAGV + w2 TET ) (w1 : w2 = 50 : 1)
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Indicators Strategies
el eh sl sh
vl vh wl,1 wl,2 … wl,k wh,1 wh,2 … wh,k
Experimental Setting
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Simulation Scenario
Loading Jobs 150 ~ 170 containers loaded per day
Discharging Jobs 150 ~ 170 containers discharged per day
Transshipment 80%
Duration of Simulation 10 days of initialization + 5 days of evaluation
Average Occupancy Rate 65%
Number of Scenarios 100 for learning, 100 for testing
NTGA Setting
Population size 100
Number of Evaluations 100,000
• Performance on 100 test scenarios:
• The t-test has shown that the difference is statistically significant
Experimental Results
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vl(sec)
vh(sec)
Average AGV delay(sec)
Average ET waiting (sec)
Pair of Strategies withOptimal vl and vh
118.9 1984.0 42.30 105.80
Pair of Strategies withHand-picked vl and vh
1500.0 2400.0 47.36 114.68
Single Strategy withBest Overall Performance
- - 44.65 130.98
• Comparison of the two representative strategies:
• Stacking locations of the discharged containers
• When the workload is low, the seaside crane tries hard to move as
many discharged containers to the landside positions as possible
Experimental Results
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Low Workload
High Workload
Se
asi
de Landsid
e
Average Travel Distance: 25.7
Average Travel Distance: 5.5
Experimental Results
• Comparison of the two representative strategies:
• Stacking locations of the export containers
• When the workload is low, the landside crane can move the export
containers at positions nearer to the seaside without interference
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Se
asi
de
Low Workload
Average Travel Distance: 42.3
High Workload
Average Travel Distance: 13.8
Landsid
e
Conclusion
• Previous methods derive a single strategy that shows overall best
performance in a variety of situations
• But the performance in a certain situation can be worse than that of
the strategy custom-designed for that particular situation
• We have proposed to derive a set of a few representative strategies
each for a particular (extreme) situation
• Given a new situation, we can apply the representative strategies
probabilistically according to their relevancies to the current situation
• A case study with the workload of the seaside crane as a sole
indicator of a situation has shown that a pair of good representative
strategies can be derived that works significantly better than a single
overall best strategy
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