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The simultaneous operation of the automated storage and retrieval machines (ASRs) in an automated warehouse can increase the likelihood that high power demand peaks tum unstable the electric system. Furthermore, high power peaks mean the need for more electrical power contracted, which in turns leads to more fixed operation cost and inefficient use of the electrical installations. In this context, we present a multi-objective genetic algorithm approach (MOGA) to implement demand-side management (DSM) in an automated warehouse. It works minimizing the total energy demand, but without increasing substantially the time for the operation. Simulations show the performances of the new approach.
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A Multi-Objective GA to Demand-side Management in an Automated
Warehouse
J. J. Cárdenas, A. García, J. L. Romeral, J. C. Urresty
MCIA Group, Universitat Politècnica de Catalunya
C/ Colon 1 TR 2-225, 08222, Terrassa, Catalonya, Spain
{juan.jose.cardenas; antoni.garcia; luis.romeral; julio.urresty}@mcia.upc.edu
Abstract
The simultaneous operation of the automated storage
and retrieval machines (ASRs) in an automated
warehouse can increase the likelihood that high power
demand peaks turn unstable the electric system.
Furthermore, high power peaks mean the need for more
electrical power contracted, which in turns leads to
more fixed operation cost and inefficient use of the
electrical installations. In this context, we present a
multi-objective genetic algorithm approach (MOGA) to
implement demand-side management (DSM) in an
automated warehouse. It works minimizing the total
energy demand, but without increasing substantially the
time for the operation. Simulations show the
performances of the new approach.
1. Introduction
Warehouse is a facility, which provides the services
about material storage and management to a
manufacturing firm or customer. Its efficiency is
depended about many factors and it is important because
costs incurred are reflected in the production or
distribution accounts, and are ultimately on to the
consumer [1]. Generally speaking, the efficiency of
warehouse operations is influenced by many factors such
as warehouse layout, storage policy, order picking
policy, etc. [2].
On other hand, it is observed that the simultaneous
operation of the automated storage and retrieval
machines (ASRs) in an automated warehouse can
increase the likelihood that high power demand peaks
turn unstable the electric system. Apart from instability,
these peaks cause the deterioration of the power quality,
increasing the dips and swells events, even operation
stops caused for power cuts. In general, the factories
oversize their electrical installations such that the
probability of this happens are very low. The over sizing
is to use cable with size greater than necessary, has
greater electrical cabinets and boxes, as well as to has
generators and transformers of greater power capacity.
Of course, this increases significantly the cost of
building an automated warehouse and the problems
about power quality remain. Furthermore, it is usual that
the utilities charge in the electrical bill the contracted
power, which is the power that the utilities foresee
available for a specify costumer. If the costumer over
pass this power it has to pay penalties, which increase
the electrical bill.
Hence, making efficient use of electricity is as
important as the optimization of any other resource or
raw material. In addition, energy optimization issues are
raising more and more due to the current worldwide
energetic problem. Therefore, it is essential to look for
methods or algorithms in order to improve the energy
use efficiency, even when we have to decrease a little the
performance of other parameters.
Nowadays, at scientific literature we can find
dissertations about subjects related with automated
warehouse, focusing in problems like optimization of the
best route of the ASRs, minimizing the storage and
retrieval times, and making policies to establishing what
it is the best way to allocation of the goods in the
warehouse. All these subjects are important in order to
reduce the operating time and improve the efficiency of
the system [3-6]. However, the simultaneous problem of
power peaks in factory installations has not been taken
into account directly in the scientific literature.
A simply solution in order to improve the energy used
could be sorting the start of the ASRs so that the
simultaneous start is avoided. It could be useful since the
peak power of rotating machines generally happen at the
beginning of the movement. However, this solution has
several buts: the peaks not always appear at the
beginning, and there are peaks at the end or in the middle
of the movement. Also, the length of the peaks is
variable and it depends on random variables as the
weight of the load, the distance to the goal place where
the load will be stored and the start point, the velocity of
the ASRs in x-axis as y-axis, etc. This shows clearly that
the problem is not trivial and it is not deterministic for its
random nature and it requires of a dynamic algorithm. So
stochastic methods are naturally selected for modelling
and optimization solution of such kind of problem [7, 8].
This is the main reason because the use of Genetic
Algorithms (GA) as first approach to search for the
optimal timing distribution of ASRs.
GA can run to optimize more than one goal. For
instance, having the energy management as an
scheduling problem, as already introduced, other
objectives can be taken into consideration, i.e, GA tries
to reduce the total energy necessary, but without
increasing substantially the time for the total movements.
This kind of GA is known as Multi-objective GA [9].
First in the paper, we present the modeling of ASRs
that is indispensable for the application. This is
presented in the Section II. In the Section III we explain
how deal with the problem using a MOGA and introduce
the main concepts about this evolutionary algorithm.
Section IV presents the got simulation results and finally
Section V draws some conclusions and further work.
2. Load Profile Modeling of ASRs
In a warehouse, the automated storage and retrieval
machines (ASRs) pick up and unload the pallets loaded
of goods, from a single starting point to some places on
the shelves. Each storage place has associated x and y
coordinates on the shelves. Normally the path followed
for the ASRs has triangle shame, as it is showed in the
Fig. 1. We have called cycle to this kind of movement.
Fig. 1. The typical path followed by the ASRs
(a cycle)
These movements are continually made (hence the
name “cycle”) until the planning of storage and retrieval
is finished. Considering this, we have made
measurements of different movements to random
coordinates on the shelves with and without load on the
ASRs. We have extracted from the real data a model that
is easy to use and it requires a few resources to its
management. Therefore, for a particular point (,),
we have obtained a model for each movement
decomposing it in x and y sub movements. We also have
assumed that the starting point has the coordinates (0, 0).
For this first approach, we have made the analysis and
management for only the movement with load that goes
from point 0 to the point 1 (Fig. 1) and return to 0 point
without load for two (2) ASRs. The aim of this is to
simplify the development but demonstrating the
feasibility and suitability of using such algorithms in this
type of problem. Moreover, to expand the GA to the full
cycle, and later do it to higher number of ASRs and
cycles will be an easy task. It is due that we have used
generic vector indexation for all variables, as explained
in the next section.
It should be noted that the load profile data could also
be extracted from a prognosis module of load profiles.
Therefore, we have not directly used the real data
because we suppose that in a full application we will
have a prognosis module of load profiles. This
hypothetical prognosis module could has as main inputs
the allocation coordinates [X, Y] from optimization
allocation module. It would be expected that such load
profile prognosis is not so accuracy and detailed for a
load profile with minutes’ resolution. Despite this, the
most important is that the general algorithm for DSM
does not ask for an accuracy prognosis of a load profile.
However, it is required that the prognosis shows the
form of the load profile and especially indicates with any
degree of accuracy and reliability of the occurrence of
power peak demand.
The measurements of currents were made with and
without load on the ASRs. The selected load profiles
(Fig. 2, Fig. 3 and Fig. 4) show clearly the main
characteristics of each one of the movements. It was
detected a strong dependency among them and the input
variables X, Y (Cartesian coordinates of the positions in
the warehouse) and the load weight. However, the form
of each profile in general is mainly dependent of the kind
of movement to execute (translation on the x-axis in
forward and reverse movement, elevation or descent on
the y-axis). As expected, the load weight and X, Y
position influence mainly the maximum peaks and the
duration of the profiles.
Fig. 2 is a clear example of the simplicity of the used
models. We can see in red, the real Load Profile (LP) of
some tested ASRs and in black, the proposed model.
This LP is for a particular movement, in this case the
translation on x axis (as it was explained former).
Fig. 2. The load profile of an ASR without load
in forward movement on the x-axis
Only five points characterize the model proposed for
this movement, and only three of them are
t1x tsu1 tba1 tntba2
Iini
In
Imax
Time (s)
Current (A)
Real Data
Model Data
(Ifin, tb a2)
y 1 (Unload)
2
(Reload)
(Starting point – load - unload)
0
x
representatives. The others are the initial and the final
points. These points are:
1. Init point: (Iini, t1x);
2. Maximun peak: (Imax, tsu1)
3. Nominal current: (In, tba1);
4. Down point: (In, tn);
5. Final point: (Ifin, tba2)
For the others movements (up and down) the
modeling are similar, the only different is the amount of
parameters because as we said before the LP is depend
about the kind of movement.
In the Fig. 3, again, we have in red the real data and in
black the proposed model for the up movement. In this
case, the parameters of the model are:
1. Init point: (Iini, t1y);
2. Nominal current: (In, tsu1);
3. Down point: (In, tn);
4. Final point: (Ifin, tba1)
Fig. 3. The load profile of an ASR without load
in up movement.
Finally, in the Fig. 4 we have the model and real data
for the down movement. The main parameters are:
1. Init point: (Iini, t2y);
2. Current first peak: (Ipeak1, tsu1)
3. Nominal current: (In, tba1) to (In, tn);
4. Current second peak: (Ipeak2, tsu2);
5. Final point: (Ifin, tba2)
Each of these movements is related to its
corresponding motor on the ASR. It has a motor for
movement in each axis, hence the LP in Fig. 2
corresponds to the motor for movement in x-axis
(horizontal translation) and the LP in Fig. 3 and Fig. 4
correspond to the motor of the movement in y-axis (up
and down). Therefore, to get the total LP of a storage
process (round trip) we have superimposed the
corresponding LPs depending on their temporal location.
In the Fig. 5 is showed the LP for a full movement of
storage below to an ASR. The LP is divided in two parts:
at the top is the LP of the axis-x movement and the
bottom is the LP of the axis-y movement.
Fig. 4. The load profile of an ASR without load
in down movement.
Fig. 5 shows how the timeline is segmented for each
of the steps performed by the ASR in a storage
movement.  and  are the start times. So ∆ and
∆ are the used delays to avoid the simultaneous start
of the motors among those belong to the same ASR and
among the motors of the different ASRs in the
warehouse. The translation movement with load is made
between and  times; the up movement with load,
between and  times; so far as the going movements
are executed, then the going time is determinate for the
longest between and . When [X, Y] position are
gotten the fork movement is executed. This is to leave
the load on its storage position and it takes the time
interval between and the final going time ( or as
appropriate). Then, the ASR has to return to the starting
position and pick up the next load. The return without
load movement has the following sequence: again there
are delay times to avoid simultaneous start and these are
∆ and ∆; the return horizontal and the down
movements are executed between  and , 
and  times, respectively. The total time of the whole
movement will be the maxim between  and
. It has been show the modeling of the load
profiles, and it is an important highlights their simplicity
and practicality, which make it suitable to be
implemented for a prognosis algorithm, for example,
mean artificial neuronal networks.
t1x Tx tf t2x Txtotal
0
5
10
15
20
Time (s)
Current (A)
t1y Ty tf t2y Tytotal
0
5
10
15
20
Time
(
s
)
Current (A)
A ASR LP for X motion
A ASR LP for Y motion
Fig. 5. Decomposed Full LP for an ASR.
t1y tsu1 tn tba1
Iini
In
Time (s)
Current (A)
Real Data
Model Data
(Ifi n, tba2)
t2y tsu1 tba1 tn tsu2 tba2
Iini=In
Ipeak2
Ipeak1
Time (s)
Current (A)
Real Data
Mode l Da ta
(Ifi n, tba2)
3. Genetic Algorithm Solution
The proposed solution based on a Multi-Objective
Genetic Algorithm (MOGA) is presented in the Fig. 6 as
a general block diagram. Its main objective is to get the
optimal delay times [∆, ∆, ∆, ∆]Mx4 (M is the
number of ASRs) for each ASR in the warehouse but
without increasing substantially the time for the
operation. The first block has as inputs the [X, Y]Mx2
coordinates, which determine the position where the
goods have to be stored or retrieved. This block is used
to get the LP prognosis, which has been replaced on this
occasion for data derived from actual measurements (see
section 2). The next block is the MOGA optimization,
where the MOGA is executed and it has as outputs the
delays that optimize the use of the available electric
power. The final block is only used to visualize the
results and do the comparison between the init and final
data.
For this first implementation we have only had into
account two ASRs (M = 2), which are named A and B. In
addition, the route used by the ASRs is only a movement
of going and back. The aim of this is to simplify the
development but demonstrating the feasibility and
suitability of using such algorithms in this type of
problem. However, there are no constraints to increase
the number of ASRs relative to the MOGA
implementation. The having more ASRs or machines to
management mainly affect the convergence time of the
MOGA. This was tested in another application where
fictitious load profiles were used to simulate the
management of multiples machines (for example, more
than 10 machines). Although the convergence time was
increased, the generation’s number remains about
constant and such increase it was not so much in
comparison with simulations with a low number of LPs
(for example, less than 10 machines) The extension from
two ASRs to M ASRs does not have enough problem
since a generic vector and matrix indexation has been
used.
Fig. 6. The general block diagram of the
proposed solution.
3.1. LP Prognosis
An important premise for the good performance of
this block is that it must be possible to have a schedule
of the allocation of goods for a certain period. Therefore,
taking advantage of the modelling here presented, it is
possible to implement an algorithm to do the prognosis
of the load profile in function of the [X, Y] coordinates.
It could be an algorithm with artificial neural networks
or even an easier algorithm like a lookup table. This part
of the whole application is pending of developing. Now,
we have used the directly obtained models from the real
data.
In order to implement this module, we divided it in
two parts, as showed in the Fig. 7: The “Get Model
Parameters” and the “Make Load Profile” sub models.
The first has the task of getting the main parameters of
each LP, as showed in “Load Profile modelling of
ASRs” section. Now it is made of a semi-automated
way. The second sub model uses the obtained parameter
to concatenate the vector that represents each LP. These
vectors are A.lp and B.lp and others parameters that are
incasuled in A and B structures.
Fig. 7. Block diagram of the prognosis module.
3.2. MOGA and GA solution
Multi objective problem looks for the optimization of
two or more utility functions since it is normal that in
optimization problem we want to minimize or maximize
more than one variable. Like this case, where we seek to
decrease the power peaks but without affect the
performance of the whole storage system, particularly
the times of operation. In order to get these objectives,
here we propose a multi objective genetic algorithm.
In the multi objective optimization, is normal that
whereas one variable is being optimized the other one(s)
is (are) being affected negatively. Then the search of an
optimal solution has to be traded off in some way. So the
concept of nondominated or noninferior variables and
Pareto optimality appear [10].
GA consists on searching algorithms based on the
mechanics of natural selection and natural genetics. They
combine survival of the fittest among string structures
(chromosomes) with a structures yet randomized
information exchange to form a search algorithm with
some of the innovative flair of human search. In every
generation, a new set of artificial chromosomes (strings)
are created using pieces of the fittest of the old; an
occasional new part is tried for good measure; these new
chromosomes are gotten means functions or operators
that mainly emulate the evolutionary processes of
selection, mating and mutation. While randomized,
genetic algorithms are no simple random walk, they
efficiently exploit historical information to speculate on
new search points with expected improved performance.
These algorithms are computationally simple yet
powerful in their search for improvement. Furthermore,
they are not fundamentally limited by restrictive
assumptions about the search space (assumptions
concerning continuity, existence of derivatives,
unimodality, and other matters) Genetic Algorithms have
been developed by John Holland, his collogues, and his
students at the University of Michigan [10].
The Fig. 8 shows the flowchart of a standard GA.
Firstly, the initial population is obtained by means of
random initialization of the each chromosome of the
population. The number of individuals or chromosomes
is a very important parameter of the GA. So the diversity
of the population depends on population size and that
guarantees the no getting into local minimum.
Nevertheless, a very large population could make so
slow the execution of the GA. For this application, we
chose a population initial of 60 individuals (it is a good
start point to try with a population of 15, where is
the number of fitness functions to be optimized).
Fig. 8. Flowchart of a GA.
Next it is executed the calculation of the fitness
functions. This is the function objective, which has to be
minimized. In this case, we want to minimize the power
peaks of the total load profile. Therefore, the fitness
functions are determinate by means of the next
equations:
: time.
: number of the actual iteration.
: number of ASRs.
,: value of the fitness function 1 for the iteration
(Power peak value)
,: max power peak for the iteration .
,: the load profile of the ASR , in the iteration
. : vector or matrix [∆, ∆, ∆, ∆]Mx4 of time
delays that determinate the sequence of start of the
ASRs.
,: value of the fitness function 2 for the iteration
(total delay time value)
,: total time of the total load profile for the
iteration .
,: initial total time of the prognosis of the total
load profile.
, 
,  ,
 1
, 
, , (2)
  (3)
min (4)
Then the equation (4) is the target of the MOGA and
the vector is formed for the time delays that
determinate the start of the ASRs as it is showed in the
Fig. 5. Thus, the immediate coding of the chromosome
of the GA is the showed in the Fig. 9. The first 4 gens
belong to the A ASR and the next 4 to the B ASR.
Fig. 9. String coding for the GA of the
proposed solution.
The next step of the GA is the evaluations of the
several optimization criteria are met. If so, the GA is
stopped, or else, the evolutionary operators are used in
order to get the next generation.
The used operators in this application were the
selection, crossover and mutation ones. As its name
suggests the selection consists in to select the best
individuals from actual population. There are many ways
to execute this operator [10]. Here we pass them to the
next generation directly. The number of selected
individuals is another parameter of the GA and
determinates the degree of opportunity reproduction of
the best individuals. This is named the selective pressure.
The crossover or mating is the process of crossing over
the genetic material from the parents to create the
genetic material of the children. The crossover can be
done of different ways. In this case, we have used the
scattered function, which takes the genetic material from
two parents and crosses over them following a generated
random binary vector. Where the binary vector is 1 the
gens are taken from parent 1 and in another case from
parent 2. For example, if p1 and p2 are the parents
p1 = [a b c d e f g h]
p2 = [1 2 3 4 5 6 7 8]
And the binary vector is [1 1 0 0 1 0 0 0], the function
returns the following child:
child1 = [a b 3 4 e 6 7 8]
Mutation operation applies random changes to
individual parents to form children. Mutation provides
genetic diversity and enables the genetic algorithm to
search a broader space. We have used Gaussian
mutation, which adds a random number taken from a
Gaussian distribution with mean 0 to each entry of the
parent vector.
In summary, the final settings of the GA used were:
Initial population: 60 random generated
individuals
Next generation: 2 selection + 16 crossover + 2
mutation
Selection: stochastic uniform.
Crossover: scattered
Mutation: Gaussian
Next, we continue with the simulation results that
were got by means of this configuration of the GA first
approach solution.
4. Simulation Results
In the Fig. 10 is presented the simulation results. The
initial LPs are at the top plot, the GA LP result are at the
middle, and MOGA LP results are at the bottom plot. In
all, the load profile of A, B and the total is in blue, red
and black respectively. With a simple inspection, we can
notice the differences in terms of duration, appearance
and peak profiles. In the initial load profiles, we have a
maxim peak of about 56 A that occurs around the 4
seconds.
This peak is generated by the maxim peak of A and
the rising load profile of B. Remember that each load
profile is built by the addition of the load profile of each
motor in the same ASR and the total load profile by the
addition of the two ASRs under test, A and B. These
initial profiles are the supposed prognostic load profiles.
At the middle are the final load profiles after the GA
execution and reordered the start times of each motor in
both ASRs. There we can see as they have changed.
Now the maxim peak on the total load profile is 46 A at
the 5.5 s time. It has been reduced in 21 %, which is an
appreciable result. However, the total time has been
increased. The initial total time was about 29 s and after
the rearrangement, this was about 34 s, 5 s more than
initial time. At the bottom of the plot, the final load
profiles after the MOGA execution. Now, note carefully
that the maxim power peak has decreased with respect to
the initial one, but the total time remains constant. This
shows the effectiveness of the MOGA versus the GA.
However, the only disadvantage of the MOGA is that
it took more iterations than GA. The table 1 we can see
the summary of the results of both implementations.
The Fig. 11 shows the Pareto front obtained by the
MOGA. This lets us see the behaviour no lineal of the
functions to optimize. In addition, we can see as the
performance of the best individual decreases in terms of
maximum delay, whereas performance increases in
terms of reducing peak.
Fig. 10. Initial (at the top) LPs, GA (at the
middle) and MOGA (at the bottom) LP results.
Description GA MOGA Unit Observation
ASR number 2 2 uni A and B
Motors for control 2 2 uni x and y axis
Total searched delays 8 8 uni 4 by ASR
Allowed maximum
delay 5 5 s
Iterations or
generations 52 123
Maximum got delay 4,9 5 s
Initial total time 29,4 29.4 s
End total time 34 29.5 s
With MOGA
the total delay
is less
Initial maximum total
load peak 56 56 A
End maximum total
load peak 44 44,49 A
Load peak reduction 21% 21% %
Table 1. Summary results for the Implemented
GA and MOGA.
The CPU time used by the MOGA is considerably
longer than the used by the GA. The first takes about 90
seconds and the second about 3 seconds. Take into
account that due to the nature stochastic of both
algorithms the CPU time changes in each execution, then
the given values are the average times for several
simulations. The CPU was an Intel® Core™2 Quad
CPU Q6600 @ 2.400 GHz.
0 5 10 15 20 25 30 35
0
10
20
30
40
50
60
Time (s)
Current (A)
0 5 10 15 20 25 30 35
0
10
20
30
40
50
60
Time (s)
Current (A)
A ASR LP
B ASR LP
Total L P
A ASR LP
B ASR LP
Total L P
0 5 10 15 20 25 30 35
0
10
20
30
40
50
60
Time (s)
Current (A)
A ASR LP
B ASR LP
Total L P
Fig. 11. Pareto front.
Despite these results, the MOGA and GA algorithms
are considered feasible of being used since they will be
used in off line application, together the algorithms for
optimizing the pallets location. These are typically
executed before the storage and retrieval process begins.
5. Conclusions
It is important to notice that energy optimization
issues are raising more and more due to the current
worldwide energetic problem.
A MOGA and GA approach for solving the
sequencing problem to get optimal use of available
power in an automated warehouse was implemented
with appreciable results about reducing the instantaneous
maxim power demand without increasing substantially
the time for the operation.
This shows the feasibility and the potential of this
kind of algorithm to solve problems of DSM in
automated warehouse.
To develop a full DSM application, the next step is to
implement a prognosis algorithm to get the load profile
prognosis. This algorithm could be a neural network in
order to take advantage of the method of modelling
proposed here. By this way, the whole system can be
tested in a real application.
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... TheFig. 5 shows an example the demand optimization where the maximum demanded power has been reduced by means of a genetic algorithm [3, 4], which look for the optimum scheduling of consumptions to avoid peaks and use the same or less energy in the affected process. The upper graphic in theFig. ...
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Building and planning for industrial storage and distributionIntelligent control mechanism of part picking operations of automated warehouse
  • J Drury
  • P Falconer
J. Drury and P. Falconer, Building and planning for industrial storage and distribution, 2 ed.: Architectural Press, 2003. [2] S. Chwen-Tzeng, "Intelligent control mechanism of part picking operations of automated warehouse," in Industrial Automation and Control: Emerging Technologies, 1995., International IEEE/IAS Conference on, 1995, pp. 256-261.