Cost Optimization of Feed Mixes by Genetic Algorithms

powemryologistAI and Robotics

Oct 23, 2013 (4 years and 15 days ago)

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1



Cost
Optimization of F
eed

Mixe
s
by G
enetic Algorithms


M. Akif ŞAHMAN
1
, *Mehmet ÇUNKAŞ
2
, Şeref İnal
3
, Fatma İNAL
4
, Behiç COŞKUN
5
,

Uğur TAŞKIRAN
6


1,2,6)
Selc
uk
U
nivers
ity,
Faculty of
Technical Education
,

Department of
Electronics and
Comp
uter

Education

42
003,
Konya
, Turkey

3)

Selc
uk
U
nivers
ity
,
Faculty of Veterinary Medicine,
Zootechny
,

420
40
,
Konya
, Turkey

4,5)

Selc
uk
U
nivers
ity
,
Faculty of Veterinary Medicine
,
Animal Nutrition and
Nutritional
Diseases,
42
0
40
,
Konya
, Turkey

1
akifsahman@gmail.com,
2
mcunkas
@
selcuk.edu.tr



*
Corresponding author



ABSTRACT


The cost optimization is a key element to determine the least
-
cost feed mixture according
to animals’
nutrient requirements
an
d the effective use of the sources.
In this
paper
,
the
cost
optimization of feed
s

is
performed

by

genetic algorithm
,

considering

the growing style and
type, age, nutritional requirement and feedstuff costs for poultry and different types of
animals
.

The
pr
oposed method

is

compared with linear programming
approach

to
measure

its

performance
.
The
obtained
results

show

that Genetic algorithms could be applicable
to

the
cost optimization of
the
feed

mixture
s
.

In addition, a software program is
developed

by usin
g
Delphi
environment
, which

provides flexible
,

extensible and user
-
friendly
framework

for
tuning

the heuristic relevant parameters
and improving

the solution

quality
.

Key words:

feed mixes,
poultry,
ruminant,
genetic algorithms, cost optimization.


1.

I
ntrod
uction

The
problems related to inadequate nutrition

that

arise from rapid population growth are
more prevalent in the world
.

Although there has been production growth, the
problems

could
not be solved both quantitatively and qualitatively.
On
the contrary,

the
unequal income
distribution creates more problems for the low income section of the population [1].

For
2


human beings to grow up and to live
a

health
y

life, they need to include some protein to their
diet.
Poultry meat and eggs are the primary supplies

of the mentioned protein sources.

Balanced and adequate nutrition

is required for
animals to be healthy and productive. Also
considering the animals’ consumption, to meet their
nutrition
al

requirement
s
,

feed

mixes

should be prepared.
The feeding is m
ost i
mportant factor
affecting the production cost in

animal
breeding industry

s
uch

that
it is

about 70 to 75% of the total production cost.
This is
also for only if one applies a scientific feeding program, otherwise the cost will be more than
the
aforemention
ed percentages
.
The
feeding requirements change according to the animals’
kind, age, and the productivity expected
from the

animals.

Consequently feeding cost is so
important for the feed
industry

that
i
t is only possible

to
meet the
nutritional

requiremen
ts of
the animals

if the stockbreeders have
a

scientific approach to the problem [2].

When the feed

mixes

are prepared
, it is desired that it should both meet the animals’
nutritional needs and be low cost.
In such cases,

it is necessary to
u
tilize

optimiz
ation
techniques
.

L
inear
and non
-
linear
programming techniques have been used
for over two
decade
in many studies
:

the allocation of milk resources for cheese making [
3
]
,
animal diet
formulation [
4
], life cycle assessment [
5
],
e
valuati
on

of
nitrogen taxati
on scenario

[
6
],

o
ptimiz
ation of the performance r
esponse
to energy d
ensity in
b
roiler
feed f
ormulation

[
7
],
c
ost and benefits for the segregation of compound feed [
8
]
.


The

present

studies
have
demonstrated advantage of utilizing the optimization procedur
es
to
meet
the mentioned
objectives
. However in

determining least
-
cost feed mixes
, the
linear
/
non
-
linear constraints are

increasingly complex

and difficult to
handle
.

In such conditions,
application of standard
linear or
non
-
linear programming techniques

are both time consuming
and insufficient.

In recent years,
Genetic Algorithms, therefore, have

wide application
in
various
fields

of
science

and technology

such as
bioinformati
cs
,
manufacturing
,
engineering
,

ec
onomics
,

3


mathematics
,

chemistry
,
physics

and
etc. One of the advantages of the genetic algorithms
(GA) over standard nonlinear programming techniques is that GA can find global minimum
instead of local minimum. The other advantage is that GA does not need derivative
calculation of the function that m
ay not be readily available or very hard to calculate [
9
]. GA
can reach to solutions quickly and be applied on the complex optimization problems
easily
and plainly [10
].

In this study,
a
n

approach
finding
least
-
cost

feed mixes
, which satisfy the nutrition
al
requirements for poultry and different types of animals (cattle, sheep and rabbits etc.),
is
proposed

by using genetic algorithm
s
.

So the complex constraints are handled taking into
account relationships between ingredients and the nutritional value of
the
feed mixes
.
The
results obtained

are

compared to
linear programming model
.

The overall r
esults show that the
genetic algorithms can be used for

determining
least
-
cost feed mixes
.

Furthermore
, a

software
program is

developed

by using object oriented vis
ual Delphi environment
for poultry animals
and domestic animals (cattle, sheep and rabbits)
.

It has ability to illustrate
visually
the
optimization results

and
to
analysis
the relevant
parameter
s

in simulation
.

2.


M
aterial
s

and
M
ethod
s

The database used in

t
his study
was

taken from Selcuk University
Faculty of
Veterinary
Medicine

[11].

The nutritional values and
the
contents of feeds used in the feed mixes

wer
e

available

in the aforementioned database
.
The nutritional needs for
s
o
me animal species
were

taken
from the supplier firm
s

guide booklets and NRC [
12
] and
their values
were

added to the
database.

While the feed mixes are
formed
,
the
ingredient
s

are chosen according to
economical

status
,
appropriateness

for the digestive system of the animals, and nutrit
ional value
.

First, the

nutri
en
ts of the feeds obtained by chemically
are offered to the users.
Also approximate price
of the
ingredient
s,
as well as
the maximum and minim
um values which can be mixed in
to the
4


feed
,

are added to the database. These are not
constant and can be changed according to
animal species, raw material stock and current market prices

[11]
.

T
he
nutri
ents

for the poultry animals

can be

arranged as:
crude
p
rotein (
C
P
),
M
etaboli
zable

E
nergy (ME),
C
alcium (Ca),
Avail
able
P
hosphor
us

(
NP
P
),
S
odium (Na),
M
ethionin
e

+

C
yst
e
ine

(Met+
Cy
s
),
L
ysine

(
L
ys
),
T
hreonine

(T
h
r), Tr
yptophan

(
Tr
y
),
linoleic

a
cid
(LA).
As
for cattle, sheep
,

and rabbit

are
crude

protein (
C
P
),
M
etaboli
zable

E
nergy

(ME),
C
alcium

(Ca),
P
hosphor
us

(P),
S
odium

(Na),
Crude fiber

(
C
F
),
A
sh

(
Ash
)
. These
nutritional
needs are pre
-
calculated with the tolerance limits for the chosen animal species
,

and listed into the database.


The primary objective here is to determine the feed mixes which meet the animals’
nutritio
nal needs and have

m
ost appropriate cost.
By using Genetic algorithm (GA), t
his

optimization problem is
attempted

to be solved
.
GA
is

a
well
-
known
algorithm among

the
stochastic algorithms

whic
h imitate

the biological process

and
optimizes the functions

accordingly

[1
3
]
.

In t
his study, a

computer program
was

developed
using Delphi7
programming language
to optimize
the cost of
feed mix
e
s for both poultry and other farm
animals (cattle, sheep, rabbit etc.)
[19]
.

Real
-
coded G
enetic
A
lgorithm

(RGA)
was

preferred

for program develop
ment.
The chromosomes
involving

the possible solutions
in
the
R
GA
are
represented with real
-
number values which
are

within

the limits of solution space
. This
feature
is the basic difference between the binary G
A

(BGA)

and RGA

[
14
].
The precision is
one of
the important points for the solution of the problem. Because the
B
GA is represented
by using “1” and “0”, chromosome dimensions become extremely large resulting limited
precision.
I
t encodes parameters as finite
-
length strings such that
the encoding and d
ecoding
processes
waste much
computation time

and lose precision of parameters
.

Therefore,

RGA
coded by using real valued numbers has advantageous over
B
GA
, and
converges

faster
to

find
global
optimum [
15
].
The f
low chart
of
the
proposed method

is given in
Fig
.

1.

5


First
, animal data and feed data which may meet the
nutritional
needs of the animal

should be
entered to the system
.

After inputting the data about the animals and the feeds,
the following

steps are run one by one in order
.



Form the object functio
n
,



Define the constraints and limits of the p
roblem,



Generate

the
initial

population
,



Calculate the penalty

values

according to constraints and limits
,



Calculate
the fitness values of
the population according to object function
,



Apply
s
e
lection
,

c
rossover,

mutation
,



Test the convergence
, and repeat the process until achieving the
desired

solution.

2
.1

Animal

and feed
data

To determine whether a feedstuff will satisfy an animal needs, n
utrient contents of the
ingredients are considered

in
manufacturing and t
he analysis of
feedstuff
.

The
nutrient
requirements

for the poultry and cattle are given in Table 1 and Table

2
.

Table 3
and Table 4
contain

the nutrient content of feed ingredients
,

the unitary cost of
each

ingredient
, and the
lower

and
the upper
ingredie
nts
limits
for poultry

and catt
le.
T
he
unitary cost of e
ach

ingredient

in the tables is given as Turkish Kurush (
e
xchange rate about 1
US penny = 1.6 TR Kurush)
. However
the optimization results are presented both as US
penny and TR Kurush (Fig.
3

and Fig.6
).
E
leven ingredients and ten nutrients
for poultry,
as
well as

seven

ingredients and
eight

nutrients

for cattle

have been used

in this study.


2
.2

Initial population

Wh
ile
the initial population is
generated

randomly,
the lower and the upper
ingredients

l
imits
in the feed

mixes
(Table 3
-
4) should

be taken into consideration.
Let
x = (x
1
,x
2
, . . . ,x
n
)
,

where
x
i
,
i

=
1
,. . . ,n

indicates

the proportion of ingredient
i
th

in the
feed mix

and
n

is the
total number of ingredients available.

6


T
he
initial populati
on is
generated

as follows:






(1)

w
here

P
H
and

P
L

are

the lower
and upper
limit
s

of
parameter
s
, respectively.

The
is
the
random number produced in closed interval
[0, 1]

for
j
th population and
i
th
pa
rameter (ingredient)
.


Then t
he

object
function
, the feed cost
,

is defined as
:









(
2
)

w
here
c
i

is the unit price of ingredient
i
.

2
.3

Constraints

Some of the
ingredient amounts

should equal to specified values at the preparatio
n of the
feed mixes to meet the nutritional needs.
These amounts reflect
total values of the
ingredients
in the feed mix
es
. Consequently, some constraints

are

imposed

in the optimization.

Nineteen

constraint functions are defined
as equation (3)
for poultr
y
according to

Table 1.

In th
e same

way,
nine

constraint functions are defined
for cattle
according to

Table 2.





………………….









(3)


7


Th
e
sum of violated constraints for
each

chromosome (
individual
)

of the population is

calculated as follows
:









(4)

Where


rep
resents

the
sum of violated constraints

of
j
th

population.

The
k

is the
number of

constraints.

The
Ap
j

is
an
additio
nal

penalty
defined to increase the quality of
solutions
.

T
he entire feed mix should be 100

kg

in total
. The values over and under this value
are also
added to

total
penalty
value as additional penalty (
Ap
j
)
.
Besides, s
in
ce t
he orders of
magnitude of the various constraints are much different from one to another
,
the
constraint
functions

are normalized
.


2
.4

Selection

T
ournament selection is used

as selection method
.
T
he
number of tournaments is equal to
the
number of the
individuals

of population
. The

random number
s

are
generated for
which
the
individuals of population

are
subject
ed

to

the tournament. The winners are transferred to the
next generation as the parents. The selection process is done according to the below sta
ges
.

If both chromosomes
are
in the non
-
feasible region
, the one which has lower penalty
value

is
transferred to
next generation
.

If one of the chromosomes is in the

feasible region
, this
chromosome is

transferred to
next generation
.
If both chromosomes ar
e in the
feasible region
,
the fitness values

for these two chromosomes

are

calculated and the chromosome having the
best
fitness value is chosen
[
16
]
.

Besides
, elitism method is also included in
the
selection
process. According to elitism, some individual
s

determined by the users are
transferred to
next generation, which are not subject to tournament.

2
.5

Crossover

Crossover is
an operator

used
in order to
increas
e

the diversity of the population and
produc
e

better chromosomes.
One
-
point or multiple
-
point c
rossover
may be
applied on the
8


population
by using the crossover rate
.
The
individuals

of population

are

chosen according to
crossover
rate
,
and
paired

randomly.
One and more random points are chosen in the selected
pair of strings and the substrings are e
xchanged as of the chosen points.

So t
h
e crossover
mixes information from two
-
parent string, producing
new
offspring
.

T
he

one
-
point crossover

which

is a combination of heuristic crossover method and extrapolation crossover

is used in
this study
, and

can be

defined as

follows
: [
1
7
]








(
5)










(6)

Where
α

is a random point se
lected to perform the crossover,

β is randomly produced
value between

0
and

1
.
The
strings of parent
are mixed by using equation (6) and the new
generation
becomes

as
follows
:







(7)

2
.6

Mutation

An

impor
tant operator of the GA is mutation
, which makes random changes on
chromosomes and thus it
increase
s

the diversity
in the population in order to avoid local
optimum

[1
8
]
.

A

random number is produced
in interval [0, 1]
for
every

gene

of individual

in
popula
tion
,

and compared to mutation
rate.

If this random number is
below the mutation
rate,
the gene is

mutated
.

That is,
the old value is replaced by the recently
produced
values.


2
.7

Convergence t
est

N
ew generations
have

now
been

achieved

us
ing

the genetic o
perators like selection,
crossover and mutation.
Naturally
,

the

generation

is

the

parent of the next generation and t
his
process continues until reaching
a predetermined

generation

number
or
meeting
an
object
.
9


The most important thing here is the choosing
of the stopping criterion
which requires the
evaluation of

the problem accordingly. In th
is

study,
the
generation

number

is
preferred

as
stopping criterion.

After the completion of the loop, the

optimization results

are displayed as
a
l
ist.

3.

The Software Pr
ogram

The software allows users to be able to perform

their experiments through an easy

and
simple
visual programming paradigm

as well as to tune
the relevant parameters in a
simulation
, and
to
illustrate the optimization results
by d
ynami
c and static grap
hical displays
.
The
main
interface of
the software working

in a

Windows environment

is
demonstrated

in

Fig.
2
.
The
explanation
s
related to the parts of
the
interface
which are
numbered

as shown in
Fig.2 are

given
in the following
.


T
he

species and type of a
nimals

are shown

in Part
-
1
.
Unlike other animals;
t
here is
a

type
selection

for the poultry animals
o
n the interface.

T
he constraint values are displayed

in Part
-
2
, which are the values after the optimization
.
In addition, the c
onvergence graphs for the pe
nalty and cost are drawn according to changes
during optimization pro
cess. These graphs are accessed

by pressing desired button on the top
of the screen.

T
he
ingredients
are
presented

in Part
-
3
.
This section allows us to review available
ingredients before

starting the optimization, and
to

choose ingredients from available list
according to our decision.

The
ingredients

which will be included to the optimization can be
chosen by clicking “+” and “

” buttons
.

Also the optimization results related to poultry
or
other animals (Sheep
-

Cattle


Rabbit) are shown.

Total cost and penalty value
s

dynamically
change while the program

is running
.

10


T
he g
enetic parameters like population number, generation (iteration) number, crossover
,

and mutation rates can be
set

in Pa
rt
-
4
.
Renovation

rate
is

also used to
avoid

the local
minimums.


T
he features like
retrieving

and
recording

simulation data,

choosing and removing

of
the feed and animal data,
producing a new solution

from random strings
or

load
ing

an initial
solution

fro
m
last simulation session
,

and solving by convergence for bad penalty
values

can
be done
in Part
-
5.

The solv
ing by convergence is
designed

to get better solutions by using the
previously found
solutions.
So the a
ppropriate
one

from the previously found
sol
utions

is

chosen and the program is rerun according to the given
settings
. With the button “
save
ration”
a form related to recording of the rations is opened.
On the other hand “
read

rations” button is
used to reenter the previously calculated and recorded

rations’ values to the system
.
The
button
s,
“clear feeds”

and
“clear animals”

are
used to delete

feeds and animal data,
respectively. The “analysis by value
s
” is the solution process
for the manually entered
values

of feeds which are
already put in
to the
system
.

4.

The Simu
la
tion Results

In this section, the results obtained from
GA

optimization
are presented
and compare
d

with
linear programming
model
.

The values suggested in
the
literature are preferred

for the settings
of the parameters
.
Since G
A

is a rando
m search algorithm,
different results
may
be obtained
at the end of

the

every run

depending on the initial random seeds
.
So
, t
en

independent runs
that have different random seeds are performed

to achieve a good solution.
The

parameters

used
in simulations
are

given
in the following.

Number of the Population


: 200

Number of the
generation



: 1000

Crossover rate




:
0.
8

Mutation rate




: 0.
01

11


4.1.

The simulation results for
poultry

In this case
, poultry

species
and type
were

chosen

as follows:

Poultry Specie
s


:
Chicken



Meat Type



Breeder

Poultry Type


: Arbor Acres
Broiler

Breeder
,
Start
er

(0
-
4 Hf)

After completing the simulation, the best solution was shown

in Fig. 3. In addition,
penalty value, total cost, and total amount of feed mixes were given.
The
penalty
value

is very
low as can be seen from the
F
ig
.
3
. The state of the constraints
for
the best solution

obtained

is
given in the Fig
.

4
. When the results carefully
are
examined, it can be seen that
crude
protein
(
CP
) and

metabolizable
energy (ME) value
s are

over
,

Met
h
ion
in
e



Cystine (Met+
Cyss
)
values are

under, and the rest is equal to the given values.
If one thinks that these values
obtained with zero tolerances, the results are greatly acceptable.
T
he requirement values
are

not
available yet f
or con
strain
t
s of
Threonine (T
hr
) and Tryptophane (Tr
y
)
, and
there is no
upper limit for
Linoleic
Acid

(LA).
Therefore the

mentioned three
constraints
are excluded
from optimization
.

The c
onvergence graphic

of penalty values

can be seen in the Fig
.

5
.
It is impo
rtant to
form

a mix
of
the 100

kg, consequently
the
feed
amount

is attempted to
complete

to 100

kg.
Last penalty

shows the penalty value after the missing
amount

to
complete

the 100

kg is
distributed. If the

Fig.
5

is examined carefully,
the
algorithm conve
rges to the result quickly.

4.2.

The simulation results for cattle

The
cattle species and type were chosen as follows:


Animal

Species


:
Cattle

Animal

Type


:
Cattle Milk Feed, 18, 2600

After completing the simulation, the best solution was shown in Fig. 6. M
oreover, penalty
value, total cost, and total amount of feed mixes were given.
The state of the constraints for
the best solution obtained is given in the Fig. 7.
Total
nutrients

for all ingr
edients are in the
12


constraint

values for th
is case.

The obtained
ration meets the needs of the animal.

I
t can be
seen from Fig
.

6
, there is no penalty
value

after the simulation
.

The penalty convergence and
the
cost converge
nce are given in Fig
.

8

and Fig
.

9
,
respectively.
As can be seen from the Fig
.
9
, t
he last calcul
ated cost shows the cost after the
amounts

are adjusted for 100

kg.

A small increase or decrease

in final c
ost
can be
according
to
the required
ingredient
which
is
inclu
d
ed

to
complete

the predetermined 100

kg value.
While the cost is 33.59 Krs/Kg before t
he rations
are completed to

100

kg,
after being
completed

the final cost

becomes 33.61 Krs/Kg
.
It is shown that
the
final
cost increases
a
small amount
.

4.3.

Comparison

Coşkun et al [
11]

have developed least
-
cost mix
preparation

program

for both poultry and
cat
tle

by using
linear programming technique through
MS Excel
Solver
.
For example,
let’s

consider
a
Broiler Commercial
.

Table 5

and 6
show the
ingredients

limits
in the feed

mixes
and t
he nutritional requirements
, respectively
.

The
constraint functions
can be

defined
as
equation (3)
using
the constraint values given in
Table
6
.

C
ost optimization using these data
was performed by linear programming technique and Genetic Algorithms
.

T
he results obtained
from GA
were

compared with the results of Coşkun et al [11].
Table
7

shows the comparison results

which are
obtained by using the same ingredients and
constraints

for both approaches
.

Where
, “0” and “1” denote the selection of appropriate
ingredient
and
i
nappropria
te
ingredient
, respectively
.
For example,
for broiler commercial,
the
i
nappropria
te ingredient
s

were

obtained by excluding
two
ingredients
from

Table 5.

The
removed ingredients are
Soybean meal (48 % CP
) and DL
-
Methionine.

So, the number of
ingredient include
d in optimization
was
decrease
d

from sixteen to fourteen

for the selection of
i
nappropria
te ingredient
.
In the same way
, f
or layer type, f
ourteen and twelve ingredients
were

used for
the
selection of
appropriate
and i
nappropria
te

ingredient
, respectively
.
Besides,
13


t
welve and eleven ingredients

for sheep, as well as eleven and ten ingredients for cattle (dairy
cattle feed)
wer
e
used

for

appropriate and i
nappropria
te selection, respectively.

So
, the cost
optimization
was

performed

according to the chosen ingr
edients
.
As regards
the
appropriate
ingredients, both

methods are very close to one another in the penalty and
the
cost values
for
commercial

broiler
.

As regards
the
inappropriate ingredients, the penalty value is 583.2 in
GA, whereas it is
712.8 in the li
near model. The
cost is slightly lower in the GA.

On the other
hand, the optimization
results obtained

by selecting
the
appropr
iate ingredients for sheep
show

that the penalty values are zero in both method, but the cost in the GA is lower than the
linear
model.


Occasionally,
GA

could
not
successful
in handling the
difficulties
at
finding

the
appropriate feed mixes for poultry. On the other hand, it converges to the optimum results
easily for cattle.
It can be said that although the incomplete
or

inappropr
iate
ingredients are
selected, GA is able to produce acceptable solutions. Therefore GA can be favorable to the
cost optimization of the feed mixes, especially when the linear programming does not produce
the
solutions.

5.

Conclusions

This paper presented th
e application of genetic algorithms to the
cost optimization
of
the
feed mixes
for

poultry and cattle
.

The
optimization encompasses the
find
ing
least
-
cost

ingredients

in

the
feed

mixes
.
For the poultry,
because of
managing of many
constraints

at the
same

t
ime
, the results without penalties
could

not be obtained.
But for the cattle, zero penalty
value

was

reached quickly and
the
optimum results
were

achieved
. The
obtained

results
were

compared
to linear programming m
odel developed i
n

MS Ex
cel Solver. Consequ
ently,
the
experiments based on
the developed
software

framework

indicate

that GA
method
can

be a
practical tool
for the cost optimization of feed

mixes
.

In the future

studies
,
a hybrid method
14


involving
Linear Programming Techniques and GA may be develop
ed
, so it

may be possible
to produce
results which do

not have
any

penalty
value
s for poultry animals

as well
.




References

1.

Coskun, B., Seker, E., Inal, F.,

Animal Nutrition,

Konya:
Selçuk
University Press,

1997
, (in Turkish).

2.

Dogan

I.
, D
ogan

N.,

A
kcan

A.
,
Using Goal Programming in Rational and Economical
Animal Nutrition
.

Turk J Vet Anim
.

Sci
.

(2000),

24
,

233

238
.

3.

Kerrigan G.L, Norback J.P, Linear programming in the allocation of milk resources
for cheese making. Journal of Dairy science,
(1986),
69(5)
, 143
2
-
1440.

4.

Alan G. Munford “
The use of iterative linear programming in practical applications of
animal diet formulation
”, Mathematics and Computers in Simulation,
(1996),
42
(
2
-
3
),
255
-
261.

5.

Azapagic,
A, Clift, R.. Linear Programming as a Tool in Life Cycle Assessment.
International Journal of Life Cycle Assessment
, (1998),

3(6), 305
-
316
.

6.

Berntsen J., Petersen B.M., Jacobsen B.H., Olesen J.E., Hutchings N.J. Evaluating
nitrogen taxation scenarios using
the dynamic whole farm simulation model FASSET.
Agricultural Systems (2003)
,
76
,

817

839.

7.

Guevara V. R. Use of Nonlinear Programming to Optimize Performance Response to
Energy Density in Broiler Fee
d Formulation.

Poultry Science
(
2004
),

83
,
147

151.

8.

Gryso
n N., Eeckhout M. and Neijens T., Cost and benefits for the segregation of GM
and non
-
GM compound feed
,

(2008),
12
th
EAAE Congress, Gent (Belgium)
.

9.

Pillay P., Nolan R., Haquue T., “Application of genetic algorithms to motor parameter
determination for t
ran
sient torque calculations”,
IEEE Trans. On Ind. Appl
.,
(1997),
33, 1273
-
1282.

10.

Çunkaş M. Intelligent design of induction motors by multiobjective fuzzy genetic
algorithm, Journal of Intelligent Manufacturing,
(
2008
),
(in press)
.

11.

Coşkun B, İnal F, İnal Ş. R
ation Programs
.
Selçuk University, Faculty of Veterinary
Medicine
,
http://veteriner.selcuk.edu.tr/bolum/hbesleme/
,

last access : 27.11.2008

15


12.

NRC Nutrient Requirements of Poultry, Ninth Revised Edition, National Academy
Pres, Washington D.C., 1994.

13.

Im C.H., Jung H.K., Kim Y
.J. Hybrid Genetic Algorithm for Electromagnetic
Topology Optimization. IEEE Transactions on Magnetics 39(5), (2003), 2163
-
2169.

14.

Goldberg, D.E.,

Genetic Algorithms in Search, Optimization, and Machine Learning
:

New York: Addison Wesley, 1989.

15.

Hwang S.F., H
e R.S., Improving real
-
parameter genetic algorithm with simulated
annealing for engineering problems. Advances in Engineering Software 37 (2006)
406

418.

16.

Osyczk A.,
Evolutionary Algorithms for Single and Multicriteria Design
Optimization
:

A Springer

Verla
g Company, 2001.

17.

Haupt Randly L., Haupt Sue E
., Practical Genetic Algorithms
:

A Willey


Interscience
Publication, USA, 1998.

18.

Martínez M., García
-
N
ieto S., Sanchis J., Blasco X.

Genetic algorithms optimization
for normalized normal constraint method under
Pareto construction. Advances in
Engineering Software (2008) (in press).

19.

Şahman M.A. C
ost optimization of feed mixes by using genetic algorithms
, M
aster

Thesis, Selcuk University,
Konya,

2008.











16





Table Captions

Tabl
e

1
The nutritional

requirement
s in poultry

Tabl
e

2
The nutritional

requirements in cattle

Tabl
e

3

The nutrient content
s

of feed ingredients for poultry

Table

4
The nutrient content
s

of feed ingredients for cattle

Table 5
The nutrient contents of feed ingredients for broiler commercial

Table 6
The nutritional requirements in Broiler commercial

T
a
bl
e

7

Optimization results for

genetic algorithms and linear programming


Figure Captions

Fig.

1

Flow chart
for
cost optimization of the feed mixes

Fig.
2

Main interface of feed

mix preparation p
rogram

Fig.

3

Ingredient
amounts,

price

and penalty value for poultry

Fig.

4
.

The nutrient content
s

of

feed
mix obtained for poultry

Fig.
5

Convergence of

penalty values for poultry

Fig.

6

Ingredient
amounts,

price

and penalty value for cattle

Fig.

7

The
nutrient content
s

of

feed
mix obtained for cattle

Fig.
8

Convergence of

penalty values for cattle

Fig.
9

The cost
development

of feed mix
for

cattle

(
Exchange rate about 1 US penny = 1.7 Krs
)





17



Tabl
e

1
The nutritional

requirements in poultry

Poultry Kin
d

Chicken
-
Meat Type
-
Breeding

Poultry Type

Arbor Acres Broiler Breeding, Starter (0
-
4 Wks)

Nutri
ents

Min

Max

Crude Protein(CP,%)

17

18

Metabolizable Energy (ME,kcal/kg)

2800

2915

Calcium (Ca,%)

0,9

1

Available Phosphorus (AP,%)

0,45

0,5

Sodium (Na,%)

0,18

0,2

Methionine / Cystine (Met+Cys,%)

0,72

0,76

Lysine (L
ys
,%)

0,92

0,98

Threonine (Thr,%)

0,52

0,54

Tryptophan (Try,%)

0,17

0,19

Linoleic Acid (LA,%)

1

-




Tabl
e

2
The nutritional

requirements in cattle

Animal Species

Cattle

Animal Type

Cattl
e, Milk Feed
,18,2600

Nutrients

Min

Max

Crude protein

(
C
P,%)

18

-

M
etaboli
zable

Energy
(ME,kcal/kg)

2,6

-

Calcium

(Ca,%)

0,8

1,5

P
hosphor
us

(P,%)

0,5


S
odium (Na,%)

0,2

0,4

Crude fiber

(
CF
,%)

-

14

Ash

(
Ash
,%)

-

9










18



Tabl
e

3

The nutrient cont
ent
s

of feed ingredients for poultry


x
1

x
2

x
3

x
4

x
5

x
6

x
7

x
8

x
9

x
10

x
11

Nut ri
ent
s

Corn, Yellow

Wheat

Middlings

Wheat grain,

hard red


winter

Soybean meal,

44 % CP

Poultry By
-

Product Meal

Dicalcium

Phosphate

Limestone

Sodium

Chloride

Vitamin
-

Mineral

Premix

L
-
lysine
Hydrochloride

DL
-
Methionine

(CP,%)

8.
5

15

14.
1

44

60

0

0

0

0

94.
4

58.
7

(ME,kcal/kg)

3350

2000

2900

2230

2950

0

0

0

0

4600

36.
8

(Ca,%)

0.
02

0.
12

0.
05

0.
29

3

24

38

0.
3

0

0

0

(
NP
P,%)

0.
08

0.
3

0.
13

0.
27

1.
7

16.
2

0

0

0

0

0

(Na,%)

0.
02

0.
12

0.
04

0.
01

0.
4

0.
06

0.
05

39

0

0

0

(Met +Cys,%)

0.
36

0.
53

0.
51

1.
28

1.
97

0

0

0

0

0

99

(L
ys
,%)

0.
26

0.
69

0.
37

2.
69

3.
1

0

0

0

0

79

0

(Thr,%)

0.
29

0.
49

0.
39

1.
72

2.
17

0

0

0

0

0

0


(Try,%)

0.
06

0.
2

0.
16

0.
74

0.
34

0

0

0

0

0

0

(LA,%)

1.
82

1.
87

0.
59

0.
4

2.
54

0

0

0

0

0

0

Cost,Kr
s
*

40

30

35

40

30

75

1.
2

7

180

650

650

Lower limit

(
kg
)

0

0

0

0

0

0

0

0.
25

0.
25

0

0

Upper
l
imit (
kg
)

70

10

60

40

30

4

10

0.
4

0.
35

0.
1

0.
5

* Exchange rat e about 1 US penny = 1.
7

Kurush

(Krs
)



Table

4
The nutrient content
s

of feed
ingredients for cattle


x
1

x
2

x
3

x
4

x
5

x
6

x
7

Nutri
ent
s

Corn, 3100

Soybean Meal,
Solvent

Extracted,

44 % CP

Cottonseed

Meal, Solvent

Extracted,


32 % CP

Limestone

Sodium

Chloride

Vitamin
-

Mineral Premix

Dicalcium

Phosphate

Dry Matter(DM)

89

91

92

10
0

100

100

100

(CP,%)

10

46,8

35

0

0

0

0

(ME,Mcal/kg)

3.
47

3

2.
51

0

0

0

0

(Ca,%)

0.
3

0.
32

0.
18

35

0

0

24

(P,%)

0.
29

0.
71

1.
2

0

0

0

18

(Na,%)

0.
02

0.
04

0.
06

0.
06

39.
34

0

0.
03

(CF,%)

2.
6

7

16

0

0

0

0

(Ash,%)

1.
5

6.
6

6.
9

100

100

0

100

Cost,
Krs
*

35

50

2
5

2.
5

10

250

55

Lower limit
(
kg
)

0

0

0

0

0.
25

0.
25

0

Upper limit
(
kg
)

70

40

30

7

0.
5

0.
5

3


* Exchange rat e about 1 US penny = 1.
7

Kurush

(Krs
)


19


Table 5

The nutrient contents of feed ingredients for broiler commercial


x
1

x
2

x
3

x
4

x
5

x
6

x
7

x
8

x
9

x
10

x
11

x
1
2

x
1
3

x
1
4

x
1
5

x
16

Nut ri
ent
s

Barley

Corn, Yellow

Wheat

Bran

Wheat grain,

hard red winter

Fish meal, Anchovy,
64 % CP

Meat and Bone meal,
42 % CP

Soybean meal,

44 % CP

Soybean meal,

48 % CP

Soybean seeds, heat
processed

Sunflower meal,

23 % CP

Dicalc
ium

Phosphate

Limestone

Sodium

Chloride

Vitamin
-

Mineral Premix

L
-
lysine
Hydrochloride

DL
-
Methionine

(CP,%)

11

8.
5

15,70

14.
1

64,20

42,70

44

47,50

35,50

23,30

0

0

0

0

94.
4

58.
7

(ME,kcal/kg)

2640

3350

1300

2900

2580

1930

2230

2440

3300

1415

0

0

0

0

4600

36.
8

(Ca,%)

0,03

0.
02

0,14

0.
05

3,73

12,90

0.
29

0,27

0,25

0,35

24

38

0.
3

0

0

0

(
NP
P,%)

0,17

0.
08

0,20

0.
13

1,97

6,10

0.
27

0,22

0,11

0,14

16.
2

0

0

0

0

0

(Na,%)

0,04

0.
02

0,05

0.
04

0,65

0,95

0.
01

0,02

0,03

0,20

0.
06

0.
05

39

0

0

0

(Met +Cys,%)

0,42

0.
36

0
,55

0.
51

2,60

0,91

1.
28

1,39

1,07

1

0

0

0

0

0

99

(L
ys
,%)

0,40

0.
26

0,61

0.
37

5,07

2,11

2.
69

2,96

2,25

1

0

0

0

0

79

0

(Thr,%)

0,37

0.
29

0,50

0.
39

2,82

1,32

1.
72

1,87

1,41

1,05

0

0

0

0

0

0


(Try,%)

0,14

0.
06

0,23

0.
16

0,78

0,21

0.
74

0,74

0,51

0,45

0

0

0

0

0

0

(LA,%)

0,83

1.
82

1,70

0.
59

0,20

0,31

0.
4

0,47

8,46

0

0

0

0

0

0

0

Cost,Krş
*

30

40

25

35

110

40

40

47,50

46

17,50

75

1.
2

7

180

650

650

Lower limit

(
kg
)

0

0

0

0

0

0

0

0

0

0

0

0

0.
25

0.
25

0

0

Upper
l
imit (
kg
)

20

70

10

60

8

4

40

40

10

15

4

10

0.
4

0.
35

0.
1

0.
5





Table 6
The nutritional

requirements in Broiler commercial









Poultry Kind

Chicken
-
Butcher Type
-
Commercial

Poultry Type

Ross, Male (3 Kg, 56
-
59 day) Broiler, Starter (0
-
10 day)

Nutri
ents

Min

Max

Crude Protein(CP,%)

22

25

Metabolizable Energy (ME,kcal/kg)

3010

3010

Calcium (Ca,%)

1

1

Available Phosph
orus (AP,%)

0,5

0,5

Sodium (Na,%)

0,16


-

Methionine / Cystine (Met+Cys,%)

1,09

1,09

Lysine (L
ys
,%)

1,44

1,44

Threonine (Thr,%)

0,93


-

Tryptophan (Try,%)

0,25


-

Linoleic Acid (LA,%)

1,25


-

20










T
a
bl
e

7

Optimization

results for genetic algorithms and linear programming


Linear Programming

G
enetic

Algorit
hms

Animal Species and
Type

Penalty
Values

Total Cost
[Penny/kg]

Penalty
Values

Total Cost

[Pe
nny/kg]

BROILER COMMERCIAL

Broiler, Starter


(0
-
10 day)

1*

0

39.96

1.83

39.97

0*

712.
8

39.5

583.2

39.45

LAYER TYPE

Hy
-
line Brown, Layer

(32
-
44 Wks)(DFC 100g)

1

0

34.41

39

32.7

0

229.55

34.83

217,31

34.37

SHEEP

Lamb Fattening Feed

1

0

32.73

0

32.04

0

24.
49

33.20

19,3

33.56

CATTLE

Dairy Cattle Feed, 18, 2600

1

0

31.11

0

31.27

0

0.77

30.91

0

32.64

* 1 :
Comparisons made for appropriately chosen ingredients.
, 0:
Comparisons made for inappropriately chosen
ingredients.







21











Fig.

1

Flow chart
for
cost optimization of the feed mixes







No

Ye
s

DATA INPUT

Animal and Feed Data

DEFINE

Object Function, Parameters and
Constraints

ADAPTATION OF PARAMETERS TO GA

CALCULATION OF FITNESS AND PENALTY VALUES

SELECTION

CROSSOVER

MUTATION

STOPPING CRITERIA

ELITISM

STOP

22









Fig.
2

Main interface of
the
f
eed

mix preparatio
n program









23









Fig.

3

Ingredient
amounts,

price

and penalty value for poultry












24









Fig.

4

The nut
rient content
s

of

feed
mix obtained for poultry











25









Fig.
5

Convergence of

penalty values for poultry












26









Fig.

6
:
Ingredient
amounts,

price

and penalty value for cattle

















27


















Fig.

7

The nutrient conte
nt
s

of

feed
mix obtained for cattle










28










Fig.
8

Convergence

of

penalty values for cattle



















29














Fig.
9

The cost
development

of feed mix
for

cattle

(
Exchange rate about 1 US penny = 1.7 Krs
)