Assessing the performance of bio

inspired heuristics for single row
layout problems
Berna ULUTAŞ
B.Burak ULUTA
Ş
Eskisehir Osmangazi University
Department of Industrial Engineering
30 June

2 July 2010 Oprerations Research and Industrial Engineering Conference
Sabanci University , Istanbul Turkey
Outline
•
Single
row
facility
layout
problem
(SRFLP)
•
Literature
review
•
The
algorithms
to
solve
SRFLP
•
Experiments
for
the
test
problems
•
Results
and
discussion
The
Single Row
Facility Layout Problem
Arrangement of
n
machines/departments on a straight
line in a given direction
Named as
One dimensional layout
Linear Ordering Problem (LOP) where all machines have unit
length
Objective
is
to
minimize
the
total
material
handling
costs
and
to
find
the
optimum
layout
for
machines
in
one
dimension
SRLP examples
SRLP examples
(cont’)
Literature review for
SRFLP
Karp
and
Held
(
1967
)
Dynamic
programming
Simmons
(
1969
,
1971
)
Branch
and
bound
algorithm
Love
and
Wong
(
1976
)
Linear
mixed
integer
program
Picard
and
Queyranne
(
1981
)
Dynamic
programming
Heragu
and
Kusiak
(
1988
)
T
wo
heuristic
constructive
algorithms
Heragu
and
Kusiak
(
1991
)
Nonlinear
model
Braglia
(
1997
)
Heuristics
derived
from
scheduling
problem
Djellab
and
Gourgand
(
2001
)
A
n
iterative
construction
procedure
Ponnambalam
and
Ramkumar
(
2001
),
Chen
et
al
.
(
2001
),
Ficko
et
al
.
(
2004
)
GA
Literature review for
SRFLP
(cont’)
Ponnambalam and Ramkumar (2001)
GA+SA
Ponnambalam et al. (2005)
Hybrid search heuristics
(Flow Line Analysis (FLA)+SA, FLA +GA, FLA+GA+SA)
Anjos
et
al
.
(
2005
)
Semidefinite
programming
relaxation
Solimanpur
et
al
.
(
2005
)
A
CO
Amaral
et
al
.
(
2005
)
S
A
Amaral
(
2006
)
Linear
mixed
integer
program
Teo
and
Ponnambalam
(
2008
)
ACO+PSO
Amaral
(
2009
)
Linear
programming
Samarghandi
and
Eshghi
(
2010
)
TS
Samarghandi
et
al
.
(
2010
)
PSO
The dimensions of the machines either are not considered or
are assumed to be equal (Braglia, 1996)
The locations of facilities are predetermined (Kumar et al.,
1995; Braglia, 1996)
The size of the machines is only considered in the physical
layout of the machines (Heragu and Kusiak, 1988)
The method requires too much time to construct a layout,
especially when applied to large instances of the SRFLP (Anjos
et al., 2005).
The problem in concern
Large size departments
Unequal dimensions (length)
No clearence
No backtracking
Biologically inspired computing
genetic algorithms
↔
evolution
neural networks
↔
the brain
artificial immune systems
↔
immune system
emergent systems
↔
ants, bees
rendering (computer graphics)
↔
patterning and
rendering of animal skins, bird feathers, mollusk shells
and bacterial colonies
cellular automata
↔
life
Clonal
selection
Bacterial foraging
CLONAL SELECTION ALGORITHM
AIS
algorithms
Population
based
Network
based
Clonal
selection
Bone
marrow
Negative
selection
Continuous
models
Discrete
models
m
5
m
3
m
2
m
1
m
4
m
6
Enc
oding
[m
5
m
2
m
1
m
6
m
4
m
3
] = [5 2 1 6 4 3]
Representation
Step 1: Initialization
The antibodies are randomly generated based on the
predetermined population size
For each antibody in the population, the objective
function value is calculated
Step 2: Evaluation
Selection of antibodies are made based on their objective
values
For example, layouts that have lower cost values have the
largest share on the wheel
Step 3: Selection and cloning
Step 4: Hypermutation
For
each
antibody
in
the
population,
hypermutation
operator
is
applied
Then,
objective
value
of
the
mutated
antibody
is
calculated
If
there
is
an
improvement,
the
existing
antibody
is
replaced
with
the
mutated
one
Step 5: Receptor editing operator
A
percentage
of
the
antibodies
(worst
R
%
of
the
whole
population)
in
the
antibody
population
are
eliminated
and
randomly
created
antibodies
are
replaced
with
them
.
This
procedure
enables
the
algorithm
to
search
new
regions
in
the
solution
space
.
Step 6: Repeat Steps 2

5 until termination
criterion is met
The algorithm is terminated if the best feasible solution
has not improved after a predetermined number of
iterations (i.e., 250).
BACTERIA FORAGING ALGORITHM
BFA
is based on the foraging (i.e., searching food) strategy of
Escherichia coli
bacteria
Step 1.Initialization
The bacteria are randomly generated based on the
predetermined population size
Step 2. Chemotaxis
is a foraging strategy that implements a type of local
optimization
the bacteria try to climb up the nutrient concentration,
avoid noxious substances
search for ways out of neutral media
is similar with biased random walk model
Step 3. Swarming
the bacteria move out from their respective places in
ring of cells by moving up to the minimal value
bacteria usually tumble, followed by another tumble or
tumble followed by run or swim
if the cost at present is better than the cost at the
previous time or duration then the bacteria takes one
more step in that direction
1.
N
clones
copies of the solution are generated so that there
are (
N
clones
+1) identical solutions
2.
Inverse mutation is applied to each of the
N
clones
copies
3.
The solution surviving the mutation is the non

dominated solution among the mutated solutions
4.
All other solutions are discarded
5.
Repeat the procedure for all the solutions in the
population
Tavakkoli

Moghaddam et al. (2007) A hybrid multi objective immune algorithm for a flow shop scheduling problem with
bi

objectives: Weighted mean completion time and weighted mean tardiness
Step 4. Reproduction
the
bacteria
are
stored
in
ascending
order
based
on
their
fitness
percent
of
the
least
healthy
bacteria
dies
and
others
split
into
two
which
are
placed
in
the
same
location
the
population
of
bacteria
remains
constant
Step 5. Repeat Steps 2

4 until
termination criterion is met
The algorithm steps are repeated until the termination
criterion is succeeded
Algorithm parameters
Population size : 10
Receptor editing / Reproduction rate : 10%
Problem set 1
Problems with optimum solutions
Problem set 2
Larger size test problem results for CSA
Problem set 2
Larger size test problem results for BFA
Problem set 3
Larger size test problem results for CSA
Problem set 3
Larger size test problem results for BFA
Conclusions and Results
The performance metrics:
solution quality
speed of convergence
frequency of hitting the optimum
CSA and BFA outperformed best known results available in
the literature
CSA obtained better results than BFA
Best
known
Better
Worse
Problem
set 1
CSA
100
0
0
BFA
100
0
0
Problem
set 2
CSA
81.25
6.25
12.50
BFA
12.50
6.25
81.25
Problem
set 3
CSA
35.00
45.00
20.00
BFA
15.00
5.00
80.00
Further studies
D
esign
of
experiments
to
determine
the
optimum
parameters
Experiments
with
different
termination
criteria
and
larger
population
size
New
strategies
to
improve
BFA
search
capabilities
Considering
the
elimination
and
dispersal
events
that
are
based
on
population
level
long

distance
mobile
behavior
Real
life
application
of
SRLP
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