Modified artificial immune system for single row facility layout problem

Modified Artificial Immune System For Single Row Facility Layout Problem, S Jishnu Gopal, C
Gandhimathinathan, S.Arunajadeswar, Journal Impact Factor (2015): 8.8293 Calculated by GISI
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www.iaeme.com/ijmet.asp 52 editor@iaeme.com
1,2,3
BE Mechanical, Thiagarajar College of engineering.
ABSTRACT
One of the main optimization algorithms currently available in the research field is an
Artificial Immune System where abundant applications are using this algorithm for clustering and
patter recognition processes. These algorithms are providing more effective optimized results in
multi-model optimization problems than Genetic Algorithm. The necessity of optimization is more
considerable in SRFL-[Single Row Facility system] used to optimize the cost and time. In this paper,
MAIS – [Modified Artificial Immune System] algorithm introduced newly to overcome from
existing AIS. MAIS use very small size of local search on the antibodies which can improve the
algorithm efficiently. The creditability of the proposed approach is evaluated by simulations, and the
results show the proposed approach provides better result compared with the standard AIS.
Keywords: Single Row Facility Layout; Optimization; Artificial Immune System.
INTRODUCTION
A non-overlapping arrangement of M number of autonomous machines to complete a job
with less cost and in less time is the facility layout problem where the area need to place the
machines may be equal or unequal in size, distance among the machines, time taken to complete
individual job.20% to 50% of the entire operating expenses in manufacturing are depends on the
property of material handling cost. If the facility layout is perfect then the cost can be reduced to
10% to 30%. In current research, research scholars deploying various efficient optimization
algorithms to reduce the throughput time, decrease the area utilized. This affects the entire facility
layout and can produce good performance in manufacturing system like information flow, material
flow, production and so on.
Material handling is a necessary and significant component of any productive activity. It is
something that goes on in every plant all the time. Material handling means providing the right
amount of the right material, in the right condition, at the right place, at the right time, in the right
position and for the right cost, by using the right method. It is simply picking up, moving, and lying
down of materials through manufacture. It applies to the movement of raw materials, parts in
process, finished goods, packing materials, and disposal of scraps. In general, hundreds and
thousands tons of materials are handled daily requiring the use of large amount of manpower while
the movement of materials takes place from one processing area to another or from one department
to another department of the plant. The cost of material handling contributes significantly to the total
cost of manufacturing.
MODIFIED ARTIFICIAL IMMUNE SYSTEM FOR SINGLE
ROW FACILITY LAYOUT PROBLEM
*S Jishnu Gopal1
, C Gandhimathinathan2
, S.Arunajadeswar3
Volume 6, Issue 6, June (2015), pp. 52-59
Article ID: 30120150606006
International Journal of Mechanical Engineering and Technology
© IAEME: http://www.iaeme.com/IJMET.asp
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
IJMET
© I A E M E

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RELATED WORKS
In real application, departmentsaccommodate unequal-sized and based on the past studies, the
QAP formulation is less attractive for the unequal-sized FLP (UFLP) compared to the equal-sized
FLP (Logendran and Kriausakul, 2006). This is because of the criterion choice used in finding the
best layout from various solutions are not easy for UFLP. Since formulating the UFLP as a QAP has
one major disadvantage where one must specify the possible locations for all facilities which is
discretizing the problem (Auriel and Golany, 1996). Thus, it is better to formulate the UFLP without
specifying the location especially for unequal size.
Anjoset al. [22], Anjos and Vannelli [23], Anjos and Kong [24], Hungerlander and Rendl
[25], had presented semi-definite programming relaxation providing a lower bound on the optimum
value of the SRFLP. Recently, many researchers proposed meta-heuristic methods, such as: a scatter
search algorithm by Kumar [26], a hybrid algorithm based on ant colony optimization and PSO by
Teo and Ponnambalam, [27], a genetic algorithm by Lin [28], a PSO algorithm by Samarghandiet al.
[29], and genetic algorithm by Dattaet al. [30].
Nowadays, researchers seek for various approximate methods including various local search
and metaheuristics approaches to find optimal solutions for these problems in a reasonable
computational time. Researchers have applied recent search techniques such as simulated annealing
(SA), tabu search (TS), genetic algorithm (GA), and ant colony optimization (ACO) which have
proved to be effective. Finally
Existing System [Artificial Immune System]
AISs are influential when a population of answer is vital either during the search or as an
outcome. Also, the problem has to have some notion of ‘matching’. Lastly, because at their heart
AISs are evolutionary algorithms, they are more suitable for problems that change over time rather
and need to be solved again and again, rather than one-off optimizations.In general, there are four
decisions have to be taken to implement the AIS, they are Indoctrination pattern, Likeness Measure,
Choice and Change. Once the Pattern has generated, find the likeness Measurement, for Choose the
best choice and change for the best choice.
Proposed Approach [Modified Artificial Immune System]
A major drawback in these algorithms is their slow convergence to global optimum and their
weak stability can be considered in various running of these algorithms. In this paper, improved
Artificial Immune System Algorithm is introduced for the first time to overcome its problems of
artificial immune system. That use of the small size of a local search around the memory antibodies
is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated
by simulations, and it is shown that the proposed approach achieves better results can be achieved
compared to the standard artificial immune system algorithms [33].
In this paper, we present an artificial immune system that has been extended to include the
creation process of a multitude of antigens, which are potential solution candidates. In a highly
constrained problem, the sum of all constraints implicitly represents the set of all valid and attractive
solutions. The challenge is to find an explicit representation for elements of this set. This can be
achieved by constructing larger partial solutions through aggregating building blocks until a final
solution is found. Hence, our concept consists of two parallel, cooperating
A SRL is a common layout system used in FMS, where machines are arranged in a linear
way, in those materials handling machines moves the flow from one machine to another machine.
This paper receipts AIS, EAAIS are dual planned approaches and experiment it, associate the
performance. Since, the AIS, EAAIS are tackled and solved in two stages, where the AIS in fist stage

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and the EAAIS solved in second stage. In SRFL, the machines are arranges in a line and three kind
of problems applied to find the feasible solution. The first set problem is same distance method,
where the distance between the machines are equal, the second set of problem is, the distance
between the machines are zero and the thirst set of problem is the distance between the machines are
different. The following Figure-1 depicts the common architecture of SRFL with three problems,
where S – determines the type of the problem.
Figure-1: SRFLP
L -> Distance occupied by the Machine
S -> Distance between Machines
D -> Calculated Distance between the Machines
1, 2, 3 ..5 -> Machine Numbers.
The Impartial of any kind of FLP is to determine atask of machines that harvests a minimum
material handling cost. The objective is to reduce the Job flow time, distance between machines, is
given in the following Equation-(1).
= ∑ ∑ (1)
Tij = Task Movements between Machine i to j.
dij = straight-lined space between machine i to j
COij = Cost of the material handling from ith
place to jth
[of machine location].
In this paper, the extended automatic artificial immune system is predefined a combined
min_sum, min_max values as minMax value for controlling the congestions in the loading and
unloading in total congestion of all parts and congestion among family parts. The objective function
can be written with minMax layout problem, which is defined as [equ -1]:
minMax [cost] =∑ ! "#
$ ----[1]
Algorithm of MAIS
Generally the MAIS functionality is defined as a step wise process:
1. Setting the number of repetitions on each individual %1 ≥ % ∈ ) )*+, -./.
2. The number of P1 on each Election R, ∀ , 1 *2345 6 24
3. Let t be the time and c be the cost ∀ , 8 < :;_-./ , 8"
4. Get similarities by measuring sm for each individual in P1.
d12 d23 d45d34
L1 L2 L3 L4 L5S12 S4
5
S2
3
S3
4
42 3 51
AG
V

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5. Generate more election E, k number of times, n number of best individuals P1, should be
proportional to the Election rate with uniqueness in the string. Where = ∝ 2
6. Eliminate the most highest OFV of E ?%, where ? is considerably less number
7. Check t, c ≤ :;(AIS)
8. Check for E == NE // new E
9. if E == NE, Eliminate the E endif.
Repeat 5,6
Eliminate string with less OFV; get new string pattern and the low sm cells can be replaced by
the higher values.
Repeat from 4 until c <cost (AIS) for unique string.
Figure-2: MAIS Flowchart
Start
Assume R, P, ?
Let optv = OFV (AIS)
For a =1 to R; for b=1 to P; for c = 1 to K
Next c, b, a
Calculate OFV(E)
Generate random sequence for each individuals of P
K = P/ ?
If OFV(E) <optv
If NE == E
Optv = OFV ( E )
Eliminate NE
Change E and produce NE
Display OFV, E as Best Sequence and OFV

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Pseudo Code for MAIS
1. Let N be the Number of Machines
2. Let P be the population where P ≤ factorial(N)
3. optv = OFV(AIS) // OFV for N machines
4. Let R be the number of Iteration
5. Define K // for dividing P, using top-down approach
6. For I = 1 to P
7. Generate random sequences E
8. End
9. K = P / ? // ? be a constant
10. For a = 1 to R
11. For b = 1 to P
12. For c = 1 to K
13. Calculate OFV(E)
14. If ( OFV(E) <= optv )
15. Optv = OFV(E)
16. End
17. Eliminate E <- max(max(OFV(E))
18. Change similarity of each NE, to generate a matured
19. antibody of the P.
20. If ( strcmp(NE, E)
21. Eliminate NE and Goto step 18
22. End If
23. End c
24. End b
25. End a
26. Display E, OFV (E) as the best sequence and OFV.
Numerical Illustration
The algorithm and the pseudo code is hand simulated and verified, validated by a JAVA
program and obtained a best Optimal Cost value for 12, 15, 20 and 30 Machines in the following
parameters. And the complete Numerical Illustration of the AIS algorithm is given below in detail.
Set the Population size P = 50,
Assume division k = 5,
The number of iteration = 1000 and
The r% = 20%
Step 1: The random population is initialized as P, each individual of P is a string, which is
generated until the size of the P. Example string S = “3 11 9 4 7 8 12 5 1 10 2 6” is indicating a
SRFL for 12 machine problem. Where the total number of population is 50, and total number of
individuals in the population is divided into 10 x 5. Send the first 10 population for process
Step 2: Calculate the similarity value sm using the objective value of each S. And the Objective
Value is calculated using equ (1)
OFV = 2 ∑ B,
2 =
CDE
Fℎ454 2 4 − )5 ) 5 ,+ :; ---- equ (1)

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Step 3: Check the OFV (s), find the maximum OFV value based S Eliminate in the Current step
and pass S to Step 5. Example the s1,s2,.. s3 are the three string with OFV is given. From that the
string s3 is eliminated due to more OFV and it is shown in figure-4.
s1
s2
s3
Figure-3: String Elimination due to Highest OFV
Step 4: The election of string S is based on the rate of election and it defined by equ (2) given
below.
=+48 I, 4 =
JK L M
∑ JK "N
OPQ
--- equ (2)
Step 5: Every string S is changed by inverse as well as pair wise and compare the OFV of each
string, to get the minimum OFV. [The number of elected string gets increased than the original P
size].
The following Figure-5 illustrates the inverse change of the string S, where the numbers of
machines are 12, and the inverse operation is started at location 3 to 8.
Figure-4: Inverse Change of String
Step 6: Every string S is changed by pair wise and compare the OFV of each string, to get the
minimum OFV. [The number of elected string gets increased than the original P size].
The following Figure-6 illustrates the pair wise change of the string S, where the numbers of
machines are 12, and the pair wise operation is started at location 3 to 8.
Figure-5: Pair wise Change of String
Step 7: if the changed string is matched with the old string, the new string is eliminated and repeat
the steps 5, 6. Example in Figure-7, same string newly generated is eliminated.
3 11 9 4 7 8 12 5 1 10 2 6
3 11 5 12 8 7 4 9 1 10 2 6
Original String →
Changed String ←
3 11 9 4 7 8 12 5 1 10 2 6
3 11 5 4 7 8 12 9 1 10 2 6
Original String →
Changed String ←
3 11 9 4 7 8 12 5 1 10 2 6
3 11 5 12 8 7 4 9 1 10 2 6
3 11 5 12 8 7 4 9 1 10 2 6
322
323
356

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Figure-6: Strings should be Unique.
Else the cost of the changed string is lesser than the original string, the original string and the
OFV is replaced by the changed string and its OFV value. Else the pair wise changes are applied for
changing the string.
Step 7: After the election, and changes, all the E in the population P are sorted in increasing order
according their COST.
Step 8: repeat step 3 to 7 until all the strings gets eliminated.
Step 9: take the next 10 size of population and repeat next iteration.
Step 10: Generate population of size 20 again and repeat the same processes until number of
repetition or until
:; =" < :; -./"
RESULTS AND DISCUSSION
The complete solutions for this paper are implemented in JAVA – computer programming
language and find the optimal solutions for AIS and EAAIS and the results are discussed. There are
the three problems of same clearance, without clearance, and different clearances are resulted here.
The optimal value can be obtained for different clearance problems, and thesame clearance,
difference clearance are the traditional problems obtained as best solutions given in table-1.
The clearance between the machines is the same in the first andsecondset of problems. We
haveconsidereda thirdset of problems in which the clearance between the machines is different.
Thethird set contains the eight problems of the first set with a difference that the distances between
the machines is reported in [Appendix] are assumedas the requiredclearance between the machines.
We havenot generated random data as clearance between the machines in order to make the problem
datareproducible.
EAAIS Time OFV for 20 machines OFV for 30 machines
1. 33.45 3516.11 11135.62
The above table shows that OFV obtained by EAAIS is on 20 machine layout and 30
machine layouts. For the 20 machine layout the obtained OFV is 3516.11 comparatively with the
AIS and for 30 machines the OFV is 11135.62, depicted diagrammatically in Figure-7.
3 11 5 12 8 7 4 9 1 10 2 6
3 11 5 12 8 7 4 9 1 10 2 6

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Figure-7: OFV obtained by EAAIS for 20, 30 Machine layout.
The overall performance of the AIS and EAAIS is given above with the best OFV and the
sequence where the OFV obtained.
REFERENCES
1. R. Logendran & T. Kriausakul, “A methodology for solving the unequal area facility layout
problem using distance and shape-based measures” International Journal of Production
Research, Volume 44, Issue 7, 2006.
2. Amaral, A.R.S. 2006. On the exact solution of a facility layout problem. Eur. J. Oper. Res. 173
508-518.
3. Anjos, M.F., A. Kennings, A. Vannelli. 2005. A semidefinite optimization approach for the
single-row layout problem with unequal dimensions. Discrete Optim. 2 113-122.
4. M. F. Anjos and A. Vannelli, “Computing Globally Opti- mal Solutions for Single-Row
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Layout Problem,” 4th IEEE Conference on Automation Science and Engineering, Washington
DC, 23-26 August 2008.
9. H. Samarghandi and K. Eshghi, “An Efficient TabuAlgo- rithm for the Single Row Facility
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105. doi:10.1016/j.ejor.2009.11.034
10. D. Datta, A. R. Amaral and J. R. Figueira, “Single Row Facility Layout Problem Using a
Permutation-Based Ge-netic Algorithm,” European Journal of Operational Re-search, Vol.
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11. Parvinder and Dr. V.K. Suman, “Artificial Immune System: A Review” International journal
of Computer Engineering & Technology (IJCET), Volume 4, Issue 6, 2013, pp. 436 - 442,
ISSN Print: 0976 – 6367, ISSN Online: 0976 – 6375.
0
5000
10000
15000
1 2
ObtainedOFVvalue
20, 30 machines
Performance Evaluation of EAAIS

Modified artificial immune system for single row facility layout problem

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