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Noname manuscript No.(will be inserted by the editor)
A Hybrid Bio-Inspired Algorithm for NP-Hard JobShop Scheduling
Problem
Sundeep Vilasagarapu Ram MohanaReddy Guddeti
the date of receipt and acceptance should be inserted later
Abstract The job shop scheduling problem (JSSP) is known as a
combi-natorial optimization problem that aims to find best sequence
of operationswith optimal execution time called makespan. Research
on optimization ofthe JSSP is one of the most significant and
promising areas of optimization.Instead of the traditional
optimization methods, this paper presents an investi-gation into
the use of bio-inspired algorithms like Particle Swarm
Optimization(PSO), Cat Swarm Optimization (CSO) and Ant colony
optimization (ACO)to optimize the JSSP. And, by considering the
merits and demerits of each bio-inspired technique mentioned above,
we came up with two hybrid bio-inspiredalgorithms one is
combination of PSO+ACO and CSO+ACO. Experimentalresults demonstrate
that the hybrid bio-inspired techniques provides optimizedsolutions
that the individual, and among the hybrid algorithms
CSO+ACOoutperforms the PSO+ACO. Because of its inherently parallel
nature, ACOis well-suited to GPU implementation. So to reduce the
run time complexitywe have used GPU to implement the hybrid
algorithms.
Keywords Scheduling Job Shop Particle Swarm Optimization
CatSwarm Optimization Ant Colony Optimization GPU
1 Introduction
Best allocation of the resources to activities over time can be
make throughgood scheduling which can greatly influence the
production efficiency in man-ufacturing industries. JSSP is
considered to be one of the well-known NP-hard
Sundeep VilasagarapuNational Institute of Technology Karnataka,
Surathkal-575025, IndiaE-mail: [email protected]
Ram Mohana Reddy GuddetiNational Institute of Technology
Karnataka, Surathkal-575025, IndiaE-mail:
[email protected]
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2 Sundeep Vilasagarapu, Ram Mohana Reddy Guddeti
combinatorial optimization problem, its difficulty to find out
the optimal solu-tion among (n!)m combinations for n job and m
machines, has always been thehot issue in industrial engineering.
It is a very good essential problem which isto be solved in
real-time applications like train scheduling, production
units.Because even a small percentage of improvement in the
efficiency of the overalloperation may bring significant financial
return.
The following are some existing contributions for solving JSSP:
Sadeh etal. [1] studied a version of the JSSP in which some
operations have to be sched-uled within time windows. They
developed an incipient look-back schemes thatavail the search
procedure recover from so-called dead-end search states.
PeterBrucker et al. [2] proposed a expeditious branch and bound
algorithm for theJSSP which finds an optimal solution if the
problem is of circumscribed size.Adams et al. [3] came up with SBP
algorithm to solve JSSP. SBP has a verygood balance between
computational intricacy and the quality of engenderedschedules.
Paulli et al. [4] presented a tabu search (TS) algorithm by
defininga neighborhood structure where there is no distinction
between re-assigning orre-sequencing an operation. Jiang et al. [5]
proposed a new Lagrangian relax-ation approach where operation
precedence constraints are relaxed rather thanmachine capacity
constraints. Mitsuo et al [20] developed a new method usinggenetic
algorithm which is prodigiously time-consuming. Colorni et al. [6]
in-troduced ant colony optimization for solving JSSP by a pheromone
alterationstrategy which improves the basic ant system by utilizing
the behaviour of ar-tificial ants to perform local search. Xia and
Wu [7] proposed a particle swarmoptimisation algorithm for the
multi-objective flexible JSSP, by combining lo-cal search (by self
experience) and global search (by neighboring experience).
Table 1: Existing work and its limitationsAuthors Proposed
Methodology Limitations
Peter Brucker et al. [2] Branch and bound algorithm Provides
efficient solutionsin time only for small andmedium size
probleminstances.
Adams et al. [3] Shifting bottleneck procedure Might obtain
infeasiblesolutions. However, they didnot explain why the casemight
exist.
Paulli et al. [4] Tabu search algorithm These approaches excel
othersnot necessarily in solutionquality, but almost always
incomputation time.
Mitsuo et al. [20] Genetic algorithm Works well when
computationtime is of no concern.
Colorni et al. [6] Ant colony optimization the algorithm was far
fromreaching state-of-the-artperformance.
Xia and Wu [7] Particle swarm optimization Infirmness local
convergence& the slow convergence speed.
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A Hybrid Bio-Inspired Algorithm for NP-Hard Job Shop Scheduling
Problem 3
In short, some of the existing work and its limitations are
summarized inTable 1. Most studies indicate that a single technique
can not solve this stub-born problem. Much work has been done on
hybrid methods involving geneticalgorithm, simulated annealing,
Tabu search, and Shifting bottleneck proce-dure techniques as
hybrid methods can provide high-quality solution withinreasonable
computing time. But using hybrid bio-inspired approach very
lessresearch has been done. Li Li et al. [14] proposed a hybrid
bio-inspired ap-proach using pso and aco for flexible job shop
scheduling and tested for onlytwo problem sizes. Hence, we proposed
a combination of bio-inspired algo-rithms using cso, pso and aco to
find the nearest optimal schedules in mini-mum time.
The following are the key contributions of our work: To the best
of our knowledge, we are the first to propose a hybrid combi-
nation of CSO and ACO to solve the JSSP. To the best of our
knowledge, this is the first paper which parallelizes the
ant colony algorithm for solving the JSSP.The rest of this paper
is organized as follows: Section 2 deals with the JobShop
Scheduling Problem definition and representation; Section 3 focuses
onthe bio-inspired algorithms adapted in this paper; Section 4
discusses proposedmethodology and Section 5 deals with Experimental
Results and Analysis.Finally the Concluding remarks with future
directions are given in Section 6.
2 Job Shop Scheduling Problem
2.1 Definition of JSSP
The classic JSSP is a machine scheduling and optimization
problem which canbe defined as follows: Let us consider an n x m
JSSP, in which n representsset of jobs J={J1, ..., Jn} and m
represents set of machines M={M1, ...,Mm}.A predefined order is to
be maintained to process each job through m ma-chines. This
predefined order is known as operation precedence constraints.An
operation can be defined as processing of a job on one machine
uninter-rupted period of a given length. A set of operations can be
represented asO={Oij |i [1, n], j [1,m]} where Oij represents
processing of ith job on jthmachine.
2.2 Representation of JSSP
Special graph structure called disjunctive graph G = {V, Ca U
Da} is usedto represent the job shop scheduling problems where V -
vertices representingthe operations of jobs; Ca - conjunctive arcs
represents the fixed precedencerelation among the operations; and
Da - disjunctive arcs between every pairof operations that must be
performed on the same machine.
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4 Sundeep Vilasagarapu, Ram Mohana Reddy Guddeti
Description for this disjunctive graph: Consider there are n
jobs and, same-type m machines, we number the nodes from one to N,
where N denotes thetotal no. of actual operations in disjunctive
graph. Each arc (a, b) connectstwo actual nodes a and b, implying
that operation a has to be processedimmediately before operation b.
Each arc has the length of pa correspondingto the processing time
of operation a.
Fig. 1: Graph for an instance n=3 and m=3 JSSP.
Figure 1 is modeled for n=3 and m=3 instance where each node
representsan operation. Each tuple (j, m) p on every node implies
the job number,machine number and time required for processing of
an operation. For instance,[(1, 3) 2] at node 2 means operation 2
of job 1 has to be operated on machine3 for a processing time of 2.
And lastly the length of the longest path from thedummy start node
S to the dummy end node E is equivalent to the makespanof the
schedule.
3 Bio-Inspired Algorithms
In the following sections we describe the bio-inspired
algorithms PSO, CSOand ACO which we adapted for solving the
JSSP.
3.1 Particle Swarm Optimization
It is an evolutionary computation technique which is proposed by
Kennedyand Eberhart [21] in 1995, based on observations of the
convivial comport-ment of birds in flocks or fish in schools, as
well as on swarm theory. It hasbeen introduced to solve
optimization problems like scheduling and routingproblems which
impersonates the behavior of flying birds and the way theyexchange
their information. It needs simple mathematical operators, and
alsocomputationally competitive in terms of both time & memory
requisites.
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A Hybrid Bio-Inspired Algorithm for NP-Hard Job Shop Scheduling
Problem 5
PSO Model: It performs search operating a population (called
swarm) of in-dividuals (called particles) that are improved from
iteration to iteration. Thecorrelation across the particles &
swarm in PSO is akin to the correlationacross the chromosomes &
population in a genetic algorithm. Particles movetowards either
pbest or gbest position after every iteration where pbest is
theindividual particle best position and gbest is the global best
position amongswarm so far. The position and velocity of a particle
designates its status. Thevelocity and position of a particle k
with d-dimensions can be formulated asfollows [21]:
V kd = Iw Vkd + C1 r1() (Pkd Xkd) + C2 r2() (Pgd Xkd) (1)
X kd = Xkd + Vkd (2)
where Vkd is the particle k velocity, Pkd is the best position
found by eachparticle so far, Pgd is the best position among swarm.
The exploration andexploitation of a particle is controlled by
inertia weight Iw, C1 and C2 are theconstants adopted to determine
whether particles choose to move towards Pkdor Pgd. r1 and r2 are
the two random functions return the values in range [0,1].
PSO algorithm:
1. Initialize a swarm of particles with random positions and
velocities in theD-dimensional problem space.
2. For each particle, evaluate the desired optimization fitness
function.3. Individual particles fitness value are with its pbest.
If the current value is
better than pbest, then set the pbest value to be equal to the
current value,and the pbest position equal to the current position
in D dimensional space.
4. Compare the fitness evaluation value with the swarms best
fitness valueobtained so far. If current value is better than
gbest, then reset gbest to thecurrent particles fitness value.
5. Change the velocity and position of the particle according to
Eqs. (1) and(2) respectively.
6. Loop to step (2) until a termination criterion is met,
usually a sufficientlygood fitness or a specified number of
generations.
3.2 Cat Swarm Optimization
Shu-Chuan et al. [15] noticed the behavior of cats and presented
an evolution-ary computation technique called Cat Swarm
Optimization (CSO). All catseven though have vigorous curiosity,
mostly they are dormant. When cats arereposing they are generally
awake with high vigilantness. This entire demeanorcan be
represented in two methods:
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6 Sundeep Vilasagarapu, Ram Mohana Reddy Guddeti
Seeking mode (SM): This mode is the case where the cat is at
rest, lookingnear by and exploring the next position to move using
the four necessaryfactors in this sub-model which are described in
the below:
SMP Seeking memory pool is for initializing the no. of cats in
searchmode.
SRD Seeking range of the selected dimension is the maximum
differencebetween the new and old values in the dimensions
selected.
CDC Counts of dimension to change is the size culled to carry
themutation
SPC self-position considering is a boolean value indicating if a
cat canbe selected for the tracing mode or not.
The seeking mode working mechanism can be illustrated in the
below:
1. put j copies of the present position of catk, with j = SMP.
If the value ofSPC is true, let j=(SMP-1), and retain the cat as
one of the candidates.
2. Generate a random value of SRD.3. Calculate the fitness
values (FS) of all candidate points.4. If the FS is not equal,
calculate the probability of each candidate by Eq
(3), else the default probability value of each candidate is
1.
Pi =|FSi FSb|
FSmax FSmin (3)
5. perform mutation and replace the current position.
Tracing mode (TM): The TM represents the hunting mode of the
cat. TheTM process is described as follows:
1. Update the velocities of each catk according to the Eq
(3).
V k = Vk + r1 c1 (Xbest Xk) (4)2. Check if the velocities are of
highest order or not.3. Update the position of Catk according to Eq
(4).
X k = Xk + V k (5)
where Xbest is the position of the cat who has the best fitness
value; Vk is thecurrent velocity and Xk is the actual position of
catk. c1 is a constant and r1is a random value in the range of
[0,1].
CSO Algorithm
1. Create N cats in the process.2. Randomly sprinkle the cats
into the M-dimensional solution space and
randomly select values, which are in-range of the maximum
velocity, to thevelocities of each cat. Then haphazardly pick
number of cats and set theminto tracing mode according to MR, and
the others set into seeking mode.
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A Hybrid Bio-Inspired Algorithm for NP-Hard Job Shop Scheduling
Problem 7
3. Evaluate the fitness value of each cat by applying the
positions of cats intothe fitness function, which represents the
criteria of our goal, and keep thebest cat into memory. Note that
we only need to remember the position ofthe best cat (Xbest) due to
it represents the best solution so far.
4. Move the cats according to their flags, if catk is in seeking
mode, apply thecat to the seeking mode process, otherwise apply it
to the tracing modeprocess. The process steps are presented
above.
5. Re-pick number of cats and set them into tracing mode
according to MR,then set the other cats into seeking mode.
6. Check the termination condition, if satisfied, terminate the
program, andotherwise repeat step3 to step5.
3.3 Ant Colony Optimization
Through inspecting the behavior of ants, Marco Dorigo in 1992
presented aevolutionary computation technique called Ant Colony
Optimization (ACO)to search for an optimal path in a graph. The
original idea has since diversifiedto solve a wider class of
numerical problems, and as a result, several problemshave emerged,
drawing on various aspects of the behavior of ants.
Ant colonies exhibit very interesting behaviors: one ant has
limited capa-bilities, but the behavior of a whole ant colony is
highly structured. They arecapable of finding the shortest path
from their nest to a food source, withoutusing visual cues but by
exploiting pheromone information. While walking,ants can deposit
some pheromone on the path. The probability that the antscoming
later choose the path which is proportional to the amount of
pheromoneon the path, previously deposited by other ants.
The basic model of the ACS is that: m ants are initially placed
at a startpoint with n decision points to the destination. Each ant
builds a tour byrepeatedly applying a stochastic greedy rule, which
is called the state transitionrule.
S ={argmaxqEr [(p, q)][(p, q) ], if e < e0 (exploitation)S,
otherwise
(6)
(p, q) represents an edge between point p and q, and (p, q)
stands for thepheromone on edge (p, q). (p, q) is the desirability
of edge (p, q), which isusually defined as the inverse of the
length of edge (p, q). e is a random numberuniformly distributed in
[0, 1], e0 is a user-defined parameter with (0e01), is the
parameter controlling the relative importance of the desirability.
Eris the set of edges available at decision point r. S is a random
variable selectedaccording to the probability distribution given
below.
P (p, s) =
[(r, s)] [(r, s) ]
qEr[(r, s)] [(r, s) ], if e < e0(exploitation)
0, otherwise(7)
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8 Sundeep Vilasagarapu, Ram Mohana Reddy Guddeti
The selection strategy used above is also called roulette wheel
selection sinceits mechanism is a simulation of the operation of a
roulette wheel.
A certain amount of pheromone is dropped when an ant goes by. It
is a con-tinuous process, but we can regard it as a discrete
release by some rules. Herewe introduce two kinds of pheromone
update strategies, called local updatingrule and the global
updating rule.
Local updating rule: While constructing its tour, an ant will
modify the amountof pheromone on the passed edges by applying the
local updating rule.
(p, s) = (1 ) (p, s) + 0 (8)where is the coefficient
representing pheromone evaporation (0
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A Hybrid Bio-Inspired Algorithm for NP-Hard Job Shop Scheduling
Problem 9
The next step is to compute the fitness of each particle for its
new positionthrough Eqs. (1) and (2). The absolute value of Vkd and
Xkd may be great.Thus, the particle may overshoot the problem
space. Therefore, the Vkd islimited to the range of [-n, n] and Xkd
is limited to a range of [1, n]. Thecomputational result of Eq. 2
will generate repetitive code (job number) inevery segment, i.e.
one job is processed on the same machine repeatedly. Thisbreaches
the constraint conditions in JSSP. We call the computation
resultsthat breach constraints illegal solutions. Illegal solutions
can be converted tolegal solutions by modification.
The process of modifying solutions is as follows:1. Inspect each
particle on each machine and note the job numbers which are
repetitive and absent.2. According to the increment order of
their process, sort the absent job num-
bers on each machine of a particle.3. Then for each particle
replace those absent job numbers for repetitive ones
on each machine from low to high dimensions.From the above steps
we obtain the legal solution and as ACO has the
best positive feedback system for meteoric discovery of best
solutions. Weintegrated the ACO module to the PSO which is shown in
Figure 2. Thecomplete procedure of the ACO Module is described
below:
ACO Module:1. Initialize all the parameters.2. calculate the
number of subsets according to the jobs number.3. Initialize the
positions with the optimum solutions obtained from the above
module.4. Construct the first scheduling according to transition
possibilities and state
transition rule. Compute object function for the first
scheduling;5. Carry out local search. Adjust the initial scheduling
obtained by step 4
according to local search method. Compute object functions. Save
the bestone and carry out local updating according to it;
6. Carry out global updating according to the best scheduling
obtained fromthe very beginning to now;
7. According to the maximal generation defined in the algorithm,
repeat step4 to step 6 until the terminated condition is met. Make
the best schedulingobtained as the optimum scheduling of this
subset;
8. Obtain the optimum scheduling of this subset. Repeat step 3
to step 7 untilthe number of maximal subsets is met;
9. Compare the optimum scheduling obtained in step 8 and make
the bestone as the global optimum scheduling.
4.2 JSSP Using CSO and ACO
CSO Module: For n-jobs and m-machines, the solution is presented
by a se-quence of n x m operations. In order to apply CSO to the
JSSP, a generic
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10 Sundeep Vilasagarapu, Ram Mohana Reddy Guddeti
Fig. 2: Combined PSO and ACO Architecture.
solution of the problem should be encoded. Each solution is
represented by asequence of all operations. The operations are
numbered from 1 to n*m. Everyprocess is represented by a pair moi
and toi (z [1,(n*m)] ), where moi andtoi represents the machine on
which the process oi will be executed, and theprocessing time of
operation ok.
The matrix information shown below has 5 rows and (n*m) columns.
It isdeveloped to represent all the information about each
operation:
O1 O2 O3 O4 O5 O6 O7 O8 OiJo1 Jo2 Jo3 Jo4 Jo5 Jo6 Jo7 Jo8 JoiSo1
So2 So3 So4 So5 So6 So7 So8 SoiMo1 Mo2 Mo3 Mo4 Mo5 Mo6 Mo7 Mo8
MoiTo1 To2 To3 To4 To5 To6 To7 To8 Toi
where Oi: The number of operations in schedule (i
[1,(n*m)]).
Joi : The job of operation oi.Soi : The sequence of operation oi
in corresponding job.Moi : The machine name where the operation oi
will be processed.Toi : The processing time of operation oi.
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A Hybrid Bio-Inspired Algorithm for NP-Hard Job Shop Scheduling
Problem 11
1. Initialize the position of the cats with a random solution
and its flag byMR.
2. To correct the random solution consider a new as the new
solution andold as the current solution. The process of correction
is described asfollow:
(a) Scan the vector solution old.(b) The first available
operation is added to task queue of new and deleted
from old.(c) Repeat (a) and (b) until old vector is cleared.
Finally we will obtain
a valid solution.3. Now calculate the makespan (schedule length)
of the valid schedule solution
and update xbest.4. Changing the position of each cat with
respect to its mode indicated by its
flag5. Updates the value of the flag of each cat according to
MR.6. Check for the termination condition. If yes, exit else repeat
the steps 3, 4
and 5.
To integrate the above module with the ACO, the optimum
solutions ob-tained from the CSO module are given as input and
repeat the steps describedin the above ACO module.
4.3 Parallel Framework of ACO
The structure of sequential ACO algorithm is highly suitable for
paralleliza-tion. The behavior of a single ant during the iteration
is totally independentof the behavior of all other ants during that
iteration which provides scope fortask parallelism. This behavior
of the ants was the motivation to develop analgorithmic strategy
for parallelization.
Stefan [22] proposed a simple parallelization strategy for the
ACO. Wemodified it according to our problem and made the ants to
compute the sched-ules in parallel. This would result in a
master-slaves paradigm as shown inFigure 5. The master initializes
the information about the problem (the initialpheromone trail 0 and
the data set n x m matrix), and captures the globalknowledge (the
pheromone matrix, the best found solution) acquired duringthe
search process represented by the workers. Each worker handles an
antprocess. At each iteration, the master distributes the pheromone
matrix to allslaves. Each slave receives the pheromone matrix,
constructs a feasible sched-ule and sends the result to the master.
After receiving all the solutions, themaster updates the trail
levels and checks for the best schedule found so far,and then the
process is iterated.
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12 Sundeep Vilasagarapu, Ram Mohana Reddy Guddeti
Fig. 3: Combined CSO and ACO Architecture.
Fig. 4: Master-Slave paradigm for parallel ant colony
algorithm
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A Hybrid Bio-Inspired Algorithm for NP-Hard Job Shop Scheduling
Problem 13
5 Experimental Results and Analysis
All the algorithms have been coded in MATLAB 2011a and tested on
the HPdesktop with Intel I7 3.40 GHz Processor, 8 GB RAM and NVIDIA
NVS 300GPU having 2 compute units and 512 MB RAM. The proposed
experimentis to obtain the optimum solutions for the JSSP using
hybrid bio-inspiredalgorithms.
To explain the effectiveness and performance of the proposed
algorithms inthis paper, various kinds of benchmark job-shop
instances with different sizeshave been selected to compute. All
instances are downloaded from the OR-Library
(http://people.brunel.ac.uk/mastjjb/jeb/orlib/files/jobshop1.txt).Table
2 contain the results of bio-inspired algorithms tested on forty
Lawrenceinstances LA01-LA40 and table 3 constain the other
different benchmark in-stances Abz5-Abz9,Orb1-Orb10,FT06,FT10,FT20.
The columns in the table,problem is for instance name, n for no. of
jobs and m for no. of machines,BKS for best known solution so far,
the error percentage is obtained by Eq(11), combination of pso-aco
and cso-aco are the best solutions obtained byapplying these hybrid
algorithms to each instance on average 15 times.
Error% = (BestBKS)BKS
100 (11)
Setting parameters: In PSO Swarm size of 20, the maximum number
of itera-tive generations is set to 400, inertia weight of 0.9 and
acceleration constantsC1, C2 each equal to 2.0. In CSO, SMP 5, CDC
8, C1 2.05, r1 [0,1], inertia weight of 0.8. In ACO, 2, 0.1, 0.1
and themaximum number of iterative generations is set to 800.
For the combination of cso and aco maximum no of instances x%
optimalresults the error percentage is 0% for all these instances.
Using combination ofcso and aco for most of the instances
LA01-LA12, it reaches the BKS in lessthan 60 seconds. And for
instances LA31-LA35, it reaches the BKS within1800 seconds for all
instances. On the other side pso and aco combinationgot optimal
results for y% and it takes on average less than 90 seconds forthe
instances LA01-LA15 and less than 210 seconds for the instances
2600seconds.
With the support of ACO for inherent parallelism, we implemented
themodule of ACO in parallel using MATLAB. There is no much
difference in theoptimal results further compared to the serial
hybrid algorithm but obtainedthese results in less time. From the
graph shown in Figure X, we can easilyconclude that serial
implementation of hybrid algorithms are having greatestrunning time
compared to parallel implementation . This is because GPUsare more
suitable for running data-parallel workloads than CPUs, and theACO
approach utilizes parallelization. And the speed up factor of
cso-acocombination is 2.19 and pso-aco combination is 1.76.
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14 Sundeep Vilasagarapu, Ram Mohana Reddy Guddeti
Table 2: Results obtained for hybrid algorithms using Lawrence
instancesProblem N M BKS Using PSO and ACO Using CSO and ACO
LA01 10 5 666 666 666LA02 10 5 655 655 655LA03 10 5 597 597
597LA04 10 5 590 590 590LA05 10 5 593 593 593LA06 15 5 926 926
926LA07 15 5 890 890 890LA08 15 5 863 863 863LA09 15 5 951 951
951LA10 15 5 958 958 958LA11 20 5 1222 1222 1222LA12 20 5 1039 1039
1039LA13 20 5 1150 1150 1150LA14 20 5 1292 1292 1292LA15 20 5 1207
1207 1207LA16 10 10 945 945 945LA17 10 10 784 784 784LA18 10 10 848
848 848LA19 10 10 842 842 842LA20 10 10 902 902 902LA21 15 10 1046
1047 1053LA22 15 10 927 927 927LA23 15 10 1032 1032 1032LA24 15 10
935 938 938LA25 15 10 977 977 977LA26 20 10 1218 1218 1218LA27 20
10 1235 1236 1235LA28 20 10 1216 1216 1216LA29 20 10 1157 1164
1157LA30 20 10 1355 1355 1355LA31 30 10 1784 1784 1784LA32 30 10
1850 1850 1850LA33 30 10 1719 1719 1719LA34 30 10 1721 1721
1721LA35 30 10 1888 1888 1888LA36 15 15 1268 1269 1268LA37 15 15
1397 1401 1397LA38 15 15 1196 1208 1173LA39 15 15 1233 1240
1233LA40 15 15 1222 1226 1228
6 Conclusion and Future Work
To improve the performance for large scale data, bio-inspired
algorithms likeparticle swarm optimization (PSO), cat swarm
optimization (cso), ant colonyoptimization (ACO) techniques are
used. The main aim is to develop a hybridbio-inspired algorithm
that gives the best optimum solution. Experimentalresults shows
that combination CSO-ACO outperforms PSO-ACO with lesspercentage of
error for benchmark data sets. In addition to that, the
parallelcombination have a speed up factor of 2.19 for cso-aco and
1.76 for pso-aco
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A Hybrid Bio-Inspired Algorithm for NP-Hard Job Shop Scheduling
Problem 15
Table 3: Results obtained for hybrid algorithms using Abz,Orb,FT
instancesProblem N M BKS Using PSO and ACO Using CSO and ACO
Abz5 10 10 1234 1234 1234Abz6 10 10 943 943 943Abz7 20 15 654
654 654Abz8 20 15 634 634 634Abz9 20 15 656 656 721Orb1 10 10 1059
1059 1059Orb2 10 10 888 888 888Orb3 10 10 1005 1005 1005Orb4 10 10
1005 1005 1005Orb5 10 10 888 889 888Orb6 10 10 1010 1013 1010Orb7
10 10 397 401 397Orb8 10 10 899 899 899Orb9 10 10 934 934 934
Orb10 10 10 944 944 944Ft06 6 6 55 55 55Ft10 10 10 930 930
930Ft20 20 5 1165 1175 1165
Fig. 5: Results of serial and parallel hybrid algorithms.
combinations which shows that running time of parallel hybrid
algorithms ismuch lesser than their serial implementation.
Acknowledgements The authors are grateful to Liu et al. [1] for
their proposed workwhich provided scope and the foundation for our
work.
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16 Sundeep Vilasagarapu, Ram Mohana Reddy Guddeti
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