Basics of Optimization & Cohort Intelligence: A Socio-inspired Optimization Technique

Basics of Optimization
and
Cohort Intelligence: A Socio-Inspired Optimization
Technique
Anand J Kulkarni
PhD, MASc, BEng, DME
Head & Associate Professor
Department of Mechanical Engineering
Symbiosis Institute of Technology
Symbiosis International University
Pune 412 115, MH, India
Email: anand.kulkarni@sitpune.edu.in;
kulk0003@ntu.edu.sg
Ph: 91 20 3911 6468
Odette School of Business
University of Windsor
401 Sunset Avenue
Windsor, Ontario N9B 3P4
Canada
E-mail: kulk0003@uwindsor.ca
Ph: 1 519 253 3000 (x4939)

Agenda
• Basics of Optimization
• Contemporary Algorithms
• Cohort Intelligence
• Validation
• Test on Combinatorial Problems
• Applications to Real World Problems
• Recent Developments and Future Directions
10/25/2017 Symbiosis International University & University of Windsor 2

What is optimization about?
• Extreme states (i.e. minimum and maximum states out of many or possibly
infinitely many)
Ex. Natural (physical) stable equilibrium state is generally a ‘minimum potential
energy’ state.
• Human activities: to do the best in some sense (Intrinsic Human Nature)
• set a record in a race (shortest/minimum time, etc.)
• retail business (maximize the profit, etc.)
• construction projects (minimize cost, time, etc.)
• power generator design (maximize efficiency, minimize weight, etc.)
• Best job out of several choices
310/25/2017 Symbiosis International University & University of Windsor

• Understand and analyze the natural/physical phenomena
• Mathematically model it
• Solve real world problems

• Real world issues:
• Requirements and constraints imposed on products, systems,
processes, etc.
• Creating feasible design (solution)
• Creating a best possible design (solution)
• “Design optimization”: highly complex, conflicting constraints and
considerations, etc.

Importance of Optimization
• Greater concern about the limited energy, material, economic
sources, etc.
• Heightened environmental/ecological considerations
• Increased technological and market competition

A Simple Example
• 5 X 7 metal sheet
• 𝑥 can take different values between 0 and 2.5
• Infinite box designs (solutions)
• Aim: Biggest box volume (Maximization)

A Simple Example
• Setting obtain stationary points
or
 '
0f x 
0.96x  3.04x 
   0.96 15.02 ; 3.04 3.02f f  
    
 
 
3 2
' 2
2
''
2
5 2 7 2 4 24 35 , 0 2.5
12 48 35
24 48
f x x x x x x x x
df
f x x x
dx
d f
f x x
dx
       
   
  

9
-10
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5 6

A Simple Example
• Roots and Optima
• Find roots by setting
• For maximum and
• For minimum and
  0f x 
 '
0f x 
 ''
0f x 
 ''
0f x 
 '
0f x 

Local and Global Optimum
• An objective function is at its local minimum at the point if
for all feasible within its small neighborhood of
14
    *
f fX X
*
Xf
X
*
X

Local and Global Optimum
• An objective is at its global minimum at the point if
for all feasible .
15
    *
f fX X*
Xf
X

Design of a Can

Basic Definitions
• A design problem is characterized by a set of design
variables (decision variables)
• Single Variable
• Multi-Variable
where
    2
min 2 logf x x x 
    
    
5
1 2 1 2
5
1 2
min , 2 log
2 log
f x x x x
f x x
 
 X
 1 2,x xX

• 3D view of 2D optimization

Basic Definitions
• Design variables
• Continuous (any value between a specific interval)
• Discrete (the value from a set of distinct numerical values)
• Ex. Integer values, (1, 4.2, 6 11, 12.9, 25.007), binary (0, 1), etc.
• Combinatorial Optimization Problem
• Mixed (discrete & continuous) variables

• Discrete Problems

• Combinatorial Problems

23
http://mathgifs.blogspot.in/2014/03/the-traveling-salesman.html

Basic Definitions
• Unconstrained Optimization Problems
• No restrictions (Constraints) imposed on design variables
• Constrained Optimization Problems
• Restrictions (constraints) are imposed on design variables and the
final solution should satisfy these constraints, i.e. the final solution
should at least be feasible.
• The ‘best’ solution comes further

Basic Definitions
• Depending on physical nature of the problem: ‘Optimal Control
Problem’
• Decomposing the complex problem into a number of simpler sub-
problems
• Linear Programming (LP): If the objective and constraints are linear
• Non-Linear programming (NLP): If any of it is non-linear

General Problem Statement
• Side constraints
• (Splitting into two inequality constraints)
 
 
 
:
0 , 1,...,
0 , 1,...,
, 1,...,
j
k
i
Minimize f
Subject to
g j m
h k l
x i n
 
 

X
X
X
l u
i i ix x x 

Active/Inactive/Violated Constraints
• Inequality Constraints
27
   
1
2
3
4
,
12 5 3000
10 14 4000
50 50
50 50
f f B R
g B R
g B R
g B B
g R R

  
  
     
     
X

• The set of points at which an inequality constraint is active forms a
constraint boundary which separates the feasible region points from
the infeasible region points.

• An inequality constraint is said to be violated at a point , if it is
not satisfied there i.e. .
• If is strictly satisfied i.e. . Then it is said to be inactive at
the point .
• If is satisfied at equality i.e. . Then it is said to be active
at the point .
29
jg
  0jg X
jg   0jg X
X
X
  0jg Xjg
X

30
1 2
2
3
4
5
240000000
10 0
450000
2 0
2
2 0
0
0
g
bd
g
bd
g d b
g b
g d
  
  
  
  
  

• Based on these concepts, equality constraints can only be either
active i.e. or violated i.e. at any point .
31
  0jh X   0jh X X

• Equality & inequality constraints
32
   1 2
1 1 2
2 1 2
3 1 2
1 1 1
2 2 2
,
4 2 12
1
2 4
0 0
0 0
f f x x
h x x
h x x
h x x
g x x
g x x

  
   
  
    
    
X
Design Space
Feasible Region
Infeasible Region

Convexity
• A set of points is a convex set, if for any two points in the set, the
entire straight line segment joining these two points is also in the set.

Convexity
• A function f(X) is convex if it is defined over a convex set and for any
two points of the graph f(X), the straight line segment joining these
two points lies entirely above or on the graph.

Algorithms
• Exact Methods/Algorithms
• Approximations Methods/Algorithms
• Artificially Intelligent methods
• Bio-/Nature-inspired Methods
• Self-organizing Systems

Contemporary Algorithms
• Evolutionary Algorithms
• Genetic Algorithms

• Swarm Intelligence

Contemporary Algorithms

Cohort Intelligence: A Socio
Inspired Optimization Method

Cohort Intelligence
• A Socio-inspired Self Organizing System
• Includes inherent, self realized and rational learning
• Self control and ability avoid obstacles (jumps out of ditches/local solutions)
• Inherent ability to handle constraints
• Inherent ability of handling uncertainty

Conference Publications
• Kulkarni, A.J., Durugkar I.P., Kumar M. (2013): “Cohort Intelligence: A
Self Supervised Learning Behavior”, in Proceedings of IEEE
International Conference on Systems, Man and Cybernetics,
Manchester, UK, 13-16 October 2013, pp. 1396-1400
• Kulkarni, A.J., Baki, F., Chaouch, B. (2014): A New Variant of the
Assignment Problem: Application, NP-hardness and Algorithms,
Optimization Days, Montreal, Canada, May 5-7, 2014

Book Chapters
• Gaikwad, S., Joshi, R., Kulkarni, A.J. (2016): “Cohort Intelligence and
Genetic Algorithm along with Modified Analytical Hierarchy Process to
Recommend an Ice Cream to a Diabetic Patient”, Advances in Intelligent
and Soft Computing, Satapathy, Bhateja, Joshi (Eds), Springer, Vol 468, pp.
279-288
• Gaikwad, S., Joshi, R., Kulkarni, A.J. (2015): “Cohort Intelligence and
Genetic Algorithm along with AHP to recommend an Ice Cream to a
Diabetic Patient”, Lecture Notes in Computer Science, Vol. 9873, Springer,
pp. 40-49
• Shastri, A.S., Jadhav, P.S., Kulkarni, A.J., Abraham, A. (2016): “Solution to
Constrained Test Problems using Cohort Intelligence Algorithm”, Advances
in Intelligent and Soft Computing, Vol. 424, Springer, pp. 427-435

Journal Publications
• Sarmah, D., Kulkarni, A.J. (2017): “Image Steganography Capacity Improvement using
Cohort Intelligence and Modified Multi Random Start Local Search Methods Arabian
Journal for Science and Engineering”, (In Press: Arabian Journal for Science and
Engineering)
• Patankar, N.S., Kulkarni, A.J. (2017): "Variations of Cohort Intelligence", (In Press: Soft
Computing)
• Kale I.R., Kulkarni, A.J. (2017): “Cohort Intelligence Algorithm for Discrete and Mixed
Variable Engineering Problems”, (In Press: International Journal of Parallel, Emergent and
Distributed Systems)
• Shah, P., Agashe, S., Kulkarni, A.J. (2017): “Design of Fractional PID Controller using
Cohort Intelligence Method”, (In Press: Frontiers of Information Technology & Electronic
Engineering)
• Dhavle S.V., Kulkarni, A.J., Shastri A., Kale I.R. (2017): “Design and Economic Optimization
of Shell-and-Tube Heat Exchanger using Cohort Intelligence Algorithm” (In Press: Neural
Computing and Applications)

Journal Publications
• Kulkarni, O., Kulkarni, N., Kulkarni, A.J., Kakandikar, G. (2016): “Constrained
Cohort Intelligence using Static and Dynamic Penalty Function Approach for
Mechanical Components Design” (In Press: International Journal of Parallel,
Emergent and Distributed Systems)
• Kulkarni, A.J., Shabir, H. (2016): “Solving 0-1 Knapsack Problem using Cohort
Intelligence Algorithm”. International Journal of Machine Learning and
Cybernetics, 7(3), pp. 427-441
• Kulkarni, A.J., Baki, M.F., “Chaouch, B.A. (2016): “Application of the Cohort-
Intelligence Optimization Method to Three Selected Combinatorial Optimization
Problems”, European Journal of Operational Research, 250(2), pp. 427-447
• Krishnasamy, G., Kulkarni A.J., Paramesaran, R. (2014): “A hybrid approach for
data clustering based on modified cohort intelligence and K-means”, Expert
Systems with Applications, 41(13), pp. 6009-6016

Book
• Kulkarni, A.J., Krishnasamy, G., Abraham,
A.: “Cohort Intelligence: A Socio-inspired
Optimization Method”, Intelligent Systems
Reference Library, 114 (2017) Springer,
(DOI 10.1007/978-3-319-44254-9), (ISBN:
978-3-319-44254-9)

What is a Cohort
• A group of candidates interacting and competing with one another to
achieve some individual goal which is inherently common to all the
candidates.
Exhibits a Self Organizing System

What is a Cohort?
• They (We??) need a supervisor like a friend/colleague which can work
with us, right?

Can Individuals Learn from Peers?
• “Hole in the Wall” experiment by Dr. Sugata Mitra (1999)
• With no supervision or formal teaching, children can teach
themselves and each other, if motivated by curiosity and peer
interest.
http://www.hole-in-the-wall.com/MIE.html10/25/2017 Symbiosis International University & University of Windsor 48

Cohort Intelligence Algorithm
• Initialize number of candidates in the cohort, quality variations ,
and set up interval reduction factor
• Step 1 The probability associated with the behavior being followed by
every candidate in the cohort is calculated
• Step 2 Using roulette wheel approach every candidate selects
behavior to follow from within the available choices
C t
r

• Step 3 Every candidate shrinks/expands the sampling
interval of every quality based on whether condition
of saturation is satisfied
• Step 4 Every candidate forms behaviors by sampling
the qualities from within the updated sampling
intervals
• Step 5 Every candidate follows the best behavior from
within its behaviors
• Step 6 Cohort behavior saturated?
• NO? go to Step 1

• Step 7 Convergence?
• NO? go to Step 1
• Accept the current cohort behavior as final solution

Cohort behavior
saturated?
Y
N
START
Initialize number of candidates in the cohort,quality
variations, and set up interval reduction factor
STOP
Accept the current
cohort behavioras
final solution
Every candidateshrinks/expandsthe sampling interval of
every quality based on whether condition of saturationis
satisfied
Using roulette wheel approach every candidate selects
behavior to follow from within the available choices
The probability associated with the behavior being
followed by every candidatein the cohort is calculated
N
Every candidateforms behaviorsby sampling the qualities
from within the updated sampling intervals
Every candidatefollows the best behaviorfrom within its
behaviors
Convergence?
Y
 
 
 
1
1
, 1,...,
1
c
c
C
c
c
f
p c C
f
 

x
x
   
   
 ? ? ?
2 , 2
c c c
i i i i ix r x r          
   , 1,...,c
f c Cx
      1
,..., ,...,C c C
f f fF x x x
   1Minimize ,... ,...,
Subject to , 1,...,
i N
lower upper
i i i
f f x x x
x i N

    
x
 1,...,c C  1 ,... ,...,c c c c
i Nx x xx  c
f x
Candidates Qualities Behavior
Possibility of
being followed
Neighborhood
space
New Qualities &
Behaviors
Cohort
Solutions

Roulette Wheel Selection

Learning Attempt
𝐿
2
1
3
4
5
1
4
5
2
3
𝑝1 𝑝1
+ 𝑝2
𝑝1
+ 𝑝2
+ 𝑝3 𝑝1
+ 𝑝2
+ 𝑝3
+𝑝4
𝑝1
+ 𝑝2
+ 𝑝3
+𝑝4
+𝑝5
= 1
0
𝑥1
𝑥2
𝑥1
𝑥2
𝛹2
𝛹3
𝛹4
Learning Attempt
𝐿 + 1
Roulette Wheel
Selection
𝑟𝑎𝑛𝑑 = 0,1
𝛹1
𝛹2
𝛹3
𝛹4
𝛹5

• Ackley Function
Variable 1
Variable2
-6 -4 -2 0 2 4 6 8
-6
-4
-2
0
2
4
6
8
Variable 1
Variable2
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5
-4
-3
-2
-1
0
1
2
3
4
5
Variable 1
Variable2
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5
-4
-3
-2
-1
0
1
2
3
4
5
Variable 1
Variable2
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5
-4
-3
-2
-1
0
1
2
3
4
5
(a) Learning Attempt 1 (b) Learning Attempt 10
(c) Learning Attempt 15 (d) Learning Attempt 3010/25/2017 Symbiosis International University & University of Windsor 56

Problem
RHPSO [13] CPSO [16]
LDWPSO
[16]
SQP [15] Proposed CI
Best
Mean
Worst
Best
Mean
Worst
Best
Mean
Worst
Best
Mean
Worst
Best
Mean
Worst
FE SD Time (sec)
Sphere
1.5000E-323
3.5078E-245
5.0380E-248
1.4356E-81
3.4213E-12
1.7103E-10
1.5387E-06
1.2102E-04
1.1486E-03
3.5657E-28
2.5749E-27
8.8173E-27
2.0000E-15
2.4900E-06
1.7780E-05
5 0.80
18750 4.5800E-03 1.55
Rosenbrock
1.5606E-08
1.2061E-07
3.0398E-07
1.1856E-08
9.3949E-03
9.0066E-02
2.8453E_03
3.1101E+00
1.1050E+01
7.5595E-12
1.4352E+00
3.9866E+00
0.0000E+00
0.0000E+00
0.0000E+00
5 0.80
9750 0.0000E+00 5.20
Ackley
0.0000E+00
0.0000E+00
0.0000E+00
8.8178E-16
1.5952E-08
6.3330E-07
1.3078E-04
5.9934E-03
2.5325E-02
1.5245E+01
1.9090E+01
1.9959E+01
1.2322E-07
2.0911E-07
2.6499E-07
5 0.85
11250 4.3200E-08 1.50
Griewank
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
2.1287E-10
6.4174E-09
1.6949E-02
1.7072E-01
7.2835E-01
2.8879E-09
3.5357E-01
3.6312E+00
7.3960E-03
1.7100E-02
4.9183E-02
5 0.997
18750 8.8300E-03 2.00
0 20 40 60 80 100 120 140 160
0
200
400
600
800
1000
1200
Learning Attempts
Behavior
Candidate 1
Candidate 2
Candidate 3
Candidate 4
Candidate 5
0 50 100 150 200 250
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Learning Attempts
Behavior
Candidate 1
Candidate 2
Candidate 3
Candidate 4
Candidate 5
C r

Cohort Intelligence
• Packing Problem
10/25/2017 58Symbiosis International University & University of Windsor
 
 
1
1
where (
( )
0,, ,) 1 1
N
i i
i
N
i i
i
i
Maximize f
Subject to f W
x if w x N
v x




  


v
w
w

Feasibility-based Rule
1. If the solution of candidate c is feasible:
1.1. Adds a randomly chosen object from the candidate being followed
respecting feasibility.
1.2. Replaces a randomly chosen object with another randomly chosen one
from the candidate being followed respecting feasibility.
2. If the candidate c is infeasible:
• 2.1. Removes a randomly chosen object from within its knapsack.
• 2.2. Replaces a randomly chosen object with another randomly chosen one
from the candidate being followed, such that the total weight of the
candidate c decreases.

Candidate 1 follow 3

Performance

Cohort Intelligence
• Traveling Salesman Problem
Problem
Name
Cities Reported
Optimum
Cohort
Intelligence
Solution
Standard
Deviation
Burma 14 14 30.8785 30.8785 0.00
P 01 15 284.3809 284.381 0.00
Ulysses 16 16 74.1087 73.9876 0.099
Groetschel 17 17 2085 2085 1.90
Groetschel 21 21 2707 2707 0.98
Ulysses 22 22 75.5975 75.5975 0.37
Groetschel 24 24 1272 1272 14.85
Fri 26 26 937 937 8.38
Bays 29 29 9074 9108.8 192.26
0 0 0
1 1 1
𝐸𝑡 𝑉𝑡𝑗 𝑊𝑡𝑗
𝑃𝐸𝑡 𝑃𝑉 𝑡𝑗
𝑃 𝑊 𝑡𝑗
(a) (b) (c)

Hybridization

K-means Algorithm

Clustering/Classification Problems
• Data 150- 1500, Dims 3 to 13, Clusters 2-6
Dataset Criteria K-means K-means++ GA SA TS ACO HBMO PSO CI MCI K-MCI
Iris Best 97.3259 97.3259 113.987 97.457 97.366 97.101 96.752 96.8942 96.6557 96.655 96.6554
S.D 12.938 5.578 14.563 2.018 0.53 0.367 0.531 0.347 0.0002 0 0
NFE 80 71 38128 5314 20201 10998 11214 4953 7250 4500 3500
Wine Best 16555.7 16555.68 16530.5 16473 16666 16531 16357.28 16346 16298 16295 16292.4
S.D 874.148 637.14 0 753.08 52.073 0 0 85.497 2.118 0.907 0.13
NFE 285 261 33551 17264 22716 15473 7238 16532 17500 16500 6250
Cancer Best 2988.43 2986.96 2999.32 2993.5 2982.8 2970.5 2989.94 2973.5 2964.64 2964.4 2964.38
S.D 2.469 0.689 229.734 230.19 232.22 90.5 103.471 110.801 0.094 0.007 0
NFE 120 112 20221 17387 18981 15983 19982 16290 7500 7000 5000
CMC Best 5703.2 5703.2 5705.63 5849 5885.1 5701.9 5699.26 5700.98 5695.33 5694.3 5693.73
S.D 1.033 0.955 50.369 50.867 40.845 45.634 12.69 46.959 0.482 0.198 0.014
NFE 187 163 29483 26829 28945 20436 19496 21456 30000 28000 15000
Glass Best 215.73 215.36 278.37 275.16 279.87 269.72 245.73 270.57 219.37 213.03 212.34
S.D 2.456 2.455 4.138 4.238 4.19 3.584 2.438 4.55 1.766 0.923 0.135
NFE 533 510 199892 199438 199574 196581 195439 198765 55000 50000 25000
Vowel Best 149399 149394.6 149514 149370 149468 149396 149201.6 148976 149140 148985 148967
S.D 3425.25 3119.751 3105.54 2847.1 2846.2 3485.4 2746.041 2881.35 495.059 43.735 36.086
NFE 146 129 10548 9423 9528 8046 8436 9635 15000 13500 7500

Design and Economic Optimization of Shell
and Tube Heat Exchanger (STHE)
Tube outlet
Shell outlet Tube inlet
Shell inlet
Baffles
Baffle Spacing
Shell Diameter
Tube Diameter
𝑚: mass flow rate 𝐾𝑔/𝑠 𝐶 𝑝: Specific Heat 𝐾𝐽/𝐾𝑔 𝐾
𝑇𝑖: Inlet Temperature 𝐾 𝜇 : Dynamic Viscosity 𝑃𝑎 𝑠
𝑇𝑜: Outlet Temperature 𝐾 𝑘 : Thermal Conductivity 𝑊/𝑚 𝐾
𝜌 ∶ Density 𝐾𝑔/ 𝑚3
𝑅𝑓: Fouling Resistance 𝑚2
𝐾/𝑊
Physical Properties 𝑚 𝑇𝑖 𝑇𝑜 𝜌 𝐶 𝑝 𝜇 𝑘 𝑅𝑓
Case 1 (Kern 1950)
Shell side: Methanol 27.8 95 40 750 2.84 0.00034 0.19 0.00033
Tube side: Sea water 68.9 25 40 995 4.20 0.00080 0.59 0.00020
Case 2 (Kern 1950)
Shell side: Kerosene 5.52 199 93.3 850 2.47 0.00040 0.13 0.00061
Tube side: Crude oil 18.8 37.8 76.7 995 2.05 0.00358 0.13 0.00061
Case 3 (Sinnot 2005)
Shell side: Distilled water 22.07 33.9 29.4 995 4.18 0.00080 0.62 0.00017
Tube side: Raw water 35.31 23.9 26.7 999 4.18 0.00092 0.62 0.00017

Case 1 Results Comparison
68
Parameters
Original
Study GA PSO ABC BBO ITHS I-ITHS CI
𝐷𝑠(𝑚) 0.894 0.83 0.81 1.3905 0.801 0.762 0.7635 0.7800
𝐿(𝑚) 4.83 3.379 3.115 3.963 2.04 2.0791 2.0391 1.9367
𝐵(𝑚) 0.356 0.5 0.424 0.4669 0.5 0.4988 0.4955 0.500
𝑑 𝑜(𝑚) 0.02 0.016 0.015 0.0104 0.01 0.0101 0.01 0.010
𝑃𝑡(𝑚) 0.025 0.02 0.0187 - 0.0125 0.1264 0.0125 0.0125
𝐶1(𝑚) 0.005 0.004 0.0037 - 0.0025 0.0253 0.0025 0.0025
𝑛 2 2 2 2 2 2 2 2
𝑁𝑡 918 1567 1658 1528 3587 3454 3558 3734.1233
𝑣𝑡(𝑚/𝑠) 0.75 0.69 0.67 0.36 0.77 0.782 0.7744 0.7381
𝑅𝑒𝑡 14925 10936 10503 - 7642.49 7842.52 7701.29 7342.7474
𝑃𝑟𝑡 5.7 5.7 5.7 - 5.7 5.7 5.7 5.6949
ℎ𝑡(𝑊/𝑚2
𝐾) 3812 3762 3721 3818 4314 4415.918 4388.79 4584.7085
𝑓𝑡 0.028 0.031 0.0311 - 0.034 0.0354 0.03555 0.0343
∆𝑃𝑡(𝑃𝑎) 6251 4298 4171 3043 6156 6998.7 6887.63 5862.7287
𝑎 𝑠(𝑚2
) 0.032 0.083 0.0687 - 0.0801 0.07602 0.07567 0.0780
𝐷𝑒(𝑚) 0.014 0.011 0.0107 - 0.007 0.00719 0.00711 0.0071
𝑣𝑠(𝑚/𝑠) 0.58 0.44 0.53 0.118 0.46 0.48755 0.48979 0.4752
𝑅𝑒𝑠 18381 11075 12678 - 7254 7736.89 7684.054 7451.3906
𝑃𝑟𝑠 5.1 5.1 5.1 - 5.1 5.08215 5.08215 5.0821
ℎ 𝑠(𝑊/𝑚2
𝐾) 1573 1740 1950.8 3396 2197 2213.89 2230.913 2195.9461
𝑓𝑠 0.33 0.357 0.349 - 0.379 0.3759 0.37621 0.3780
∆𝑃𝑠(𝑃𝑎) 35789 13267 20551 8390 13799 14794.94 14953.91 13608.4472
𝑈 (𝑊/𝑚2
𝐾) 615 660 713.9 832 755 760.594 761.578 764.5084
𝑆 (𝑚2
) 278.6 262.8 243.2 - 229.95 228.32 228.03 227.1607
𝐶𝑖(€) 51507 49259 46453 44559 44536 44301.66 44259.01 44132.5190
𝐶𝑜(€/𝑦𝑒𝑎𝑟) 21111 947 1038.7 1014.5 984 964.164 962.4858 955.9112
𝐶𝑜𝐷(€) 12973 5818 6778.2 6233.8 6046 5924.343 5914.058 5873.6607
𝐶𝑡𝑜𝑡 (€) 64480 55077 53231 50793 50582 50226 50173 50006.1797

Cost Comparison for Case 1
51507 49259 46453 44559 44536 44301.66 44259.01 44132.519
12973
5818
6778.2
6233.8 6046 5924.373 5914.058 5873.6607
0
10000
20000
30000
40000
50000
60000
70000
Original
Study
GA
PSO
ABC
BBO
ITHS
I-ITHS
CI
Total discounted operating cost
Capital investment

Case 2 Results Comparison
Parameters
Original
Study GA PSO ABC BBO ITHS I-ITHS CI
𝐷𝑠(𝑚) 0.539 0.63 0.59 0.3293 0.74 0.32079 0.31619 0.4580
𝐿(𝑚) 4.88 2.153 1.56 3.6468 1.199 5.15184 5.06235 1.3833
𝐵(𝑚) 0.127 0.12 0.1112 0.0924 0.1066 0.24725 0.24147 0.125
𝑑 𝑜(𝑚) 0.025 0.02 0.015 0.0105 0.015 0.01204 0.01171 0.0100
𝑃𝑡(𝑚) 0.031 0.025 0.0187 - 0.0188 0.01505 0.01464 0.0125
𝐶1(𝑚) 0.006 0.005 0.0037 - 0.0038 0.00301 0.00293 0.0025
𝑛 4 4 2 2 2 1 1 2
𝑁𝑡 158 391 646 511 1061 301 309 1152.888
𝑣𝑡(𝑚/𝑠) 1.44 0.87 0.93 0.43 0.69 0.8615 0.8871 0.6522
𝑅𝑒𝑡 8227 4068 3283 - 2298 2306.77 2303.46 1450.0174
𝑃𝑟𝑡 55.2 55.2 55.2 - 55.2 56.4538 56.4538 56.4538
ℎ𝑡(𝑊/𝑚2
𝐾) 619 1168 1205 2186 1251 1398.85 1435.68 1639.2213
𝑓𝑡 0.033 1168 0.044 - 0.05 0.04848 0.04854 0.0591
∆𝑃𝑡(𝑃𝑎) 49245 14009 16926 1696 5109 10502.45 11165.45 5382.9311
𝑎 𝑠(𝑚2
) 0.0137 0.0148 0.0131 - 0.0158 0.01585 0.01527 0.0114
𝐷𝑒(𝑚) 0.025 0.019 0.0149 - 0.0149 0.01188 0.01157 0.0071
𝑣𝑠(𝑚/𝑠) 0.47 0.43 0.495 0.37 0.432 0.40948 0.42526 0.5672
𝑅𝑒𝑠 25281 18327 15844 - 13689 10345.29 10456.39 8568.0357
𝑃𝑟𝑠 7.5 7.5 7.5 - 7.5 7.6 7.6 7.6
ℎ 𝑠(𝑊/𝑚2
𝐾) 920 1034 1288 868 1278 1248.86 1290.789 2062.1966
𝑓𝑠 0.315 0.331 0.337 - 0.345 0.35987 0.35929 0.3702
∆𝑃𝑠(𝑃𝑎) 24909 15717 21745 10667 15275 14414.26 15820.74 36090.0964
𝑈 (𝑊/𝑚2
𝐾) 317 376 409.3 323 317.75 326.071 331.358 381.6827
𝑆 (𝑚2
) 61.5 52.9 47.5 61.566 60.35 58.641 57.705 50.09702
𝐶𝑖(€) 19007 17599 16707 19014 18799 18536.55 18383.46 17129.8543
𝐶𝑜(€/𝑦𝑒𝑎𝑟) 1304 440 523.3 197.139 164.414 272.576 292.7937 352.885
𝐶𝑜𝐷 (€) 8012 2704 3215.6 1211.3 1010.25 1674.86 1799.09 2163.3257
𝐶𝑡𝑜𝑡 (€) 27020 20303 19922.6 20225 19810 20211 20182 19298.18

19007
17599 16707
19014 18799 18536.55 18383.46 17129.8543
8012
2704 3215.6
1211.3 1010.25 1674.86 1799.09
2168.3257
0
5000
10000
15000
20000
25000
30000
OriginalStudy
GA
PSO
ABC
BBO
ITHS
I-ITHS
CI
TotalCost(€)
Capital investment

Case 3 Result Comparison
Parameters OriginalStudy GA PSO ABC BBO ITHS I-ITHS CI
𝐷𝑠 𝑚 0.387 0.62 0.0181 1.0024 0.55798 0.5726 0.5671 0.5235
𝐿 𝑚 4.88 1.548 1.45 2.4 1.133 0.9737 0.9761 1.1943
𝐵 𝑚 0.305 0.44 0.423 0.354 0.5 0.4974 0.4989 0.5000
𝑑 𝑜 𝑚 0.019 0.016 0.0145 0.103 0.01 0.0101 0.01 0.0100
𝑃𝑡 𝑚 0.023 0.02 0.0187 - 0.0125 0.0126 0.0125 0.0125
𝐶1 𝑚 0.004 0.004 0.0036 - 0.0025 0.0025 0.0025 0.0025
𝑛 2 2 2 2 2 2 2 2
𝑁𝑡 160 803 894 704 1565 1845 1846 1548.6665
𝑣 𝑡 𝑚/𝑠 1.76 0.68 0.74 0.36 0.898 0.747 0.761 0.9083
𝑅𝑒𝑡 36409 9487 9424 - 7804 6552 6614 7889.7151
𝑃𝑟𝑡 6.2 6.2 6.2 - 6.2 6.2 6.2 6.2026
ℎ 𝑡 𝑊/𝑚2 𝐾 6558 6043 5618 4438 9180 5441 5536 4901.7267
𝑓𝑡 0.023 0.031 0.0314 - 0.0337 0.0369 0.0368 0.0336
∆𝑃𝑡 𝑃𝑎 62812 3673 4474 2046 4176 3869 4049 6200.0472
𝑎 𝑠 𝑚2 0.0236 0.0541 0.059 - 0.0558 0.0569 0.0565 0.0523
𝐷 𝑒 𝑚 0.013 0.015 0.01 - 0.0071 0.0071 0.0071 0.0071
𝑣𝑠 𝑚/𝑠 0.94 0.41 0.375 0.12 0.398 0.3893 0.3919 0.4237
𝑅𝑒 𝑠 16200 8039 4814 - 3515 3473 3461 3746.0280
𝑃𝑟𝑠 5.4 5.4 5.4 - 5.4 5.4 5.4 5.3935
ℎ 𝑠 𝑊/𝑚2 𝐾 5735 3476 4088.3 5608 4911 4832 4871 5078.1022
𝑓𝑠 0.337 0.374 0.403 - 0.423 0.4238 0.4241 0.4191
∆𝑃𝑠 𝑃𝑎 67684 4365 4271 27166 5917 4995 5062 6585.2425
𝑈 𝑊/𝑚2 𝐾 1471 1121 1177 1187 1384 1220 1229 1198.4141
𝑆 𝑚2 46.6 62.5 59.2 54.72 55.73 57.3 56.64 58.0975
𝐶𝑖 € 16549 19163 18614 17893 18059 18273 18209 18447.6373
𝐶 𝑜 €/𝑦𝑒𝑎𝑟 4466 272 276 257.82 203.68 231 238 383.4699
𝐶 𝑜𝐷 € 27440 1671 1696 1584.2 1251.5 1419 1464 2356.2566
𝐶𝑡𝑜𝑡 € 43989 20834 20310 19478 19310 19693 19674 20803.8940

16549
19163 18614 17893 18059 18273 18209 18447.6373
27440
1671 1696 1584.2 1251.5 1419 1464 2356.2566
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
OriginalStudy
GA
PSO
ABC
BBO
ITHS
I-ITHS
CI
TotalCost(€)
Capital investment

Performance Details of CI
74
Case studies
Solutions Standard
Deviation
Avg. No. of
Function
Evaluations (FE)
Avg. Comp.
Time (sec)Best
Mean
Worst
Case 1
50006.17969
0.2675 2190 0.2474
50006.52636
50006.93099
Case 2
19298.18004
0.4065 2183 0.3698
19298.65499
19299.50914
Case 3
20803.89398
0.1252 1998 0.2471
20804.06749
20804.31439

Closeness of CI Solution with Other Algorithms
75
Case studies
Total Cost (€) of
CI solution
Referred
algorithms
Solutions of Total
Cost (€)
Closeness to the
Best Reported
Solution (%)
Case 1
Original Study 64480 22.45 ↑
GA 55077 9.21 ↑
PSO 53231.1 6.06 ↑
50006.1797 ABC 50793 1.55 ↑
BBO 50582 1.14 ↑
ITHS 50226 0.44 ↑
I-ITHS 50173 0.33 ↑
Case 2
GA 20303 4.95 ↑
PSO 19922.6 3.13 ↑
19298.1800 ABC 20225 4.58 ↑
BBO 19810 2.58 ↑
ITHS 20211 4.52 ↑
I-ITHS 20182 4.38 ↑
Case 3
GA 20834 0.02 ↑
PSO 20310 2.43 ↓
20803.8940 ABC 19478 6.81 ↓
BBO 19310 7.74 ↓
ITHS 19693 5.64 ↓
I-ITHS 19674 5.74 ↓10/25/2017 Symbiosis International University & University of Windsor

Real World Combinatorial Problems
Anand J Kulkarni
Odette School of Business,
University of Windsor,
401 Sunset Avenue,
Windsor, Ontario N9B 3P4,
Canada
E-mail: kulk0003@uwindsor.ca
Ph: 1 519 253 3000 (x4939)
M F Baki
401 Sunset Avenue,
Canada
E-mail: fbaki@uwindsor.ca
Ph: 1 519 253 3000 (x3118)
Ben A Chaouch
401 Sunset Avenue,
Canada
E-mail: chaouch@uwindsor.ca
Ph: 1 519 253-4232 (x3149)

New Variant of the Assignment Problem
Row Circular Matrix 𝐶 = 𝐶𝑖𝑗
𝐶 =
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
1 2 3 4
7 8 5 6
12 9 10 11
14 15 16 13
1
3
2
4
• Find a permutation that minimizes the maximum column sum
of the rotated matrix.
• It is a variant of the assignment problem equivalent to finding
a permutation that minimizes the minimum column sum of the
rotated matrix.
• 3-Partition problem reduced to the new variant of assignment
problem proving its strong NP-hardness.

New Variant of the Assignment Problem
Circular Matrix 𝐶 =
40 30 22 13
36 29 23 7
32 30 22 7
36 32 23 17
𝜋∗1
= 3, 4, 2, 1
𝐶∗1
=
22 13 40 30
29 23 7 36
7 32 30 22
36 32 23 17
𝐼 𝑘,𝟏 = 94 100 100 105
𝑍 𝐶∗𝜋1
= 105
𝜋∗2
= 2, 3, 4, 1
𝐶∗2
=
13 40 30 22
23 7 36 29
30 22 7 32
36 32 23 17
𝐼 𝑘,1 = 102 101 96 100
𝑍 𝐶∗𝜋2
= 102
𝜋∗3
= 1, 4, 3, 2
𝐶∗3
=
40 30 22 13
29 23 7 36
22 7 32 30
17 36 32 23
𝐼 𝑘,1 = 108 96 93 102
𝑍 𝐶∗𝜋3
= 108
𝐼 𝑘 = 144 121 90 44

New Variant of Assignment Problem
Minimize 𝑍 = 𝑚𝑎𝑥 𝑘=1
𝑛 σ𝑖=1
𝑛
𝐶𝑖,𝑘−𝜋 𝑖 +1 (1)
Subject to
෍
𝑖=1
𝑛
𝑥𝑖,𝑗
= 1 ∀1 ≤ 𝑗 ≤ 𝑛 (2)
෍
𝑗=1
𝑛
𝑥𝑖,𝑗
= 1 ∀1 ≤ 𝑖 ≤ 𝑛 (3)
𝐼 𝑘 = ෍
𝑖=1
𝑛
෍
𝑗=1
𝑛
𝐶𝑖,𝑘−𝑗+1 𝑥𝑖,𝑗
∀1 ≤ 𝑘 ≤ 𝑛 (4)
𝑍 ≥ 𝐼 𝑘 ∀1 ≤ 𝑘 ≤ 𝑛 (5)
𝑥𝑖,𝑗 ∈ 0,1 ∀1 ≤ 𝑖 ≤ 𝑛, 1 ≤ 𝑗 ≤ 𝑛 (6)
• Mathematical Formulation

We refer this problem as
Cyclic Bottleneck Assignment Problem (CBAP).
Cyclic: Row circularity of matrix 𝐶
Bottleneck: minmax objective
Assignment: problem’s close affinity to the classical assignment
problem σ𝑖=1
𝑛
𝐶𝑖,𝜋 𝑖

Applications
40 30 22 13
36 29 23 7
32 30 22 7
36 32 23 17
𝑴 𝑻 𝑾 𝑹
𝑫 𝟏
𝑫 𝟐
𝑫 𝟑
𝑫 𝟒
𝐼 𝑘 = 144 121 90 44
𝑍 𝐶∗𝜋1
= 105
22 13 40 30
29 23 7 36
7 32 30 22
36 32 23 17
𝑴 𝑻 𝑾 𝑹
𝑫 𝟏
𝑫 𝟐
𝑫 𝟑
𝑫 𝟒
𝐼 𝑘 = 94 100 100 105
𝜋∗1 = 3, 4, 2, 1
• Healthcare
• The problem arises in minimizing congestion in the recovery unit
• Planning horizon of n days with cyclic scheduling
• Keep the maximum number of patients as low as possible to reduce
the requirement of beds, nurses and other variable costs
Beds, Nurses, Variable
Costs, etc.

Applications
40 30 22 13
36 29 23 7
32 30 22 7
36 32 23 17
𝑴 𝑻 𝑾 𝑹
𝑺 𝟏
𝑺 𝟐
𝑺 𝟑
𝑺 𝟒
𝐼 𝑘 = 144 121 90 44
𝑍 𝐶∗𝜋1
= 105
22 13 40 30
29 23 7 36
7 32 30 22
36 32 23 17
𝑴 𝑻 𝑾 𝑹
𝑺 𝟏
𝑺 𝟐
𝑺 𝟑
𝑺 𝟒
𝐼 𝑘 = 94 100 100 105
𝜋∗1 = 3, 4, 2, 1
• Inventory Management
• Minimizing the maximum space requirement in a retail store
• Planning horizon of n days
• Suppliers follow a cyclic schedule
Space Requirement

Illustrative Example
𝐶 =
40 30 22 13
36 29 23 7
32 30 22 7
36 32 23 17
𝜋∗1
= 3, 4, 2, 1
𝐶∗1
=
22 13 40 30
29 23 7 36
7 32 30 22
36 32 23 17
𝑍 𝐶∗𝜋1
= 105
𝑃∗1
= 0.333
𝜋∗2
= 2, 3, 4, 1
𝐶∗2
=
13 40 30 22
23 7 36 29
30 22 7 32
36 32 23 17
𝑍 𝐶∗𝜋2
= 102
𝑃∗2
= 0.343
𝜋∗3
= 1, 4, 3, 2
𝐶∗3
=
40 30 22 13
29 23 7 36
22 7 32 30
17 36 32 23
𝑍 𝐶∗𝜋3
= 108
𝑃∗3
= 0.323
4 × 4 matrix, 3 Candidates, 2 variations

𝑡 = 1
The element from 𝜋∗3 = 1, 4, 3, 2 being followed: 3
Its location in the permutation 𝜋∗1 = 3, 4, 2, 1 : 1,1
The updated permutation 𝜋1,1: 2, 4, 3, 1
Updated circular matrix 𝐶∗1 =
22 13 40 30
29 23 7 36
7 32 30 22
36 32 23 17
30 22 13 40
23 7 36 29
30 22 7 32
36 32 23 17
Maximum column sum 𝑍 𝐶1 1: 119
𝑡 = 2 The element from 𝜋3 = 1, 4, 3, 2 being followed: 1
Its location in the permutation 𝜋1 = 3, 4, 2, 1 : 1,4
The updated permutation 𝜋1,2: 1, 4, 2, 3
Updated circular matrix 𝐶∗1 =
22 13 40 30
29 23 7 36
7 32 30 22
36 32 23 17
22 13 40 30
23 7 36 29
22 7 32 30
23 17 36 32
Maximum column sum 𝑍 𝐶1 2: 144
𝑍 𝐶∗𝜋1
= min 𝑍 𝐶 𝜋1 1
, 𝑍 𝐶 𝜋1 2
and
associated permutation 𝜋∗1:
119 and
𝟐, 𝟒, 𝟑, 𝟏
90 44 144 121
119 83 79 118

Numerical Experiments and Results
0 50 100 150 200 250 300 350 400
4660
4680
4700
4720
4740
4760
4780
4800
4820
4840
Learning Attempts
CICandidateSolutions
CI Parameters Cases
Candidates Variations
25 5
Every case - 10 instances & solved 20 times

0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5x5 6x6 7x7 8x8 9x9 10x10 11x11 12x12 13x13
Avg.%gapofLBwithIP
n n
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Avg%gapofCIwithLB
n n
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
5x5 6x6 7x7 8x8 9x9 10x10 11x11 12x12 13x13
Avg.%gapofCIwithIP
n n
0
200
400
600
800
1000
1200
5x5 6x6 7x7 8x8 9x9 10x10 11x11 12x12 13x13
IP:AverageCPUTime
n n

0
2000
4000
6000
8000
10000
12000
14000
16000
18000
5x5 6x6 7x7 8x8 9x9 10x10 11x11 12x12 13x13
CIAverageFE
n n
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
15x15 20x20 25x25 30x30 35x35 40x40 45x45 50x50
CIAverageFE
n n
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
5x5 6x6 7x7 8x8 9x9 10x10 11x11 12x12 13x13
CIAverageCPUTime
n n
0
5
10
15
20
25
30
15x15 20x20 25x25 30x30 35x35 40x40 45x45 50x50
CIAverageCPUTime
n n

Problem Size Average
% gap
LP vs. CPLEX
CPLEX:
Average CPU
Time
(Sec)
CI Method
Average
% gap
LP vs. CI
Average
% gap
CPLEX vs. CI
Standard
Deviation
(SD)
CPU Time
(Sec)
Function
Evaluations
(FE)
5 4.3165 0.27 4.5496 0 0 0.038084 1620
6 3.3520 0.29 3.4857 0 0 0.082466 3169
7 2.4426 0.41 2.5067 0 0 0.141646 5070
8 1.7478 0.73 1.7815 0 0.659745 0.206037 6988
9 1.3584 4.10 1.3778 0 1.920292 0.301112 9136
10 0.9259 13.80 0.9473 0.0120 3.265155 0.359756 10750
11 0.8597 98.31 0.9739 0.1057 2.961605 0.443356 12190
12 0.7083 260.59 0.9296 0.2146 3.045473 0.537049 13601
13 0.5632 1072.93 0.8675 0.2993 2.695255 0.663312 15477
15 -- -- 0.8040 -- 2.832436 0.831481 17827
20 -- -- 0.6492 -- 2.727449 1.659961 26085
25 -- -- 0.5431 -- 2.636055 3.138706 35435
30 -- -- 0.4502 -- 2.668305 5.005378 43715
35 -- -- 0.4031 -- 2.586950 7.842689 51145
40 -- -- 0.3417 -- 2.696257 11.972532 61610
45 -- -- 0.3130 -- 2.468574 17.019936 71835
50 -- -- 0.2784 -- 2.545943 23.980858 81207

Sea Cargo Mix Problem
Deciding a sea cargo shipping schedule for freight bookings accepted in multi-
period planning horizon (Ang et al. 2007)
Maximize: profit generated by all freight bookings
Subject to:
• demand for empty containers at the port of origin is less than or equal to
the number of available empty containers at the port of origin in each
period
• total weight and volume of cargoes which will be carried to a destination
port in a period is less than or equal to the total available weight and
volume capacity of shipment to that port in a that period.
• each cargo may be carried in a certain period on or before its due date or
be refused to carry in the time horizon
• each cargo can be either accepted at its total quantity or be turned down

Total Volume and Weight
Capacity
Volume and Weight Capacity to
different destinations in
particular period
… …
… …
Destination
Ports
Origin Port
Cargoes:
Weight,
Volume, Due
date, port of
destination
Maximize:
Profit

Sea Cargo Mix Problem
Mathematical Formulation
𝑴𝒂𝒙𝒊𝒎𝒊𝒛𝒆 𝑍 = ෍
1≤𝑘≤𝐾
෍
η 𝑘≤𝑡≤𝜏 𝑘
𝑣 𝑘 𝑟𝑘𝑡 𝑥 𝑘𝑡
𝑺𝒖𝒃𝒋𝒆𝒄𝒕 𝒕𝒐
෍
𝑘∈෪𝐾𝑡
𝑣 𝑘 𝑥 𝑘𝑡 ≤ 𝐸𝑡 , ∀𝑡 ∈ ෨𝑇
෍
𝑘∈ ෪𝐾 𝑡𝑗
𝑣 𝑘 𝑥 𝑘𝑡 ≤ 𝑉𝑡𝑗 , ∀𝑡 ∈ ෨𝑇 , ∀𝑗 ∈ ሚ𝐽
෍
𝑘∈ ෪𝐾 𝑡𝑗
𝑤 𝑘 𝑥 𝑘𝑡 ≤ 𝑊𝑡𝑗 , ∀𝑡 ∈ ෨𝑇 ,∀𝑗 ∈ ሚ𝐽
෍
η 𝑘≤𝑡≤𝜏 𝑘
𝑥 𝑘𝑡 ≤ 1 , ∀𝑘 ∈ ෩𝐾
𝑥 𝑘𝑡 ∈ 0,1 , ∀𝑘 ∈ ෩𝐾 , 𝑡 η 𝑘,η 𝑘 + 1,… , 𝜏 𝑘
where ෪𝐾𝑡 = 𝑘: 𝑘 ∈ ෩𝐾 , η 𝑘 ≤ 𝑡 ≤ 𝜏 𝑘 , ∀𝑡 ∈ ෨𝑇 , ෪𝐾𝑡𝑗 = 𝑘: 𝑘 ∈ ෩𝐾 , η 𝑘 ≤ 𝑡 ≤ 𝜏 𝑘 , ξ 𝑘 = 𝑗 , ∀𝑡 ∈ ෨𝑇 , 𝑗 ∈ ሚ𝐽

𝑻, 𝑱, 𝑲 𝑵 𝒗 𝑵 𝒄 IP LP 𝐋 HAM MHA CI Performance
CPU
Time
(sec)
CPU
Time
(sec)
𝑔𝐼𝐻 𝑔 𝐿𝐻 CPU
Time
(sec)
𝑔𝐼𝑀 𝑔 𝐿𝑀 CPU
Time
(sec)
Avg Sol
% Gap
𝐠 𝐔𝐂~
Avg
Sol %
Gap
𝐠 𝐈𝐂~
CPU
Time
(sec)
𝐭 𝐂
SD
(CPU
Time)
𝐒𝐭 𝐂
SD
𝐒𝐈𝐂
SD
𝐒 𝐔𝐂
3, 5, 41 123 74 0.106 0.028 1.59 2.88 0.001 1.55 2.71 0.015 1.3188 0.2452 0.070 0.036 0.691 0.687
3, 6, 47 141 86 0.274 0.047 1.26 2.67 0.002 1.03 2.42 0.023 1.0102 0.6931 0.093 0.027 0.456 0.454
4, 3, 64 256 92 0.480 0.183 0.87 2.32 0.011 0.67 1.53 0.056 0.9958 0.5131 0.103 0.025 0.351 0.349
2, 4, 132 264 150 0.148 0.391 0.68 2.03 0.016 0.51 1.18 0.093 1.0906 1.0059 0.098 0.041 0.408 0.408
3, 3, 91 273 112 0.257 0.289 0.93 1.98 0.008 0.78 1.79 0.046 0.9250 0.8474 0.130 0.046 0.463 0.462
2, 3, 143 286 157 0.096 0.485 0.46 1.03 0.014 0.28 0.68 0.078 0.804 0.7644 0.094 0.037 0.379 0.378
𝑻, 𝑱, 𝑲 𝑵 𝒗 𝑵 𝒄 𝑵𝒊𝒏 IP LP 𝑳 HAM MHA CI Performance
CPU
Time
(sec)
CPU
Time
(sec)
𝑔 𝐿𝐻 CPU
Time
(sec)
𝑔 𝐿𝑀 CPU
Time
(sec)
Avg Sol
% Gap
𝐠 𝐔𝐂~
Avg Sol
% Gap
𝐠 𝐈𝐂~
CPU
Time
(sec)
SD
(CPU
Time)
SD
𝐒𝐈𝐂
SD
𝐒 𝐔𝐂
3, 4, 900 2700 927 10 0.722 419.1 3.92 1.12 1.72 6.17 2.2738 2.2682 0.734 0.271 0.650 0.650
4, 8, 965 3860 1033 10 1.833 1264.3 2.66 2.58 1.16 14.37 1.3321 1.3250 1.382 0.609 0.299 0.299
4, 25, 1000 4000 1204 10 1.240 2012.5 2.05 8.12 0.86 49.66 0.8452 0.8387 0.185 0.225 0.611 0.611
2, 3, 2871 5742 2885 10 1.227 5872.2 1.35 5.11 0.75 28.29 1.7398 1.7357 2.931 0.798 0.380 0.380
2, 3, 3876 7752 3890 10 1.887 199966 0.56 5.97 0.32 55.41 1.1463 1.1428 2.488 0.586 0.303 0.303
5, 37, 1954 9770 2329 10 4.151 12306.1 1.83 57.67 1.26 321.02 1.4282 1.4241 1.305 0.425 0.917 0.917
Small Scale Test Problems
Medium Scale Test Problems

𝑻, 𝑱, 𝑲 𝑵 𝒗 𝑵 𝒄 𝑵𝒊𝒏 HAM MHA CI Performance
CPU
Time
(sec)
CPU
Time
(sec)
Best Sol % Gap
𝐠 𝐔𝐂
Avg Sol % Gap
𝐠 𝐔𝐂~
Worst Sol %
Gap
𝐠 𝐔𝐂^
CPU
Time
(sec)
SD
(CPU Time)
SD
𝐒 𝐔𝐂
9, 47, 1521 13689 2376 10 80.5 447.1 3.3822 4.6675 5.8294 6.7303 0.344 0.707
3, 4, 6576 19728 6603 10 53.2 293.1 3.8078 5.2705 6.6293 61.6805 4.940 0.726
4, 5, 5286 21144 5330 10 54.5 277.7 3.6931 5.1307 6.5576 35.6223 3.819 0.835
4, 13, 5479 21916 5587 10 125.9 785.9 3.8556 5.5827 7.1253 27.2433 2.885 0.898
5, 8, 4954 24770 5039 10 89.9 454.2 4.0504 5.5827 7.0751 41.9530 3.514 0.766
8, 26, 3249 25992 3673 10 178.3 982.9 3.6647 5.2144 7.1465 28.5853 1.212 0.892
Large Scale Test Problems
10 20 30 40 50 60
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
x 10
5
Learning Attempts
CICandidateSolutions
Convergence10/25/2017 Symbiosis International University & University of Windsor 93

0
0.5
1
1.5
2
2.5
3,5,41
3,6,47
4,3,64
2,4,132
3,3,91
2,3,143
3,4,900
4,8,965
4,25,1000
2,3,2871
2,3,3876
5,37,1954
%GapofAvgCIwithIP
T, J, K
0
1
2
3
4
5
6
3,5,41
3,6,47
4,3,64
2,4,132
3,3,91
2,3,143
3,4,900
4,8,965
4,25,1000
2,3,2871
2,3,3876
5,37,1954
9,47,1521
3,4,6576
4,5,5286
4,13,5479
5,8,4954
8,26,3249
%GapofAvgCIwithUB
T, J, K
0
1
2
3
4
5
6
3,5,41
3,6,47
4,3,64
2,4,132
3,3,91
2,3,143
3,4,900
4,8,965
4,25,1000
2,3,2871
2,3,3876
5,37,1954
9,47,1521
3,4,6576
4,5,5286
4,13,5479
5,8,4954
8,26,3249
CI:SD(CPUTime)
T, J, K
0
0.5
1
1.5
2
2.5
3
3.5
3,5,41
3,6,47
4,3,64
2,4,132
3,3,91
2,3,143
3,4,900
4,8,965
4,25,1000
2,3,2871
2,3,3876
5,37,1954
CI:AverageCPUTime
T, J, K
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
3,5,41
3,6,47
4,3,64
2,4,132
3,3,91
2,3,143
3,4,900
4,8,965
4,25,1000
2,3,2871
2,3,3876
5,37,1954
CI:SD(%GapCIandIP)
T, J, K
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
3,5,41
3,6,47
4,3,64
2,4,132
3,3,91
2,3,143
3,4,900
4,8,965
4,25,1000
2,3,2871
2,3,3876
5,37,1954
9,47,1521
3,4,6576
4,5,5286
4,13,5479
5,8,4954
8,26,3249
CI:SD(%GapCIandUB)
T, J, K

Selection of Cross-Border Shippers Problem
• NAFTA
• Increase in Traffic between USA-Canada-Mexico
• Cross-Border Compliance
• Avoidance of Delays at Check Points
• Reduce Transportation Time, Cost, etc.

• Goals:
• ‘volume capacity’: total volume of containers assigned to a
shipper does not exceed its maximum capacity
• ‘fund availability’: ensures that the total expenditure
should not exceed the available fund allotted for a
particular period
• ‘due date delivery’: processing time for a good should not
exceed the due delivery date
• ‘number of maximum allowable non-compliant shippers’
• Type of good and handling ability of Shipper

Shippers:
Individual Volume and
Weight Capacity,
ability to handle type
of good,
Cross-Border
Compliant/non-
compliant,
fixed/variable cost of
shipping
… …
Containers:
Weight,
Volume, Due
date, type of
good
Goals:
Fund, Due date,
maximum
allowable non-
compliant shippers

Single Period Multi periodMathematical Formulation

𝑱, 𝑰 Δ 𝑘 𝑵 𝒗 𝑵 𝒄 𝑵𝒊𝒏 IP CI Performance
CPU
Time
(sec)
Avg Sol %
Gap
CPU
Time
(sec)
SD
(CPU
Time)
5, 41 15, 10, 8, 5, 3 625 621 10 0.4867 2.5042 2.8276 1.0843
6, 47 17, 12, 9, 6, 3 869 873 10 0.4695 2.9914 2.2563 2.3568
8, 64 22, 18, 8, 10, 6 652 586 10 0.8511 4.1836 2.7992 0.7857
4, 132 40, 32, 25, 15, 20 800 666 10 0.5818 5.7075 7.3635 3.9597
8, 91 40, 35, 25, 15, 17 922 829 10 1.2820 4.6123 6.6243 2.4293
3, 143 50, 40, 20, 15, 18 1442 1297 10 5.6789 6.1791 10.6124 5.0364
8, 900 350, 250, 150, 100, 50 5349 904 10 42.9057 5.9488 30.4846 10.0735
8, 965 400, 250, 130, 100, 85 9662 8695 10 55.9057 5.9132 37.1572 7.2841
𝑻, 𝑱, 𝑰 𝛥 𝑘 𝑁𝑣 𝑁𝑐 𝑁𝑖𝑛 IP CI Performance
CPU
Time
(sec)
Avg Sol %
Gap
CPU
Time
(sec)
SD
(CPU Time)
3, 5, 41 15, 10, 8, 5, 3 625 621 10 0.2293 4.2318 8.9319 2.5987
3, 6, 47 17, 12, 9, 6, 3 869 873 10 0.1778 2.6832 8.0473 3.5242
4, 3, 64 22, 18, 8, 10, 6 840 840 10 0.1107 2.1852 6.7515 2.5531
2, 4, 132 40, 32, 25, 15, 20 1181 1178 10 0.2932 5.0093 20.3730 6.3161
3, 3, 91 40, 35, 25,15, 17 825 822 10 0.1560 2.5276 15.3088 2.9411
8, 3, 143 50, 40, 20,15, 18 1032 1030 10 0.2230 2.1348 17.0945 3.4270
3, 4, 900 350, 250, 150, 100, 50 11104 11104 10 0.8642 5.6406 36.2087 7.8925
4, 8, 965 400, 250, 130, 100, 85 9662 8695 10 5.2541 3.8738 74.6240 14.1965
4, 25, 1000 300, 250, 200, 150, 100 27029 26026 10 40.232 6.7197 79.1075 18.0798
8, 3, 2871 900, 700, 600, 500, 171 66730 66734 10 9.9120 4.7621 73.0579 5.7850
8, 3, 3876 1400, 1000, 800, 500, 176 87946 87952 10 18.044 11.4148 108.0878 35.0878
5, 37, 1954 800, 500, 300, 200, 154 316461 316556 10 210.10 5.9746 113.6585 40.0708
9, 47, 1521 600, 400, 300, 121, 100 542795 543019 10 376.31 10.1997 93.0901 22.9238
8, 15, 6576 3000, 2000, 800, 500, 276 883635 883705 10 528.07 11.5074 141.5355 10.6661
8, 15, 5286 2000, 1000, 986, 800, 500 567372 567434 10 352.62 9.8089 130.3254 11.6471
8, 13, 5479 300, 250, 200, 150, 100 493533 493586 10 399.50 10.8206 133.1693 23.9897
8, 8, 4954 1400, 1000, 800, 500, 176 276901 276923 10 128.39 11.5375 71.7315 16.1202
8, 26, 3249 900, 800, 700, 600, 249 581894 582007 10 410.17 10.2553 133.7576 10.8573
Single Period
Multi Period

Path Planning and Obstacle Avoidance for
Swarm Robots using Cohort Intelligence
Palash Roychowdhury
Prakhar Shrivastava
Rishi Devarakonda
Siddarth Mehra
Siddharth Basu
Dr. Anand J Kulkarni

Problem Statement/Objectives
• The application is relevant to search and rescue in alien territory as
well as establishment

• Every robot is assumed
to have two sensors:
• light sensor
• proximity sensor
𝐿1
𝐿2
𝐿3
𝐿4
𝐵1
𝐵2
𝐵3
𝐵4
𝐿
Arena
Every robot is represented by
𝐵𝑖 , 𝑖 = 1,2, … , 𝑁
Receives light with an intensity
𝐿𝑖 , 𝑖 = 1,2, … , 𝑁
The goal/objective is to collectively reach the light source 𝐿 which is a possible
exit door of the arena.

• Path Planning of
swarm robots and
avoidance of
obstacles in complex
in arena using:
Linear Probability
Approach
Exponential
Probability Approach

Roulette Wheel Probability Distribution
POINT ROULETTE WHEEL POSITION PROBABILITY
START POINT END POINT
𝐵1 0 0.40 0.40
𝐵2 0.40 0.55 0.15
𝐵3 0.55 0.75 0.20
𝐵4 0.75 1.00 0.25
𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒 ෍
𝑖=1
𝑁
𝐿𝑖
𝑃𝑖= ൗ
𝐿 𝑖
𝑧
σ𝑖=1
𝑁 𝐿 𝑖
𝑧
𝑃𝑖 = (𝑃1, 𝑃2, 𝑃3,………, 𝑃𝑖)
σ𝑖=1
𝑁
𝑃𝑖 = 1

Motion of Robots
Random Number
Generation
Condition 1: Number
lies in its own region
Condition 2: Number
lies in other robot’s
region
𝑝1 + 𝑝2 + 𝑝3 +𝑝4 +𝑝5= 1
Roulette Wheel
Selection
𝑟𝑎𝑛𝑑 = 0,1
Learning Attempt
𝑛
𝐵2
𝐵1
𝐵3
𝐵4
𝐵5
𝑝1 𝑝1
+ 𝑝2
𝑝1
+ 𝑝2
+ 𝑝3 𝑝1 + 𝑝2 + 𝑝3 +𝑝4
0
𝑥
𝑦
Learning Attempt
𝑛 + 1
𝐿1
𝐿2
𝐿3
𝐿4
𝐿5
𝐵2
𝐵1
𝐵3
𝐵4
𝐵5
𝑥
𝑦
𝐿1
′
𝐿2
′
𝐿4
′
𝐿5
′
𝐵1
𝐵2
𝐵5
𝐵4
𝐿3
′
𝐵3
Following itself Following other candidate

4 Independent Cases, 20 Independent Runs
Linear Probability
𝑃𝑖 = ൗ
𝐿 𝑖
σ 𝑖=1
𝑁 𝐿 𝑖
No Obstacle
Case (NOC)
Rectangular
Obstacles Case
(ROC)
Multiple Rectangular
Obstacles Case
(MROC)
Cluttered Polygons
Obstacles Case
(CPOC)Exponential Probability
𝑃𝑖 = ൗ
𝐿 𝑖
𝑍
σ 𝑖=1
𝑁 𝐿 𝑖
𝑍
𝟓 (five) robots,
CI algorithm was coded in
MATLAB R2014b on
Windows 8.1,
Intel Core i7 2.3GHz processor speed
and
8GB RAM.

No Obstacle Case (NOC): Linear Probability &
Randomly Initiated Robots

108
Illustration 1 Illustration 2
No Obstacle Case (NOC): Exponential Probability &
Randomly Initiated Robots

109
Rectangular Obstacle Case (ROC): Linear Probability
& Randomly Initiated Robots

110
Rectangular Obstacle Case (ROC): Linear Probability
& Randomly Initiated Robots

111
Multiple Rectangular Obstacle Case (MROC):
Exponential Probability & Randomly Initiated Robots

12
Rectangular Obstacle Case (ROC): Exponential
Probability & Randomly Initiated Robots

113
Cluttered Polygonal Obstacle Case (CPOC): Linear

114
Cluttered Polygonal Obstacle Case (CPOC): Exponential

Performance of CI with Linear and Exponential Probability for No Obstacle Case (NOC)
CI with Linear Probability CI with Exponential Probability
Config.
Mean
(FE)
SD
(FE)
Mean
Time
(Seconds)
SD Time
(Seconds)
Mean
Distance
Travelled
Mean
Total Time
(Seconds)
SD Total
Time
(Seconds)
Mean
(FE)
SD
(FE)
Mean
Time
(Seconds)
SD Time
(Seconds)
Mean
Distance
Travelled
Mean
Total Time
(Seconds)
SD Total
Time
(Seconds)
1 1067 442.95 1.30 0.80 4.02 2.03 0.91 852 370.47 1.43 0.80 3.04 1.70 0.80
2 1345 423.19 2.58 0.85 5.75 2.84 1.14 1145 192.88 2.37 0.60 4.61 2.39 0.61
3 1087 517.33 2.04 0.72 3.32 2.81 0.84 1032 411.36 2.26 0.86 3.05 2.43 0.72
4 1240 460.78 2.02 0.67 6.00 2.21 0.84 1095 217.65 2.18 0.53 5.27 2.21 0.49
5 987 425.51 2.31 0.60 4.68 2.56 0.64 947 347.80 2.04 0.59 4.19 2.17 0.64
6 1347 439.04 2.27 0.85 4.23 2.58 0.92 852 367.35 1.72 0.74 3.54 1.80 0.76
7 1115 982.74 2.69 2.38 3.98 2.76 3.09 1010 539.61 2.33 0.99 3.38 2.40 1.29
8 855 359.71 1.44 0.59 5.07 1.63 0.72 742 168.11 1.46 0.54 4.23 1.49 0.52
9 975 342.85 1.82 0.87 4.13 1.88 0.92 935 214.44 1.78 0.60 3.79 1.81 0.59
10 1192 341.24 2.91 0.69 4.77 3.26 0.72 1140 133.74 2.58 0.63 4.08 2.63 0.56
11 1505 514.46 1.54 2.40 4.17 2.48 2.60 1070 314.58 1.60 0.77 3.20 1.85 0.65
12 1287 2238.89 2.25 0.72 7.60 2.65 5.74 1180 173.49 2.46 0.60 4.17 2.49 0.57
13 1230 237.86 2.36 0.60 4.93 2.62 0.64 1022 239.65 2.28 0.52 4.19 2.41 0.57
14 1170 856.73 1.90 0.73 5.20 2.23 1.34 1092 314.05 1.77 0.74 3.96 1.85 0.70
15 1382 332.99 2.23 1.32 5.10 2.25 1.23 1147 305.99 2.07 0.93 4.06 2.08 0.93
16 1832 915.33 2.89 0.68 5.78 3.43 2.17 1147 183.23 2.46 0.55 3.49 2.49 0.55
17 1152 1051.20 2.15 1.04 4.92 2.57 2.25 1025 485.90 2.07 0.64 3.61 2.14 1.20
18 1072 438.67 1.74 0.64 4.65 2.09 0.74 910 254.16 1.62 0.43 3.80 1.64 0.43
19 1040 521.71 1.18 0.72 4.29 1.79 0.89 770 286.06 1.23 0.72 3.08 1.25 0.75
20 1242 583.85 1.57 0.72 4.51 1.96 1.04 955 1075.34 1.59 0.66 4.26 1.69 2.31

CI with Linear and Exponential Probability for Multiple Rectangular Obstacles Case (MROC)
Config.
Mean
(FE)
SD
(FE)
Mean
Time
(Seconds)
SD Time
(Seconds)
Mean
Distance
Travelled
Mean
Total Time
(Seconds)
SD Total
Time
(Seconds)
Mean
(FE)
SD
(FE)
Mean
Time
(Seconds)
SD Time
(Seconds)
Mean
Distance
Travelled
Mean
Total Time
(Seconds)
SD Total
Time
(Seconds)
1 1177 465.51 0.75 0.13 4.27 1.96 0.76 517 397.35 0.88 0.14 2.47 0.98 0.64
2 1220 560.11 0.85 0.13 4.39 2.28 0.98 630 361.54 1.01 0.23 3.06 1.25 0.56
3 1660 397.33 0.71 0.17 4.30 2.52 0.76 1115 531.20 0.88 0.17 2.99 2.04 0.80
4 1290 544.73 0.44 0.08 4.37 1.18 0.50 555 272.64 0.51 0.12 2.90 0.59 0.23
5 1265 532.74 0.63 0.14 4.64 1.55 0.75 575 358.62 0.71 0.20 2.88 0.96 0.52
6 1462 685.98 0.65 0.17 4.15 1.82 0.86 602 653.97 0.77 0.18 3.19 0.97 0.85
7 1465 487.58 0.73 0.23 4.04 2.16 0.80 1155 544.03 0.82 0.14 2.89 1.70 0.73
8 740 391.20 0.78 0.14 4.55 1.16 0.54 542 96.59 0.84 0.17 3.13 0.87 0.14
9 947 497.65 0.78 0.13 3.94 1.44 0.59 557.5 247.62 0.87 0.14 2.66 0.95 0.31
10 1377 502.45 0.82 0.16 4.15 1.82 0.71 632 196.63 0.95 0.18 2.50 1.09 0.20
11 1592 353.31 0.68 0.15 4.26 2.30 0.55 1045 367.17 0.76 2.29 2.73 1.15 2.46
12 1255 406.14 0.68 0.16 4.14 1.62 0.64 580 328.41 0.79 0.22 2.285 0.98 0.40
13 1165 380.96 0.64 0.18 4.25 1.57 0.60 545 384.64 0.70 0.17 2.60 0.80 0.62
14 1465 561.29 0.36 0.05 4.46 1.08 0.40 835 487.85 0.41 0.06 3.01 0.67 0.34
15 1280 556.98 0.36 0.06 4.03 0.96 0.39 652 357.15 0.43 0.06 2.72 0.54 0.24
16 1480 342.73 0.42 0.05 4.42 1.30 0.28 652 281.88 0.55 0.07 2.30 0.63 0.23
17 1517 612.94 0.44 0.06 4.15 1.38 0.52 662 436.64 0.53 0.06 2.69 0.66 0.35
18 1260 550.15 0.47 0.10 4.31 1.13 0.46 642 429.54 0.58 0.10 3.15 0.66 0.35
19 965 601.56 0.45 0.05 3.73 0.91 0.49 502 455.07 0.50 0.05 2.70 0.57 0.36
20 1447 502.71 0.42 0.07 4.30 1.29 0.42 730 351.28 0.51 0.07 2.98 0.71 0.28

CI with Linear and Exponential Probability for Cluttered Polygons Obstacles Case (CPOC)
Config.
Mean
(FE)
SD
(FE)
Mean
Time
(Seconds)
SD Time
(Seconds)
Mean
Distance
Travelled
Mean
Total Time
(Seconds)
SD Total
Time
(Seconds)
Mean
(FE)
SD
(FE)
Mean
Time
(Seconds)
SD Time
(Seconds)
Mean
Distance
Travelled
Mean
Total Time
(Seconds)
SD Total
Time
(Seconds)
1 1085 381.58 1.18 1.89 4.70 1.73 2.01 827 350.53 1.17 0.36 3.76 1.45 0.52
2 1705 525.93 1.38 0.57 4.80 2.46 0.77 970 429.18 1.42 0.57 3.27 1.67 0.69
3 1335 529.86 1.45 1.47 4.09 2.05 1.70 770 477.73 1.34 0.29 2.91 1.48 0.59
4 1220 443.54 1.53 0.53 3.98 2.05 0.57 830 346.05 1.41 0.42 2.96 1.47 0.52
5 1212.5 369.66 1.68 0.45 4.23 2.24 0.66 810 658.66 1.47 0.38 3.40 1.57 1.29
6 1320 396.81 1.52 0.29 4.53 2.04 0.63 782 469.84 1.25 0.28 3.19 1.42 0.79
7 1245 460.44 1.35 0.36 3.84 1.92 0.92 797 457.86 1.25 0.35 3.05 1.46 0.79
8 1155 537.01 1.04 0.29 4.34 1.54 0.62 882 420.03 1.25 0.42 3.40 1.50 0.64
9 1105 373.17 1.13 0.47 3.80 1.61 0.68 782 187.49 1.21 0.82 2.64 1.23 0.84
10 1457 488.52 1.45 0.38 4.40 2.09 0.61 915 455.52 1.18 0.43 2.98 1.36 0.63
11 1012 329.10 1.73 0.70 3.83 2.09 0.80 905 201.53 1.86 0.46 3.36 1.91 0.51
12 1457 602.11 1.48 0.48 4.56 2.21 0.93 855 438.81 1.46 0.43 3.34 1.52 0.69
13 1067 609.75 1.61 0.47 4.28 2.07 1.09 840 591.33 1.48 0.66 3.64 1.80 1.26
14 1065 630.40 1.39 0.33 4.30 1.94 1.21 822 353.75 1.49 0.44 3.01 1.64 0.64
15 862 599.68 1.47 0.60 3.78 1.79 1.28 832 396.43 1.40 0.47 3.25 1.50 0.69
16 1832 669.64 1.65 0.49 4.90 3.29 1.36 1055 585.11 1.51 0.44 3.08 2.05 1.35
17 1587 465.60 1.90 0.63 4.11 2.76 0.79 1015 599.76 1.54 0.47 2.99 1.92 1.03
18 1237 650.33 1.30 0.42 4.45 2.10 1.45 820 340.38 1.51 0.43 2.87 1.64 0.51
19 1227 507.91 1.21 0.53 4.23 1.95 0.97 722 410.57 1.14 0.23 2.97 1.27 01.69
20 1430 684.84 1.25 0.61 4.18 2.21 1.54 937 538.51 1.30 0.50 2.84 1.90 0.88

The simulation shows that a
combination of different set of
obstacles and robots can be
solved by the program.
Cohort Intelligence can be
applied to enable the swarms to
move collectively towards the
source.
Collective intelligence is more
effective than individual
intelligence.
A perfect balance between linear
and high exponential probability
should be struck to avoid the
problem of local minima.
Exponential value has been taken
as 3 after observing trends of
both higher exponential and
linear probabilities.
Inference and Discussion
118

Cohort Intelligence can be effectively
used to solve complex real life tasks
such as search and rescue operations.
This project forms as a foundation for
the development of real life swarm
robots that would be capable of
achieving targets based on the principle
of Cohort Intelligence.
119
Project Conclusion and Future Direction

Project Conclusion and Future Direction
• In order to maintain a balance between collective learning and
individual intelligence, the exponential value 𝑧 was required to be
chosen based on preliminary trials. During, the preliminary trials it
was observed that for higher values 𝑧, more number of robots were
exhibiting individual intelligence rather than collective learning. As a
result, some of the robots got stuck behind the obstacles and could
not reach the target. In the near future, an approach to auto-tune
such parameter needs to be addressed. Also, CI with above two
approaches needs to be tested for complex U and V shaped obstacles.
Authors intend to apply reinforcement learning model for robots’
sapient systems

Thank you
Anand J Kulkarni PhD, MASc, BEng, DME
Head & Associate Professor
Dept of Mechanical Eng
Symbiosis Institute of Technology
Symbiosis International University
Lavale, Pune 412 115, MH, India
Email: anand.kulkarni@sitpune.edu.in
kulk0003@ntu.edu.sg; kulk0003@uwindsor.ca; kulk0003@outlook.com
URL: sites.google.com/site/oatresearch/anand-jayant-kulkarni
Ph: 91 20 39116468; 91 7030129900
ResearcherID: www.researcherid.com/rid/O-3585-2016
ORCID ID: orcid.org/0000-0001-6242-9492
Google Scholar: scholar.google.ca/citations?user=IAvtDokAAAAJ&hl=en

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