Cohort intelligence

Cohort Intelligence: A Self Supervised Learning Behavior

Anand J KulkarniPhD, MASc, BEng, DME

Symbiosis Institute of Technology, Symbiosis International University Pune

Email: [email protected]; kulk0003@{ntu.edu.sg; uwindsor.ca}Website: sites.google.com/site/oatresearch/anand-jayant-kulkarni

mailto:[email protected]

mailto:kulk0003@%7Bntu.edu.sg

mailto:uwindsor.ca

https://sites.google.com/site/oatresearch/anand-jayant-kulkarni







Agenda

• Contemporary Algorithms• Motivation• Cohort Intelligence• Validation• Test on Combinatorial Problems• Applications to Real World Problems• Future Directions

Algorithms

• Exact Methods/Algorithms• Approximations Methods/Algorithms

– Artificially Intelligent methods• Bio-/Nature-inspired Methods

– Self-organizing Systems

Contemporary Algorithms

• Evolutionary Algorithms

• Genetic Algorithms

• Probability Collectives

• Swarm Intelligence

Contemporary Algorithms

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

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

• Kulkarni, A.J., Shabir, H. (2014): “Solving 0-1 Knapsack Problem using Cohort Intelligence Algorithm”. Int J of Machine Learning and Cybernetics, (DOI 10.1007/s13042-014-0272-y)

• 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

• Kulkarni, A.J., Baki, M.F., Chaouch, B.A. (2015): “Application of the Cohort-Intelligence Optimization Method to Three Selected Combinatorial Optimization Problems”, (In Press: European Journal of Operational Research)

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.

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.html

http://www.hole-in-the-wall.com/MIE.html

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

Ctr

Cohort Intelligence Algorithm• 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 behavior as

final solution

Every candidate shrinks/expands the sampling interval of every quality based on whether condition of saturation is

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 candidate in the cohort is calculated

N

Every candidate forms behaviors by sampling the qualities from within the updated sampling intervals

Every candidate follows the best behavior from within its behaviors

Convergence?

Y

1

1

, 1,...,1

cc

C

cc

fp c C

f

x

x

? ? ?2 , 2c c ci i i i ix x

.... i i r

, 1,...,cf c Cx

1 ,..., ,...,C c Cf f fF x x x

1Minimize ,... ,...,

Subject to , 1,...,i N

lower upperi i i

f f x x x

x i N

x

1,...,c C 1 ,... ,...,c c c ci Nx x xx cf x

Candidates Qualities Behavior

Possibility of being followed

Neighborhood space

Number of Variations

Cohort Solutions

Roulette Wheel Selection

• Ackley Function

Variable 1

Var

iabl

e 2

-6 -4 -2 0 2 4 6 8

-6

-4

-2

0

2

4

6

8

Variable 1

Var

iabl

e 2

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

Variable 1

Var

iabl

e 2

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

Variable 1

Var

iabl

e 2

-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 30

Problem

RHPSO [13] CPSO [16] LDWPSO [16] SQP [15] Proposed CI

BestMeanWorst

BestMeanWorst

BestMeanWorst

BestMeanWorst

BestMeanWorst

, , FE SD Time (sec)

Sphere1.5000E-3233.5078E-2455.0380E-248

1.4356E-813.4213E-121.7103E-10

1.5387E-061.2102E-041.1486E-03

3.5657E-282.5749E-278.8173E-27

2.0000E-152.4900E-061.7780E-05

5, 15, 0.80

18750 4.5800E-03 1.55

Rosenbrock1.5606E-081.2061E-073.0398E-07

1.1856E-08 9.3949E-039.0066E-02

2.8453E_033.1101E+001.1050E+01

7.5595E-121.4352E+003.9866E+00

0.0000E+000.0000E+000.0000E+00

5, 15, 0.80

9750 0.0000E+00 5.20

Ackley0.0000E+000.0000E+000.0000E+00

8.8178E-161.5952E-086.3330E-07

1.3078E-045.9934E-032.5325E-02

1.5245E+011.9090E+011.9959E+01

1.2322E-072.0911E-072.6499E-07

5, 15, 0.85

11250 4.3200E-08 1.50

Griewank0.0000E+000.0000E+000.0000E+00

0.0000E+002.1287E-106.4174E-09

1.6949E-021.7072E-017.2835E-01

2.8879E-093.5357E-013.6312E+00

7.3960E-031.7100E-024.9183E-02

5, 15, 0.997

18750 8.8300E-03 2.00

0 20 40 60 80 100 120 140 1600

200

400

600

800

1000

1200

Learning Attempts

Beh

avio

r

Candidate 1Candidate 2Candidate 3Candidate 4Candidate 5

0 50 100 150 200 2500

0.2

0.4

0.6

0.8

1

1.2

1.4

Learning Attempts

Beh

avio

r

Candidate 1Candidate 2Candidate 3Candidate 4Candidate 5

C t r


Cohort Intelligence Parameters

• Number of candidates C

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0 5 10 15 20 25 30 35 40 45 50 55

Tim

e (s

)

No of Candidates

No of Candidates vs Time

-5.00E-04

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

0 5 10 15 20 25 30 35 40 45 50 55

Solu

tion

No of Candidates

No of Candidates Vs Solution

0

100000

200000

300000

400000

500000

600000

700000

800000

0 10 20 30 40 50 60 70 80 90 100 110

Func

tion

Eval

uatio

ns

No of Candidates

No of Candidates Vs Function Evaluations


• Number of variations t

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Tim

e (s

)

Variations in Behaviour

Variations in Behaviour Vs Time

-1.00E-200 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

Solu

tion


Variations in Behaviour vs Solution

0

5000

10000

15000

20000

25000

30000

35000

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Func

tion

Eval

ution

s


Variations in Behaviour vs Function Evaluations


• How about sampling interval reduction factor ?r

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Tim

e (s

)

Reduction Factor

Reduction Factor Vs Time

-5.00E-03

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Solu

tion

Reduction Factor

Reduction Factor Vs Solution

Combinatorial Problems

05/01/2023 University of Windsor 23

Cohort Intelligence

• Combinatorial Problems– Packing Problem

1

1

where (

( )

0,, ,) 1 1

N

i ii

N

i ii

i

Maximize f

Subject to f W

x if w x N

v x

v

w

w

Feasibility-based Rule1. 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

• Combinatorial Problems– Traveling Salesman Problem

ProblemName

Cities Reported Optimum

Cohort Intelligence

Solution

Standard Deviation

Burma 14 14 30.8785 30.8785 0.00P 01 15 284.3809 284.381 0.00

Ulysses 16 16 74.1087 73.9876 0.099Groetschel 17 17 2085 2085 1.90Groetschel 21 21 2707 2707 0.98

Ulysses 22 22 75.5975 75.5975 0.37Groetschel 24 24 1272 1272 14.85

Fri 26 26 937 937 8.38Bays 29 29 9074 9108.8 192.26

Hybridization

K-means Algorithm

Clustering/Classification Problems

x1,1 x1,2 x1,3 x1,4 x1,5 x1,6 x1,7 x1,8 x1,9 x1,10 x1,11 x1,12

K = 3 , D = 4

x2,1 x2,2 x2,3 x2,4 x2,5 x2,6 x2,7 x2,8 x2,9 x2,10 x2,11 x2,12

x3,1 x3,2 x3,3 x3,4 x3,5 x3,6 x3,7 x3,8 x3,9 x3,10 x3,11 x3,12

x4,1 x4,2 x4,3 x4,4 x4,5 x4,6 x4,7 x4,8 x4,9 x4,10 x4,11 x4,12

xC,1 xC,2 xC,3 xC,4 xC,5 xC,6 xC,7 xC,8 xC,9 xC,10 xC,11 xC,12

1 2 3

.

.

.

.

.

.

.

.

.


x1,1 x1,2 x1,3 x1,4 x1,5 x1,6 x1,7 x1,8 x1,9 x1,10 x1,11 x1,12

x2,1 x2,2 x2,3 x2,4 x2,5 x2,6 x2,7 x2,8 x2,9 x2,10 x2,11 x2,12

x4,1 x4,2 x4,3 x4,4 x4,5 x4,6 x4,7 x4,8 x4,9 x4,10 x4,11 x4,12

1 2 3

-

x8,1 x8,2 x8,3 x8,4 x8,5 x8,6 x8,7 x8,8 x8,9 x8,10 x8,11 x8,12

+ rand(.) ×



• Data 150- 1500, Dims 3 to 13, Clusters 2-6Dataset 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

Real World Combinatorial Problems

Anand J Kulkarni

Odette School of Business, University of Windsor, 401 Sunset Avenue, Windsor, Ontario N9B 3P4,Canada

E-mail: [email protected]: 1 519 253 3000 (x4939)

M F Baki


E-mail: [email protected]: 1 519 253 3000 (x3118)

Ben A Chaouch


E-mail: [email protected]: 1 519 253-4232 (x3149)

New Variant of the Assignment ProblemRow Circular Matrix

𝐶=[ 1 2 3 45 6 7 89 10 11 12

13 14 15 16] [ 1 2 3 47 8 5 612 9 10 1114 15 16 13 ][1324 ]

• 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

New Variant of Assignment Problem

Minimize (1)

Subject to

(2)

(3)

(4)

(5)

(6)

• Mathematical Formulation

Applications

[40 30 22 1336 29 23 732 30 22 736 32 23 17 ][𝑴 𝑻 𝑾 𝑹 ]

[𝑫𝟏𝑫𝟐𝑫𝟑𝑫𝟒

]𝐼 𝑘=[ 144 121 90 44 ]

𝑍 (𝐶∗𝜋1 )=105

[22 13 40 3029 23 7 367 32 30 2236 32 23 17 ][𝑴 𝑻 𝑾 𝑹 ]

[𝑫𝟏𝑫𝟐𝑫𝟑𝑫𝟒

]𝐼𝑘=[ 94 10 0 100 10 5 ]

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 1336 29 23 732 30 22 736 32 23 17 ][𝑴 𝑻 𝑾 𝑹 ]

[𝑺𝟏𝑺𝟐𝑺𝟑𝑺𝟒

]𝐼 𝑘=[ 144 121 90 44 ]

𝑍 (𝐶∗𝜋1 )=105

[22 13 40 3029 23 7 367 32 30 2236 32 23 17 ][𝑴 𝑻 𝑾 𝑹 ]

[𝑺𝟏𝑺𝟐𝑺𝟑𝑺𝟒

]𝐼𝑘=[ 9 4 10 0 100 105 ]

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

matrix, 3 Candidates, 2 variations

The element from being followed: 3

Its location in the permutation :

The updated permutation :

Updated circular matrix

Maximum column sum : 119

The element from being followed: 1

Its location in the permutation :

The updated permutation :

Updated circular matrix

Maximum column sum : 144

and

associated permutation :119 and

[ 90 44 144 121 ]

[ 1 19 83 79 118 ]

Numerical Experiments and Results

0 50 100 150 200 250 300 350 4004660

4680

4700

4720

4740

4760

4780

4800

4820

4840

Learning Attempts

CI C

andi

date

Sol

utio

nsCI 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.

% g

ap o

f LB

with

IP

n î n

00.5

11.5

22.5

33.5

44.5

5

Avg

% g

ap o

f CI w

ith L

B

n î 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.

% g

ap o

f CI w

ith IP

n î n

0

200

400

600

800

1000

1200

5x5 6x6 7x7 8x8 9x9 10x10 11x11 12x12 13x13

IP: A

vera

ge C

PU T

ime

n î n


0

2000

4000

6000

8000

10000

12000

14000

16000

18000

5x5 6x6 7x7 8x8 9x9 10x10 11x11 12x12 13x13

CI A

vera

ge F

E

n î n

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

15x15 20x20 25x25 30x30 35x35 40x40 45x45 50x50

CI A

vera

ge F

E

n î 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

CI A

vera

ge C

PU T

ime

n î n

0

5

10

15

20

25

30

15x15 20x20 25x25 30x30 35x35 40x40 45x45 50x50

CI A

vera

ge C

PU T

ime

n î n

Numerical Experiments and ResultsProblem Size Average

% gapLP 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 ProblemDeciding a sea cargo shipping schedule for freight bookings accepted in multi-period planning horizon (Ang et al. 2007)

Maximize: profit generated by all freight bookingsSubject 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 a 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

where ,

Numerical Experiments and Results, , IP LP HAM MHA CI Performance

CPUTime(sec)

CPUTime(sec)

CPUTime(sec)

CPUTime(sec)

Avg Sol % Gap

~

Avg Sol % Gap

~

CPUTime(sec)

SD(CPU Time)

SD SD

3, 5, 41 123 74 0.106 0.028 1.59 2.88 0.001 1.55 2.71 0.015 1.31880.2452

0.0700.036 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 1.01020.6931

0.0930.027 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 0.99580.5131

0.1030.025 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 1.09061.0059

0.0980.041 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 0.92500.8474

0.1300.046 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 0.8040.7644

0.0940.037 0.379 0.378

, , IP LP HAM MHA CI Performance

CPUTime(sec)

CPUTime(sec)

CPUTime(sec)

CPUTime(sec)

Avg Sol % Gap

~

Avg Sol % Gap

~

CPUTime(sec)

SD(CPU Time)

SD SD

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


, , HAM MHA CI PerformanceCPUTime(sec)

CPUTime(sec)

Best Sol % Gap Avg Sol % Gap~

Worst Sol % Gap

^

CPUTime(sec)

SD(CPU Time)

SD

9, 47, 1521 13689 2376 10 80.5 447.1 3.3822 4.6675 5.8294 6.7303 0.344 0.7073, 4, 6576 19728 6603 10 53.2 293.1 3.8078 5.2705 6.6293 61.6805 4.940 0.7264, 5, 5286 21144 5330 10 54.5 277.7 3.6931 5.1307 6.5576 35.6223 3.819 0.8354, 13, 5479 21916 5587 10 125.9 785.9 3.8556 5.5827 7.1253 27.2433 2.885 0.8985, 8, 4954 24770 5039 10 89.9 454.2 4.0504 5.5827 7.0751 41.9530 3.514 0.7668, 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 50 602

2.5

3

3.5

4

4.5

5

5.5

6

6.5x 105

Learning Attempts

CI C

andi

date

Sol

ution

s

Convergence


0

0.5

1

1.5

2

2.53,

5, 4

1

3, 6

, 47

4, 3

, 64

2, 4

, 132

3, 3

, 91

2, 3

, 143

3, 4

, 900

4, 8

, 965

4, 2

5, 1

000

2, 3

, 287

1

2, 3

, 387

6

5, 3

7, 1

954

% G

ap o

f Avg

CI w

ith IP

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, 2

5, 1

000

2, 3

, 287

1

2, 3

, 387

6

5, 3

7, 1

954

9, 4

7, 1

521

3, 4

, 657

6

4, 5

, 528

6

4, 1

3, 5

479

5, 8

, 495

4

8, 2

6, 3

249

% G

ap o

f Avg

CI w

ith U

B

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, 2

5, 1

000

2, 3

, 287

1

2, 3

, 387

6

5, 3

7, 1

954

9, 4

7, 1

521

3, 4

, 657

6

4, 5

, 528

6

4, 1

3, 5

479

5, 8

, 495

4

8, 2

6, 3

249

CI: S

D (C

PU T

ime)

T, J, K

00.5

11.5

22.5

33.5

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, 2

5, 1

000

2, 3

, 287

1

2, 3

, 387

6

5, 3

7, 1

954

CI: A

vera

ge C

PU T

ime

T, J, K

00.10.20.30.40.50.60.70.80.9

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, 2

5, 1

000

2, 3

, 287

1

2, 3

, 387

6

5, 3

7, 1

954

CI: S

D (%

Gap

CI a

nd IP

)

T, J, K

00.10.20.30.40.50.60.70.80.9

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, 2

5, 1

000

2, 3

, 287

1

2, 3

, 387

6

5, 3

7, 1

954

9, 4

7, 1

521

3, 4

, 657

6

4, 5

, 528

6

4, 1

3, 5

479

5, 8

, 495

4

8, 2

6, 3

249

CI: S

D (%

Gap

CI a

nd U

B)

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

Numerical Experiments and Results, IP CI Performance

CPUTime(sec)

Avg Sol % Gap

CPUTime(sec)

SD(CPU Time)

5, 41 15, 10, 8, 5, 3 625 621 10 0.4867 2.5042 2.8276 1.08436, 47 17, 12, 9, 6, 3 869 873 10 0.4695 2.9914 2.2563 2.35688, 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 3.95978, 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 5.03648, 900 350, 250, 150, 100, 50 5349 904 10 42.9057 5.9488 30.4846 10.07358, 965 400, 250, 130, 100, 85 9662 8695 10 55.9057 5.9132 37.1572 7.2841

, , IP CI PerformanceCPUTime(sec)

Avg Sol % Gap

CPUTime(sec)

SD(CPU Time)

3, 5, 41 15, 10, 8, 5, 3 625 621 10 0.2293 4.2318 8.9319 2.59873, 6, 47 17, 12, 9, 6, 3 869 873 10 0.1778 2.6832 8.0473 3.52424, 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 6.31613, 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 3.42703, 4, 900 350, 250, 150, 100, 50 11104 11104 10 0.8642 5.6406 36.2087 7.89254, 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 18.07988, 3, 2871 900, 700, 600, 500, 171 66730 66734 10 9.9120 4.7621 73.0579 5.78508, 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 40.07089, 47, 1521 600, 400, 300, 121, 100 542795 543019 10 376.31 10.1997 93.0901 22.92388, 15, 6576 3000, 2000, 800, 500, 276 883635 883705 10 528.07 11.5074 141.5355 10.66618, 15, 5286 2000, 1000, 986, 800, 500 567372 567434 10 352.62 9.8089 130.3254 11.64718, 13, 5479 300, 250, 200, 150, 100 493533 493586 10 399.50 10.8206 133.1693 23.98978, 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

Constraint Handling in Cohort Intelligence

Adopted from Kulkarni and Shabir (2014)

• The , and represent the slope of lines going through points , and , respectively. The overall/total probability of selecting a candidate to follow is calculated as follows:

• The candidate’s solution with better objective and constraint values closer to the boundaries will have higher probability of being followed.

0 0 0

1 1 1

𝐸𝑡 𝑉 𝑡𝑗 𝑊 𝑡𝑗

𝑃 𝐸𝑡𝑃𝑉 𝑡𝑗

𝑃𝑊 𝑡𝑗

(a) (b) (c)

Current updates• Self Organizing (Swarm) bots

Updates at the SIT

• Pattern Recognition/Script Recognition• Image Processing• Multi CI• Control Systems• Heat Exchanger Design• Mechanical Component Design• FEM

Anand J KulkarniPhD, MASc, BEng, DME

Symbiosis Institute of Technology, Symbiosis International University PuneEmail: [email protected]; kulk0003@{ntu.edu.sg; uwindsor.ca}

Website: sites.google.com/site/oatresearch/anand-jayant-kulkarni