ICTAI_2016_Presentation

WINNER DETERMINATION IN MULTI-OBJECTIVE
COMBINATORIAL REVERSE AUCTIONS
Dr. Samira Sadaoui
Professor
Department of Computer Science
University of Regina
sadaouis@uregina.ca
IEEE 28th International Conference on Tools with Artificial Intelligence (ICTAI 2016)
Shubhashis Kumar Shil
Ph.D. Candidate
Department of Computer Science
University of Regina
shil200s@uregina.ca

• Problem Description
• Motivations
• Objectives
• Winner Determination
• Genetic Algorithms
• Diversity and Elitism
• Solving Procedure
• Experimental Environment
• Simulated Datasets
• Experimental Results
• Conclusion
• Future Works
Introduction
Solution
Experiment
Conclusion
Winner Determination in Multi-Objective Combinatorial Reverse Auctions 2
INDEX

Buyer
Buyer’s Requirements and
Constraints:
• Selection of Products with Units
• Ranking of Attributes
• Objectives of Attributes
• Constraints of Attribute Values
Bidding Constraints:
• Bid Validation
• Winner Determination
3
PROBLEM
DESCRIPTION
INTRODUCTION
Bidders’ StockBidders
Seller1
Seller2
Seller3
Seller4
Seller30
2 units of Camera
3 units of Cell-Phone
2 units of Desktop
Bidding Items
Price
Pixels
Price
Memory
Battery-Standby
Price
Processor Speed
Memory
Hypothesis:
If a seller has a product,
he has sufficient amount
of that product
Sellers’ Constraints:
Constraints of Attribute Values
Winner Determination in Multi-Objective Combinatorial Reverse Auctions
Figure 1: Multi-
Objective CRA

PROBLEM DESCRIPTION
4
Multiple Products Multiple Bidders (Sellers)
Combinatorial Reverse Auction
INTRODUCTION
Multiple Units Multiple Attributes
Multiple Objectives Multiple Sources

5
Exact vs Evolutionary Algorithms
Multiple Units, Multiple Attributes and Multiple Objectives
Winner Determination
NP-Complete Problem
MOTIVATIONS
Very Few Research Works
INTRODUCTION

OBJECTIVES
6
Multiple Units
Multiple Attributes
Buyer’s Requirements and Sellers’ Constraints
Multiple Conflicting Objectives
Multiple Sourcing
Quality Solution in Reasonable Processing Time
INTRODUCTION

WINNER DETERMINATION
7
 NP-Complete
 Priori Approach
 Target: 1. Minimum procurement cost
2. Reasonable computation time
INTRODUCTION

 Survival of the fittest
 GA Operators:-
 Selection
 Crossover
 Mutation
 Why GA?:-
 Powerful search technique
 Near optimal solution
 Reasonable time complexity
8
GENETIC ALGORITHMSSOLUTION

 Diversity: Variant of Crowding Distance based on relative fitness value
Target: To prevent the population from having many similar solutions
by not allowing premature convergence to local optima.
 Elitism: Variant of Elitism with External Population
 Target: To avoid losing good solutions and help converging to the
global optima.
9
SOLUTION DIVERSITY AND ELITISM

SOLVING PROCEDURE
10
Begin:
round ← 1;
while (buyer not satisfied) do
Begin:
generation ← 1;
generate bids;
initialize chromosomes X(generation-1);
evaluate X(generation-1) by fitness function;
while (not maximum generation) do
Begin:
select X(generation) from X(generation -1) by Gambling Wheel Disk method;
recombine X(generation) by modified two-point crossover and mutation;
evaluate fitness value and relative fitness function of X(generation);
select X(generation) by performing diversity and elitism;
generation ← generation + 1;
End;
round ← round + 1;
End;
End;
SOLUTION

Table 1: Buyer’s Requirements and Constraints
11
SOLUTION SOLVING PROCEDURE
Product Attribute Ranking Objective Constraint
Camera
(3 units)
Price 1 Minimize
Pixel 2 Maximize
Cell-Phone
(2 units)
Price 1 Minimize
Memory 2 Maximize
Battery-
Standby
3 Maximize
Desktop
(2 units)
Price 1 Minimize
Processor 2 Maximize
Memory 3 Maximize
1000
10
500
4
3
2000
3
8

12
Table 2: Sellers’ Constraints
Product Attribute Seller
S1
..........
S15
.........
S30
Camera Price
Pixels
Cell-
Phone
Price
Memory
Battery-
Standby
Desktop Price
Processor
Memory
20 20 30
32 24 24
7 10 10
5 5 6
64 64 64
700 64 650
300 320 350
1200 1250 1300

13
Table 3: Sellers’ Bids
Seller Bid
S1
S2
..... …….
S15 {{800,24},{420,16,7},{1400,4,32}}
..... …….
S29 {{780,24},{420,14,6},{1350,4,64}}
S30 {{750,24},{450,16,8},{1400,4,32}}
{{800,16},{350,16,5},{}} Valid
{{1100,18},{360,16,7},{1350,4,64}} Invalid
Valid
Valid
Valid
S2: {{780,18},{360,16,7},{1350,4,64}} Valid

14
Table 4: Initial chromosomes
SOLVING PROCEDURESOLUTION
Chromosome
(Solution)
Camera Cell-Phone Desktop
Unit1 Unit2 Unit3 Unit1 Unit2 Unit1 Unit2
X1
X2 01101 10100 00110 10001 01100 00101 01110
X3 01100 10100 00101 01010 01011 01101 10001
X4 00101 10000 01001 00111 01111 01101 01001
01010 01101 00110 01110 00100 00001 01010 Infeasible
Feasible
Feasible
Feasible
X1: 01010 01101 00110 01110 00100 10001 01010 Feasible

15
SOLVING PROCEDURESOLUTION
 

S
s
I
i
sisix unittytotalUtilifitness
1 1


AI
ai
saiaisi utilityweighttytotalUtili
1



 AI
ai
ai
ai
ai
rankAI
rankAI
weight
1
)1(
1


AI
ai
aiweight
1
1
maxAai 
saisai
aisai
sai
VV
VV
utility
minmax
min



saisai
saiai
sai
VV
VV
utility
minmax
max



if then
else
(1)
(2)
(3)
(4)
(5)
Variable Description
Fitness of chromosome x
Utility of product i for seller s
Number of units of product i to be provided by seller s
Weight of attribute a of product i
Utility of attribute a of product i for seller s
Number of attributes of product i
Rank submitted by buyer of attribute a of product i
Valid bid submitted by seller s for attribute a of product i
Minimum value of buyer for attribute a of product i
Maximum value of seller s for attribute a of product i
Minimum value of seller s for attribute a of product i
Maximum value of buyer for attribute a of product i
xfitness
sitytotalUtili
siunit
aiweight
saiutility
AI
airank
saiV
aiVmin
saiVmax
saiVmin
aiVmax
Table 5: Variable Definition

Selection (Gambling Wheel Disk)
X1:
X2:
X3:
X4:
Crossover (Modified Two-Point Crossover)
X1:
X2:
X3:
X4:
Mutation (Swap Mutation)
X3: 10100 1000110010 00110 00011 00101 10010
16
Before After
10010 00110 00010 10100 10001 00101 10010
00010 00110 00011 10001 10000 00100 10000
10010 00110 00010 10001 10000 00101 10011
00100 10000 10100 10001 00010 00110 00010
10010 00110 00010 10100 10001 00101 10010
00010 00110 00011 10001 10000 00100 10000
00100 10000 10100 10001 00010 00110 00011
10010 00110 00010 10001 10000 00101 10010
10010 00110 00010 10100 10001 00101 10010
00010 00110 00011 10001 10000 00100 10000
10010 00110 00010 10001 10000 00101 10010
10010 00110 00010 10001 10000 00101 10010
10010 00110 00010 10100 10001 00101 10010
00010 00110 00011 10001 10000 00100 10000
10010 00110 00010 10001 00010 00101 10011
00110 00010 10001 10000 00100 10000 10100
10010 00110 0001100101 1001010100 10001

SOLVING PROCEDURE
17
SOLUTION
Diversity (Crowding Distance)
relFitnessx 
| fitnessx1  fitnessx1 |
maxFitnessP  minFitnessP
 [0,1] (6)
PFitnessmax = The maximum fitness value of the population p
PFitnessmin = The minimum fitness value of the population p
Elitism (External Population)
E = The population of elite chromosomes
ω
= The number of elite chromosomesψ
= The elite chromosome rate
 Update P (participant population for the next generation) by taking chromosomes from P and (ψ × ω) elite
chromosomes from E
ζ- (ψ × ω)
ζ = The number of chromosomes

SOLVING PROCEDURE
18
Table 6: Winning Solution
SOLUTION
Camera Cell-Phone Desktop
Unit1 Unit2 Unit3 Unit1 Unit2 Unit1 Unit2
S18 S10 S6 S2 S10 S8 S10

 Primary Memory: 4 GB
 Processor: Intel (R) Core (TM) i3-2330M
 Processor Speed: 2.20 GHz
19
EXPERIMENT EXPERIMENTAL ENVIRONMENT

20
EXPERIMENT SIMULATED DATASETS
Dataset 1
Number of Sellers 500
Number of
Products
Number of
Units
Number of
Attributes
2 4 5
4 8 10
6 12 15
8 16 20
10 20 25
Dataset 2
Number of Sellers 100, 200, 300,
400, 500, 600,
700, 800, 900,
1000
Number of Products 10
Total Number of Units 20
Number of Attributes 25
Dataset 3
Number of
Product
Number of
Units
Number of
Attributes
1 2 2
2 2 3
3 3 1
4 1 4
5 1 3
6 3 2
7 2 2
8 2 2
9 3 1
10 1 4
Dataset 4
Dataset 5
Total Number of Units 25

 GA Operators:-
 Chromosome Encoding: Binary String
 Number of Chromosome: 500
 Selection: Gambling-Wheel Disk
 Crossover: Modified Two-point
 Mutation: Swap Mutation
 Crossover Rate: 0.6
 Mutation Rate: 0.01
 Termination Condition: Generation Number (1000)
21
 Diversity Method:-
 Method: Variant of Crowding Distance
 Elitism Technique:-
 Technique: Elitism with External Population
 Elitism Rate: 0.2
EXPERIMENT SIMULATED DATASETS

22
Experiment 1: Computational Time
EXPERIMENT EXPERIMENTAL RESULTS
Figure 2: Computational time of WD by varying
total number of units and number of attributes
Figure 3: Computational time of WD by varying
number of sellers

Experiment 2: Statistical Analysis
Is this method
reliable/consistent/stable?
23
Figure 4: Statistical analysis of WD

24
Experiment 3: Computation Expense Comparison
Comparison 1
Heuristic Solving Algorithm Features Computation Time (Second)
Improved Ant Colony Single Unit, Multi-Attribute,
Single Objective
9
Enumeration Algorithm with Backtracking Single Unit, Single Attribute,
Single Objective
3
Genetic Algorithm for Multiple Instances of
Items of Combinatorial Reverse Auctions
Multi-Unit, Two-Attribute,
Single Objective
0.83
Proposed Method Multi-Unit, Multi-Attribute,
Multi-Objective
0.067
Comparison 2
Exact Branch and Bound Multi-Unit, Single Attribute,
Single Objective
>100
Proposed Method Multi-Unit, Multi-Attribute,
Multi-Objective
0.077

 Our proposed method is able to solve the problem of winner determination efficiently.
 The method finds the winner(s) in a reasonable processing time.
 The method is consistence.
25
CONCLUSION CONCLUSION

26
 Accuracy Test
 Parallel Genetic Algorithms
 Hybrid Evolutionary Algorithms
 Qualitative Attributes
CONCLUSION FUTURE WORKS

27
1. R. Abbasian and M. Mouhoub. “A hierarchical parallel genetic approach for the graph coloring problem”, Appl. Intell., Springer, vol. 39(3), pp. 510-528, 2013.
2. H. Bayindir, H. Kilic, and M. Rehan. “An agent-based Trading Infrastructure for Combinatorial Reverse Auctions”, In Proc. of IEEE Symposium on Intelligent Agents (IA), pp. 38-44, 2014.
3. T. Buer and H. Kopfer. “A Pareto-metaheuristic for a bi-objective winner determination problem in a combinatorial reverse auction”, Computers & Operations Research, vol. 41, pp. 208-220,
2014.
4. C. A. Coello Coello. “Evolutionary multi-objective optimization: a historical view of the field”, IEEE Computational Intelligence Magazine, vol. 1(1), pp. 28-36, 2006.
5. K. Deb. “Multi-objective optimization. Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques”, pp. 403-449, 2014.
6. A. E. Eiben and E. S. James. “Introduction to evolutionary computing”, Heidelberg: Springer, vol. 53, 2003.
7. R. Epstein, L. Henriquez, J. Catalan, G. Y. Weintraub, C. Martinez, and F. Espejo. “A combinatorial auction improves school meals in Chile: a case of OR in developing countries”,
International Transactions in Operational Research, vol. 11(6), pp. 593-612, 2004.
8. A. Giovannucci, J. Cerquides, and J. Rodríguez-Aguilar. Composing supply chains through multiunit combinatorial reverse auctions with transformability relationships among goods.
Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, 40(4), 767-778, 2010.
9. J. Gong, J. Qi, G. Xiong, H. Chen, and W. Huang. “A GA based combinatorial auction algorithm for multi-robot cooperative hunting”, In Proc. of International Conference on Computational
Intelligence and Security, pp. 137-141, 2007.
10. S. Grafakos, A. Flamos and E. M. Ensenado. “Requirements matter: a constructive approach to incorporating local stakeholders’ requirements in the sustainability evaluation of energy
technologies”, Sustainability, vol. 7(8), pp. 10922-10960, 2015.
11. D. Gupta and S. Ghafir. “An overview of methods maintaining diversity in genetic algorithms”, Int. J. Emerg. Technol. Adv. Eng., vol. 2(5), pp. 56-60 , 2012.
12. F. S. Hsieh and J. B. Lin. Virtual enterprises partner selection based on reverse auctions. The International Journal of Advanced Manufacturing Technology, 62(5-8), 847-859, 2012.
13. A. Konak, D. W. Coit, and A. E. Smith. “Multi-objective optimization using genetic algorithms: a tutorial”, Reliability Engineering & System Safety, vol. 91(9), pp. 992-1007, 2006.
14. B. Mansouri and E. Hassini. “A Lagrangian approach to the winner determination problem in iterative combinatorial reverse auctions”, European Journal of Operational Research, vol.
244(2), pp. 565-575, 2015.
15. J. Ostler and P. Wilke. “Improvement by combination how to increase the performance of optimisation algorithms by combining them.” In Proc. of the 10th International Conference of the
Practice and Theory of Automated Timetabling, pp. 359-365, 2014.
16. X. Qian, M. Huang, T. Gao, and X. Wang. “An improved ant colony algorithm for winner determination in multi-attribute combinatorial reverse auction”, In Proc. of IEEE Congress on
Evolutionary Computation (CEC), pp. 1917-1921 , 2014.
17. S. Sadaoui and S. K. Shil. “A Multi-Attribute Auction Mechanism based on Conditional Constraints and Conditional Qualitative Requirements”, Journal of Theoretical and Applied
Electronic Commerce Research (JTAER), vol. 11(1), pp. 1-25, 2016.
18. S. K. Shil, M. Mouhoub, and S. Sadaoui. “Winner determination in combinatorial reverse auctions”, In Proc. of the 26th International Conference on Industrial, Engineering & Other
Applications of Applied Intelligent Systems (IEA/AIE), Springer, pp. 35-40, 2013.
19. S. K. Shil, M. Mouhoub, and S. Sadaoui. “Evolutionary technique for combinatorial reverse auctions”, In Proc. of the 28th FLAIRS, pp. 79-84, 2015.
20. S. K. Shil, M. Mouhoub, and S. Sadaoui. “Winner Determination in Multi-Attribute Combinatorial Reverse Auctions”, In Proc. of the 22nd International Conference on Neural Information
Processing (ICONIP), pp. 645-652 , 2015.
21. C. Xu, L. Song, Z. Han, Q. Zhao, X. Wang, X. Cheng, and B. Jiao. “Efficiency resource allocation for device-to-device underlay communication systems: a reverse iterative combinatorial
auction based approach”, IEEE Journal on Selected Areas in Communications, vol. 31(9), pp. 348-358, 2013.
22. S. Wu and G. E. Kersten. “Information revelation in multi-attribute reverse auctions: an experimental examination”, In Proc. of the 46th IEEE Hawaii International Conference on System
Sciences (HICSS), pp. 528-537, 2013.
REFERENCES

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