1. Evolutionary Technique for Combinatorial Reverse Auctions
The 28th International FLAIRS Conference 2015
Evolutionary Technique for Combinatorial Reverse Auctions
Shubhashis Kumar Shil, Malek Mouhoub, and Samira Sadaoui
Department of Computer Science
University of Regina
Regina, SK, Canada
{shil200s, mouhoubm,

2. Evolutionary Technique for Combinatorial Reverse Auctions
Introduction
Motivation
Contribution
Problem
Combinatorial Reverse Auction
Problem Statement
Winner Determination
Solution
Formulation of the Problem
Genetic Algorithms
Solving Procedure
Experiments
Experimental Environment
Bidding Parameters and Genetic Algorithm Operators
Experimental Results
Conclusion
Future Works

3. Evolutionary Technique for Combinatorial Reverse Auctions
Introduction
One of the main challenges.
NP-complete problem.
Very few research works.
Exact algorithms vs evolutionary algorithms.
Motivation
Contribution
Determining the winner is one of the main challenges in the context of combinatorial reverse auctions.
This is an NP-complete problem.
There are very few research works in this field.
Nobody tackled the problem that considers multiple items, multiple instances, and multiple attributes all together along with some other bidding constraints .
Exact algorithms become unreasonable with the increase of the number of items, instances or attributes. On the other hand, evolutionary algorithms can produce approximate results.

4. Evolutionary Technique for Combinatorial Reverse Auctions
Introduction
Multiple attributes, instances, items, and constraints.
Genetic Algorithm (GA) based method in Combinatorial Reverse Auctions (CRAs).
Minimum procurement cost in a reasonable processing time.
The method is efficient and reliable.
Motivation
Contribution
We consider multiple attributes, instances and items along with some other constraints such as bidding, buyer’s and sellers’ constraints.
We propose a Genetic Algorithm (GA) based method to solve this winner determination problem in Combinatorial Reverse Auctions.
We show that the method is able to find the winner with a minimum procurement cost in a reasonable processing time.
We conduct several experiments and based on the results, we show that the method is efficient in terms of processing time as well as the quality of the solution returned. And by performing statistical analysis, we show that the method is reliable.

5. Evolutionary Technique for Combinatorial Reverse Auctions
Problem
One buyer
Multiple sellers
Multiple items
Combinatorial
Reverse
Auction
Winner Determination
Problem Statement
One buyer
Multiple sellers. Sellers are bidders.
Multiple items.

6. Evolutionary Technique for Combinatorial Reverse Auctions
Problem
Combinatorial
Reverse
Auction
Minimum procurement cost
Reasonable computation time
Winner Determination
Problem Statement
In the combinatorial reverse auction the winner determination problem is to find out the winner(s) with minimum bid price in a reasonable computation time.

7. Sellers’ Constraints: Price and Delivery rate
Evolutionary Technique for Combinatorial Reverse Auctions
Bidders’ Stock
Bidders
Seller1
Seller2
Seller3
Seller4
Seller5
Problem
Sellers’ Constraints:
Minimum price of instance(s) of item(s)
Delivery rates
Discount rates
Buyer’s Constraints:
Maximum price of instance(s) of item(s)
Maximum number of rounds
Combinatorial
Reverse
Auction
Winner Determination
2 instances of Item1
3 instances of Item2
2 instances of Item3
Bidding Items
Problem Statement
Buyer
Bidding Constraints:
Sellers’ minPrice < Cost < Buyer’s maxPrice
Winner determination
The buyer wants to buy a bundle of items which consists of 2 instances of item1, 3 instances of item2 and 2 instances of item3.
There are 5 sellers who bid for any number of items and instances they like.
In this figure, we are showing buyer, bidding items, bidders and bidders’ stock.
We consider various situations related to the seller’s stock, may be more than or less than the buyer’s requirement or out of any item(s). For example, Seller1, Seller2 and Seller5 have enough stock, but Seller3 has only 1 instance of item1 where the buyer’s requirement is 2 for that item and Seller4 has no instances of item2 at all.
5. Buyer can specify his constraints such as maximum price for each instance of item he can afford. For example, maximum price for each instance of item1, item2 and item3 is 500, 700, and 200. These maximum prices here are generated randomly from 1 to n where n = Buyer can also specify the maximum number of rounds.
6. On the other hand, sellers can specify their constraints such as minimum price for each instance of item they can afford. They also specify delivery rate and discount rate on price and delivery rate.
7. The bidding constraints is to maintain both the buyer’s and sellers’ constraints such as the bid price should be more than the sellers’ minimum price and less than the buyer’s maximum price and at the same time determining the winner in a reasonable computation time.
Price and Delivery rate
Figure 1: A sample scenario in CRAs

8. Evolutionary Technique for Combinatorial Reverse Auctions
Solution
Formulation of the Problem
Variables
Description
nb_sellers
Number of sellers
nb_items
Number of items
nb_instancesj
Number of instances requested by the buyer for item j
capacity_instancesjk
Number of instances of item j, seller k has
minPricejk
The lowest price, the kth seller can offer for the jth item
maxPricej
The highest price, the buyer can pay for the jth item
Bid(Xijk)
Bid price, the kth seller bids for the ith instance of jth item
max_rounds
The maximum number of rounds used as a terminating condition
Genetic Algorithms (GAs)
Solving Procedure

9. Evolutionary Technique for Combinatorial Reverse Auctions
Solution
Formulation of the Problem
Constraints
Xijk:1 if the ith instance of the jth item of the kth seller is selected and 0 otherwise
1 ≤ i ≤ capacity_instancesjk
1 ≤ j ≤ nb_items
1 ≤ k ≤ nb_sellers
minPricejk ≤ Bid(Xijk) ≤ maxPricej
Genetic Algorithms (GAs)
Solving Procedure

10. Evolutionary Technique for Combinatorial Reverse Auctions
Survival is the fittest
GA Operators:-
Selection
Crossover
Mutation
Why GA?:-
Powerful search technique
Near optimal solution
Reasonable time complexity
Solution
Formulation of the Problem
Genetic Algorithms (GAs)
Solving Procedure
Genetic algorithms are stochastic search algorithms inspired by the basic principles of biological evolution and natural selection. They simulate the evolution of living organisms, where the fittest individuals dominate over the weaker ones, by mimicking the biological mechanisms of evolution, such as selection, crossover and mutation.

11. Evolutionary Technique for Combinatorial Reverse Auctions
Solution
Begin:
round ← 0;
while (not maximum round) do
generation ← 0;
generate bids;
initialize chromosomes X(generation-1);
evaluate X(generation-1) by fitness function;
while (not maximum generation) do
generation ← generation + 1;
select X(generation) from X(generation -1) by Gambling Wheel Disk method;
recombine X(generation) by modified two-point crossover and mutation;
evaluate X(generation) by fitness function;
End;
round ← round + 1;
Formulation of the Problem
Genetic Algorithms (GAs)
Solving Procedure
Algorithm: Winner Determination

12. Evolutionary Technique for Combinatorial Reverse Auctions
Solution
Formulation of the Problem
where
n = number of sellers (e.g. n = 5)
rb = required number of bits to represent each seller’s item instance (e.g. rb = 3)
Genetic Algorithms (GAs)
Solving Procedure
where
p = number of items (e.g. p = 3)
mp = number of instances of itemp
1≤ P ≤ p
where
lNP = number of instances of item P for seller N
bNP = price (discounted bid price + discounted delivery rate) of item P submitted by seller N

13. Evolutionary Technique for Combinatorial Reverse Auctions
Table 1: Initial chromosome
Solution
Chromosome
Item1
Item2
Item3
Ins1
Ins2
Ins3 X1
001
010 X2
011
101
100 X3 X4
Formulation of the Problem
Genetic Algorithms (GAs)
Solving Procedure
Selection (Gambling Wheel Disk)
X1:
X2:
X3:
X4:
Crossover (Modified Two-Point Crossover)
X1:
X2:
X3:
X4:
Mutation (item wise swap)
X3:

14. Evolutionary Technique for Combinatorial Reverse Auctions
Solution
Formulation of the Problem
Table 2: Bid result
Rank
Chromosome
Item1
Item2
Item3
Cost 1 X3
S1(2)
S1(3)
S5(2)
3398 2 X2
S4(1), S5(1)
S2(3)
S3(2)
3416 3 X4
3468 4 X1
S1(1), S2(1)
S1(1), S3(1), S5(1)
3565
Genetic Algorithms (GAs)
Solving Procedure

15. Evolutionary Technique for Combinatorial Reverse Auctions
Experiments
Primary Memory: 4 GB
Processor: Intel (R) Core (TM) i3-2330M
Processor Speed: 2.20 GHz
Experimental Environment
Bidding Parameters and GA Operators
Experimental Results

16. Evolutionary Technique for Combinatorial Reverse Auctions
Bidding Parameters:-
Number of Sellers:
Number of Items: 2-10
Number of Instances: 1-100
Number of Attributes: 2 (Price and Delivery Rate)
Seller’s stock: 0-30 (per Item)
Discount Strategy: All-Units Discounts
GA Operators:-
Chromosome Encoding: Binary String
Number of Chromosome:
Selection: Gambling-Wheel Disk
Crossover: Modified Two-point
Crossover Rate: 0.5
Mutation Rate: 0.1
Termination Condition: Generation Number
Experiments
Experimental Environment
Bidding Parameters and GA Operators
Experimental Results

17. Experiment: Parameter Tuning
Evolutionary Technique for Combinatorial Reverse Auctions
Experiments
Experiment: Parameter Tuning
Experimental Environment
Bidding Parameters and GA Operators
Experimental Results
Decision: Test21
Number of Chromosome: 200
Crossover Rate: 0.5
Mutation Rate: 0.1

18. Experiment: Bid Price/Computation Time vs Number of Generations
Evolutionary Technique for Combinatorial Reverse Auctions
Experiments
Experiment: Bid Price/Computation Time vs Number of Generations
Experimental Environment
Bidding Parameters and GA Operators
Experimental Results

19. Experiment: Computation Time vs Number of Sellers/Items
Evolutionary Technique for Combinatorial Reverse Auctions
Experiments
Experiment: Computation Time vs Number of Sellers/Items
Experimental Environment
Bidding Parameters and GA Operators
Experimental Results

20. Evolutionary Technique for Combinatorial Reverse Auctions
Experiments
Experiment: Statistical Analysis of the Proposed Method
Experimental Environment
Bidding Parameters and GA Operators
Is this method reliable/consistence/stable?
Experimental Results

21. Evolutionary Technique for Combinatorial Reverse Auctions
Conclusion
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.
Conclusion
Future Works

22. Evolutionary Technique for Combinatorial Reverse Auctions
Performance comparison with some other evolutionary or exact algorithms.
Conclusion
Conclusion
Future Works
The solution our proposed algorithm is able to produce is how much near to optimal solution.
1. We are now comparing our proposed method with some evolutionary methods such as Ant Colony, Improved Ant Colony and Enumeration Algorithm with Backtracking for solving a similar problem. 2. We also are comparing our proposed method with Branch and Bound technique. 3. We are now implementing an exact method to see how optimal the result our proposed method can produce.

23. Evolutionary Technique for Combinatorial Reverse Auctions
To use big data.
Conclusion
200 sellers, total 30 instances of 10 items
Possible solution space = 20030
Conclusion
Future Works
Parallel genetic algorithms can be used to find the winner(s) more efficiently.
1. We are now comparing our proposed method with some evolutionary methods such as Ant Colony, Improved Ant Colony and Enumeration Algorithm with Backtracking for solving a similar problem. 2. We also are comparing our proposed method with Branch and Bound technique. 3. We are now implementing an exact method to see how optimal the result our proposed method can produce.
Any number of attributes can be considered.

24. Questions?
Thanks