evolutionary technique for combinatorial reverse auctions
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Evolutionary Technique for Evolutionary Technique for Combinatorial Reverse AuctionsCombinatorial Reverse Auctions
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The 28th International FLAIRS Conference 2015
Shubhashis Kumar Shil, Malek Mouhoub, and Samira SadaouiDepartment of Computer Science
University of ReginaRegina, SK, Canada
Email: {shil200s, mouhoubm, sadaouis}@uregina.ca
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
• Conclusion• Future Works
2
Motivation
Contribution
Introduction
One of the main challenges.
NP-complete problem.
Very few research works.
Exact algorithms vs evolutionary algorithms.
Evolutionary Technique for Combinatorial Reverse Auctions
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Motivation
Contribution
Introduction
Multiple attributes, instances, items, and constraints.
Genetic Algorithm (GA) based method in Combinatorial ReverseAuctions (CRAs).
Minimum procurement cost in a reasonable processing time.
The method is efficient and reliable.
Evolutionary Technique for Combinatorial Reverse Auctions
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CombinatorialReverse Auction
Winner Determination
Problem
Problem Statement
One buyer
Multiple sellers
Multiple items
Evolutionary Technique for Combinatorial Reverse Auctions
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CombinatorialReverse Auction
Winner Determination
Problem
Problem Statement
Minimum procurement cost
Reasonable computation time
Evolutionary Technique for Combinatorial Reverse Auctions
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CombinatorialReverse Auction
Problem Statement
Problem
Winner Determination
Figure 1: A sample scenario in CRAs
Evolutionary Technique for Combinatorial Reverse Auctions
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2 instances of Item1
3 instances of Item2
2 instances of Item3
Bidding Items
Buyer
Bidders’ StockBidders
Seller1
Seller2
Seller3
Seller4
Seller5
Buyer’s Constraints:1. Maximum price of
instance(s) of item(s)2. Maximum number of
rounds
Sellers’ Constraints:1. Minimum price of
instance(s) of item(s)2. Delivery rates3. Discount rates
Price and Delivery rate
Bidding Constraints:1. Sellers’ minPrice < Cost
< Buyer’s maxPrice2. Winner determination
Formulation of the Problem
Genetic Algorithms
(GAs)
Solution
Solving Procedure
Variables Descriptionnb_sellers Number of sellersnb_items Number of itemsnb_instancesj Number of instances requested by the buyer for item jcapacity_instancesjk Number of instances of item j, seller k hasminPricejk The lowest price, the kth seller can offer for the jth itemmaxPricej 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 itemmax_rounds The maximum number of rounds used as a terminating
condition
Evolutionary Technique for Combinatorial Reverse Auctions
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Formulation of the Problem
Genetic Algorithms
(GAs)
Solution
Solving Procedure
ConstraintsXijk:1 if the ith instance of the jth item of the kth seller is selected and 0 otherwise
1 ≤ i ≤ capacity_instancesjk1 ≤ j ≤ nb_items1 ≤ k ≤ nb_sellers
1 ≤ j ≤ nb_items
minPricejk ≤ Bid(Xijk) ≤ maxPricej
jsellersnb
k
cesinscapacity
i ijk cesinsnbXjk tan__
1
tan_
1
Evolutionary Technique for Combinatorial Reverse Auctions
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Formulation of the Problem
Genetic Algorithms
(GAs)
Solution
Solving Procedure
Survival is the fittest
GA Operators:-
Selection Crossover Mutation
Why GA?:-
Powerful search technique Near optimal solution Reasonable time complexity
Evolutionary Technique for Combinatorial Reverse Auctions
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Formulation of the Problem
Genetic Algorithms
(GAs)
Solution
Solving Procedure
Begin:round ← 0;while (not maximum round) do
Begin:generation ← 0;generate bids;initialize chromosomes X(generation-1);evaluate X(generation-1) by fitness function;while (not maximum generation) doBegin:
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;
End;End;
Algorithm: Winner Determination
Evolutionary Technique for Combinatorial Reverse Auctions
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Formulation of the Problem
Genetic Algorithms
(GAs)
Solution
Solving Procedure
rbn 2
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)
rbmmosomelengthChrop
P P 1
where p = number of items (e.g. p = 3)mp = number of instances of itemp1≤ P ≤ p
Evolutionary Technique for Combinatorial Reverse Auctions
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NPn
N
p
P NPi
lbXF
1 1
1)(
where lNP = number of instances of item P for seller NbNP = price (discounted bid price + discounted delivery rate) of item P submitted by seller N
Formulation of the Problem
Genetic Algorithms
(GAs)
Solution
Solving Procedure
Evolutionary Technique for Combinatorial Reverse Auctions
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ChromosomeItem1 Item2 Item3
Ins1 Ins2 Ins1 Ins2 Ins3 Ins1 Ins2
X1 001 010 010 010 010 001 010
X2 011 011 101 011 001 101 100
X3 010 011 100 101 101 011 011
X4 101 101 001 001 001 001 001
Table 1: Initial chromosome
Selection (Gambling Wheel Disk)X1:X2:X3:X4:
001 010 010 010 010 001 010001 010 010 010 010 001 010011 011 101 011 001 101 100011 011 101 011 001 101 100010 011 100 101 101 011 011101 101 001 001 001 001 001101 101 001 001 001 001 001101 101 001 001 001 001 001
Crossover (Modified Two-Point Crossover)X1:X2:X3:X4:
001 010
101 101 001 001 001 001 001101 101 001 001 001 001 001101 101 001 001 001 001 001101 101 001 001 001 001 001
010 010 010 001 010001 010 010 010 010 001 010011 011 101 011 001 101 100011 011 101 011 001 101 100
Mutation (item wise swap)
X3: 101 101 001 001 001 001 001
Formulation of the Problem
Genetic Algorithms
(GAs)
Solution
Solving Procedure
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 S5(2) S1(3) S1(2) 3468
4 X1 S1(1), S2(1)
S1(1), S3(1), S5(1)
S1(1), S2(1) 3565
Table 2: Bid result
Evolutionary Technique for Combinatorial Reverse Auctions
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Experimental Environment
Bidding Parameters and GA Operators
Experiments
Experimental Results
Primary Memory: 4 GB
Processor: Intel (R) Core (TM) i3-2330M
Processor Speed: 2.20 GHz
Evolutionary Technique for Combinatorial Reverse Auctions
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Experimental Environment
Bidding Parameters and GA Operators
Experiments
Experimental Results
Bidding Parameters:-
Number of Sellers: 40-200 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: 50-200 Selection: Gambling-Wheel Disk Crossover: Modified Two-point Crossover Rate: 0.5 Mutation Rate: 0.1 Termination Condition: Generation Number
Evolutionary Technique for Combinatorial Reverse Auctions
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Experimental Environment
Bidding Parameters and GA Operators
Experiments
Experimental Results
Experiment: Parameter Tuning
05000
1000015000200002500030000
Test
1Te
st2
Test
3Te
st4
Test
5Te
st6
Test
7Te
st8
Test
9Te
st10
Test
11Te
st12
Test
13Te
st14
Test
15Te
st16
Test
17Te
st18
Test
19Te
st20
Test
21Te
st22
Test
23Te
st24
Test
25Te
st26
Test
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Computation Time (millisecond)
152000
153000
154000
155000
156000
Test
1Te
st2
Test
3Te
st4
Test
5Te
st6
Test
7Te
st8
Test
9Te
st10
Test
11Te
st12
Test
13Te
st14
Test
15Te
st16
Test
17Te
st18
Test
19Te
st20
Test
21Te
st22
Test
23Te
st24
Test
25Te
st26
Test
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Bid Price
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Experimental Environment
Bidding Parameters and GA Operators
Experiments
Experimental Results
Experiment: Bid Price/Computation Time vs Number of Generations
150000
160000
170000
180000
190000
200000
10 20 30 40 50
Bid
Pric
e
Number of Generation
Round1 Round2 Round3
Round4 Round5
0
5000
10000
15000
20000
25000
10 20 30 40 50Co
mpu
tatio
n Ti
me
(mill
isec
ond)
Number of Generation
Round1 Round2 Round3
Round4 Round5
Evolutionary Technique for Combinatorial Reverse Auctions
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Experimental Environment
Bidding Parameters and GA Operators
Experiments
Experimental Results
Experiment: Computation Time vs Number of Sellers/Items
0
1000
2000
3000
4000
5000
6000
7000
8000
40 80 120 160 200
Com
puta
tion
Tim
e (m
illis
econ
d)
Number of Seller
Number of Item = 2 Number of Item = 4
Number of Item = 6 Number of Item = 8
Number of Item = 10
0
1000
2000
3000
4000
5000
6000
7000
8000
2 4 6 8 10Co
mpu
tatio
n Ti
me
(mill
isec
ond)
Number of Item
Number of Seller = 40 Number of Seller = 80
Number of Seller = 120 Number of Seller = 160
Number of Seller = 200
Evolutionary Technique for Combinatorial Reverse Auctions
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Experimental Environment
Bidding Parameters and GA Operators
Experiments
Experimental Results
Experiment: Statistical Analysis of the Proposed Method
Evolutionary Technique for Combinatorial Reverse Auctions
275000276000277000278000279000280000281000282000283000284000285000286000
0 10 20 30 40 50 60 70 80 90 100
Bid
Pric
e
Number of Generation
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Is this method reliable/consistence/stable?
Conclusion
Future Works
Conclusion
Our proposed method is able to solve the problem of winnerdetermination efficiently.
The method finds the winner(s) in a reasonable processing time.
The method is consistence.
Evolutionary Technique for Combinatorial Reverse Auctions
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Conclusion
Future Works
Conclusion Performance comparison with some other evolutionary or exactalgorithms.
Evolutionary Technique for Combinatorial Reverse Auctions
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The solution our proposed algorithm is able to produce is how muchnear to optimal solution.
Conclusion
Future Works
Conclusion To use big data.
Evolutionary Technique for Combinatorial Reverse Auctions
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200 sellers, total 30 instances of 10 itemsPossible solution space = 20030
Parallel genetic algorithms can be used to find the winner(s) moreefficiently.
Any number of attributes can be considered.
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Thanks
Questions?
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