Evolutionary Technique for Combinatorial Reverse Auctions

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

mailto:@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

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Motivation

Contribution

Introduction

One of the main challenges.

NP-complete problem.

Very few research works.

Exact algorithms vs evolutionary algorithms.


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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.


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CombinatorialReverse Auction

Winner Determination

Problem

Problem Statement

One buyer

Multiple sellers

Multiple items


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Problem

Problem Statement

Minimum procurement cost

Reasonable computation time


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Problem Statement

Problem


Figure 1: A sample scenario in CRAs


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2 instances of Item1



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


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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


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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


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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


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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


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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


Genetic Algorithms

(GAs)

Solution

Solving Procedure


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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


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


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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


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Experiments


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


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Experiments


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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Experiments


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)


Round1 Round2 Round3

Round4 Round5


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Experiments


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


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Experiments


Experiment: Statistical Analysis of the Proposed Method


275000276000277000278000279000280000281000282000283000284000285000286000

0 10 20 30 40 50 60 70 80 90 100

Bid

Pric

e


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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.


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Conclusion

Future Works

Conclusion Performance comparison with some other evolutionary or exactalgorithms.


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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.


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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?

Evolutionary Technique for Combinatorial Reverse Auctions

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