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 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 Future Works

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.

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.

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.

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.

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 = 1000. 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

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

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

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.

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

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

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: 001 010 010 010 010 001 010 001 010 010 010 010 001 010 011 011 101 011 001 101 100 011 011 101 011 001 101 100 010 011 100 101 101 011 011 101 101 001 001 001 001 001 101 101 001 001 001 001 001 101 101 001 001 001 001 001 Crossover (Modified Two-Point Crossover) X1: X2: X3: X4: 001 010 001 010 010 010 010 010 010 010 001 010 001 010 011 011 011 011 101 011 001 101 011 001 101 100 101 100 101 101 001 001 001 001 001 101 101 001 001 001 001 001 101 101 001 001 001 001 001 101 101 001 001 001 001 001 Mutation (item wise swap) X3: 101 101 001 001 001 001 001

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

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

Evolutionary Technique for Combinatorial Reverse Auctions 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 Experiments Experimental Environment Bidding Parameters and GA Operators Experimental Results

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

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

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

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

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

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.

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.

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