Winner Determination In Combinatorial Auctions Research Articles

A Graph Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions

Combinatorial auctions are increasingly being used to allocate bundles of items among interested bidders. However, as the number of bundles increases, it takes exponentially longer to solve for the winners in the auction. In such situations, regular solvers such as IBM CPLEX or AMPL fail to produce the optimal solution either completely due to computational limitations or in reasonable time. We propose an Ant Colony-based algorithm (TrACA) that produces optimal or near-optimal results within specified time. Experiments are performed on 90 instances to show and compare the performance of TrACA to the current state-of-the-art memetic algorithm (MA). Results indicate that in a given run-time, the median of results from TrACA statistically significantly outperforms MA results in 85% of the cases. Further, the best value from TrACA is at least as good as MA values in 100% of the cases. Additionally, to better understand the why deterministic algorithms fail or take too long for approximating winners in such auctions, we analyze empirical hardness of tested instances and use a standard supervised learning method to build a predictive model of TrACA run-times. Using the predictive model, we highlight factors that make winner determination in combinatorial auctions computationally hard to estimate and show why TrACA is better suited to handle such hard instances.

Winner Determination in Combinatorial Auctions using Hybrid Ant Colony Optimization and Multi-Neighborhood Local Search

A combinatorial auction is an auction where the bidders have the choice to bid on bundles of items. The WDP in combinatorial auctions is the problem of finding winning bids that maximize the auctioneer’s revenue under the constraint that each item can be allocated to at most one bidder. The WDP is known as an NP-hard problem with practical applications like electronic commerce, production management, games theory, and resources allocation in multi-agent systems. This has motivated the quest for efficient approximate algorithms both in terms of solution quality and computational time. This paper proposes a hybrid Ant Colony Optimization with a novel Multi-Neighborhood Local Search (ACO-MNLS) algorithm for solving Winner Determination Problem (WDP) in combinatorial auctions. Our proposed MNLS algorithm uses the fact that using various neighborhoods in local search can generate different local optima for WDP and that the global optima of WDP is a local optima for a given its neighborhood. Therefore, proposed MNLS algorithm simultaneously explores a set of three different neighborhoods to get different local optima and to escape from local optima. The comparisons between ACO-MNLS, Genetic Algorithm (GA), Memetic Algorithm (MA), Stochastic Local Search (SLS), and Tabu Search (TS) on various benchmark problems confirm the efficiency of ACO-MNLS in the terms of solution quality and computational time.

A clique-based exact method for optimal winner determination in combinatorial auctions

Given a set of items to sell and a set of combinatorial bids, the Winner Determination Problem (WDP) in combinatorial auctions is to determine an allocation of items to bidders such that the auctioneer’s revenue is maximized while each item is allocated to at most one bidder. WDP is at the core of numerous relevant applications in multi-agent systems, e-commerce and many others. We develop a clique-based branch-and-bound approach for WDP which relies on a transformation of WDP into the maximum weight clique problem. To ensure the efficiency of the proposed search algorithm, we introduce specific bounding and branching strategies using a dedicated vertex coloring procedure and a specific vertex sorting technique. We assess the performance of the proposed algorithm on a large collection of benchmark instances in comparison with the CPLEX 12.4 solver and other approaches. Computational results show that this clique-based method constitutes a valuable and complementary approach for WDP relative to the existing methods.

Improved Monkey-King Genetic Algorithm for Solving Large Winner Determination in Combinatorial Auction

Abstract Using GA solve the winner determination problem (WDP) with large bids and items, run under different distribution, because the search space is large, constraint complex and it may easy to produce infeasible solution, would affect the efficiency and quality of algorithm. This paper present improved MKGA, including three operator: preprocessing, insert bid and exchange recombination, and use Monkey-king elite preservation strategy. Experimental results show that improved MKGA is better than SGA in population size and computation. The problem that traditional branch and bound algorithm hard to solve, improved MKGA can solve and achieve better effect.

A Winner Determination Algorithm for Combinatorial Auctions Based on Hybrid Artificial Fish Swarm Algorithm

Abstract The problem of winner determination in combinatorial auctions is a hotspot electronic business, and a NP hard problem. A Hybrid Artificial Fish Swarm Algorithm(HAFSA), which is combined with First Suite Heuristic Algorithm (FSHA) and Artificial Fish Swarm Algorithm (AFSA), is proposed to solve the problem after probing it base on the theories of AFSA. Experiment results show that the HAFSA is a rapidly and efficient algorithm for The problem of winner determining. Compared with Ant colony Optimization Algorithm, it has a good performance with broad and prosperous application.

Combinatorial auction under fuzzy environment

Combinatorial auction (CA) mechanism allows bundling of multiple items in packages, which can be solved through a clearing method termed as the winner determination problem (WDP). However, to date, there has yet to be a CA model that accounts for the fuzziness of bidders’ submitted prices. The imprecision in submitted prices is the result of the time gap between bid placement and winning bid announcement, which reflects the bidders’ expected values of the goods at the point of contract sale. Despite this common understanding, conventional CA modeling still treats the prices as deterministic. This causes a major shortcoming when an uncertain environment is assumed to be deterministic and solved through conventional WDP. This study shows that a fuzzy environment modeled via a deterministic WDP approach provides overly optimistic revenue for the auctioneer. A method of using possibilistic distributions of submitted prices to account for price uncertainty is proposed and formalized as Fuzzy Combinatorial Auction Winner Determination Problem (Fuzzy CA WDP). The difference in optimal solutions in deterministic WDP and fuzzy WDP reflects the amount of over estimation when a fuzzy situation is treated as though it is precise. It also reflects the information value when the uncertainty inherent in the fuzzy environment is resolved. Given that the information value is quantified in unit dollars, the fuzzy WDP approach allows the auctioneer to estimate its “true” revenue despite price uncertainties.

Approximation Techniques for Utilitarian Mechanism Design

This paper deals with the design of efficiently computable incentive-compatible mechanisms for combinatorial optimization problems with single-minded agents each possibly having multiple private parameters. We focus on approximation algorithms for NP-hard mechanism design problems. These algorithms need to satisfy certain monotonicity properties to ensure truthfulness. Since most of the known approximation techniques do not fulfill these properties, we study alternative techniques. Our first contribution is a quite general method to transform a pseudopolynomial algorithm into a monotone fully polynomial time approximation scheme (FPTAS). This can be applied to various problems like, e.g., knapsack, constrained shortest path, or job scheduling with deadlines. For example, the monotone FPTAS for the knapsack problem gives a very efficient, truthful mechanism for single-minded multiunit auctions. The best previous result for such auctions was a 2-appro-xi-ma-tion. In addition, we present a monotone PTAS for the generalized assignment problem with any constant number of private parameters per agent. The most efficient way to solve packing integer programs (PIPs) is linear programming–based randomized rounding, which also is in general not monotone. We show that primal-dual greedy algorithms achieve almost the same approximation ratios for PIPs as randomized rounding. The advantage is that these algorithms are inherently monotone. This way, we can significantly improve the approximation ratios of truthful mechanisms for various fundamental mechanism design problems like single-minded combinatorial auctions (CAs), unsplittable flow routing, and multicast routing. Our primal-dual approximation algorithms can also be used for the winner determination in CAs with general bidders specifying their bids through an oracle.

Empirical hardness models

Is it possible to predict how long an algorithm will take to solve a previously-unseen instance of an NP-complete problem? If so, what uses can be found for models that make such predictions? This article provides answers to these questions and evaluates the answers experimentally. We propose the use of supervised machine learning to build models that predict an algorithm's runtime given a problem instance. We discuss the construction of these models and describe techniques for interpreting them to gain understanding of the characteristics that cause instances to be hard or easy. We also present two applications of our models: building algorithm portfolios that outperform their constituent algorithms, and generating test distributions that emphasize hard problems. We demonstrate the effectiveness of our techniques in a case study of the combinatorial auction winner determination problem. Our experimental results show that we can build very accurate models of an algorithm's running time, interpret our models, build an algorithm portfolio that strongly outperforms the best single algorithm, and tune a standard benchmark suite to generate much harder problem instances.

Editor's puzzle

As usual, you are allowed to use computers to help you solve this puzzle, but the final argument should be human-readable and as strong as possible. Solutions should be sent to the editor at conitzer@cs.duke.edu with subject header SIGecom Exchanges Puzzle. The author(s) of the most elegant solution (as judged by the editor) will be allowed to publish his or her or their proof in the next issue of the Exchanges (ties broken towards earlier submissions). To make the solution accessible to a wide audience, try to minimize technical jargon in the proof. The editor will not give any feedback on submitted solutions and ignore any requests for hints, etc. Also, the previous issue’s puzzle on combinatorial auction winner determination was solved by each of Daniel Lehmann, Peter Stone, and Mukund Sundararajan, who submitted very similar solutions, but they did not consider their solutions elegant enough to publish. If someone submits a more elegant solution to that puzzle, I will be happy to publish it in the next issue. Hint (for that puzzle): think about prices and duality, though integrality plays a role... Now, let us get to this issue’s puzzle:

CABOB: A Fast Optimal Algorithm for Winner Determination in Combinatorial Auctions

Combinatorial auctions where bidders can bid on bundles of items can lead to more economically efficient allocations, but determining the winners is 𝒩𝒫-complete and inapproximable. We present CABOB, a sophisticated optimal search algorithm for the problem. It uses decomposition techniques, upper and lower bounding (also across components), elaborate and dynamically chosen bid-ordering heuristics, and a host of structural observations. CABOB attempts to capture structure in any instance without making assumptions about the instance distribution. Experiments against the fastest prior algorithm, CPLEX 8.0, show that CABOB is often faster, seldom drastically slower, and in many cases drastically faster—especially in cases with structure. CABOB's search runs in linear space and has significantly better anytime performance than CPLEX. We also uncover interesting aspects of the problem itself. First, problems with short bids, which were hard for the first generation of specialized algorithms, are easy. Second, almost all of the CATS distributions are easy, and the run time is virtually unaffected by the number of goods. Third, we test several random restart strategies, showing that they do not help on this problem—the run-time distribution does not have a heavy tail.

Modeling and Heuristic for Winner Determination in Combinatorial Auctions

Modeling and Heuristic for Winner Determination in Combinatorial Auctions

COMBINATORIAL AUCTIONS MATHEMATICAL FORMULATIONS AND OPEN ISSUES

The widespread use of the Internet fostered the establishment of hundreds of sites that support on-line auctions of products and services, some of which also support combinatorial auctions. Finding the optimal combination of winning bids in combinatorial auctions is a difficult task. This paper presents the combinatorial auction problem, classifies combinatorial auctions by the different procedures used during the bidding process, presents some of the applications of combinatorial auctions, and develops mathematical models of combinatorial auctions. The mathematical models are used to identify some of the problem properties and prove that winner determination in combinatorial auctions has the same level of difficulty as solving the allocation problem facing an auctioneer. The paper concludes with the discussion on some of the complexities involved in combinatorial auctions.

BOB: Improved winner determination in combinatorial auctions and generalizations

Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary or substitutable. Determining the winners is NP -complete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper presents a more sophisticated search algorithm for optimal (and anytime) winner determination, including structural improvements that reduce search tree size, faster data structures, and optimizations at search nodes based on driving toward, identifying and solving tractable special cases. We also uncover a more general tractable special case, and design algorithms for solving it as well as for solving known tractable special cases substantially faster. We generalize combinatorial auctions to multiple units of each item, to reserve prices on singletons as well as combinations, and to combinatorial exchanges. All of these generalizations support both complementarity and substitutability of the items. Finally, we present algorithms for determining the winners in these generalizations.

Algorithm for optimal winner determination in combinatorial auctions

Combinatorial auctions, that is, auctions where bidders can bid on combinations of items, tend to lead to more efficient allocations than traditional auction mechanisms in multi-item auctions where the agents' valuations of the items are not additive. However, determining the winners so as to maximize revenue is NP -complete. First, we analyze existing approaches for tackling this problem: exhaustive enumeration, dynamic programming, and restricting the allowable combinations. Second, we study the possibility of approximate winner determination, proving inapproximability in the general case, and discussing approximation algorithms for special cases. We then present our search algorithm for optimal winner determination. Experiments are shown on several bid distributions which we introduce. The algorithm allows combinatorial auctions to scale up to significantly larger numbers of items and bids than prior approaches to optimal winner determination by capitalizing on the fact that the space of bids is sparsely populated in practice. The algorithm does this by provably sufficient selective generation of children in the search tree, by using a secondary search for fast child generation, by using heuristics that are admissible and optimized for speed, and by preprocessing the search space in four ways. Incremental winner determination and quote computation techniques are presented. We show that basic combinatorial auctions only allow bidders to express complementarity of items. We then introduce two fully expressive bidding languages, called XOR-bids and OR-of-XORs, with which bidders can express general preferences (both complementarity and substitutability). The latter language is more concise. We show how these languages enable the use of the Vickrey–Clarke–Groves mechanism to construct a combinatorial auction where each bidder's dominant strategy is to bid truthfully. Finally, we extend our search algorithm and preprocessors to handle these languages as well as arbitrary XOR-constraints between bids.

An Efficient Approximate Algorithm for Winner Determination in Combinatorial Auctions

Auctions on the Internet have become especially popular in Electronic Commerce. Amongthe various studies on the Internet auctions, those on combinatorial auctions have lately attracted considerable attention. Combinatorial auctions simultaneously sell multiple items with interdependent values and allow the bidders to bid on any combination of items. Therefore, they tend to increase the buyers’ utilities and the seller’s revenue.

Approaches to winner determination in combinatorial auctions

Combinatorial auctions, i.e., auctions where bidders can bid on combinations of items, tend to lead to more efficient allocations than traditional auctions in multi-item auctions where the agents' valuations of the items are not additive. However, determining the winners so as to maximize revenue is NP -complete. First, existing approaches for tackling this problem are reviewed: exhaustive enumeration, dynamic programming, approximation algorithms, and restricting the allowable combinations. Then, we overview our new search algorithm for optimal anytime winner determination. By capitalizing on the fact that the space of bids is necessarily sparsely populated in practice, it enlarges the envelope of input sizes for which combinatorial auctions are computationally feasible. Finally, we discuss eMediator, our electronic commerce server that implements several techniques for automatically facilitating commerce, including an auction house with generalized combinatorial auctions. To our knowledge, our implementation is the first Internet auction to support combinatorial auctions, bidding via graphically drawn price–quantity graphs, and by mobile agents.