Winner Determination Problem Research Articles

An efficient local search algorithm for the winner determination problem

Combinatorial auction, which allows bidders to bid on combinations of items, is an important type of market mechanism. The winner determination problem (WDP) has extensive applications in combinatorial auctions, and attracts more and more attention due to its strong relevance to business. However, this problem is intractable in theory as it has been proven to be NP-hard, and is also a challenging combinatorial optimization problem in practice. This paper is devoted to designing an efficient heuristic algorithm for solving the WDP. This proposed heuristic algorithm dubbed abcWDP is based on an effective yet simple local search framework, and equipped with three novel strategies, i.e., configuration checking, free-bid exploiting, and pseudo-tie mechanism. Extensive computational experiments on a broad range of benchmarks demonstrate that abcWDP performs much better than state-of-the-art algorithms and CPLEX in terms of both revenue and running time. More encouragingly, our abcWDP algorithm as a sequential algorithm even achieves better computational results than the multi-thread implemented algorithm $$\hbox {CA}_\mathrm{RA}$$ , which confirms its efficiency.

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 multi-unit combinatorial auction based approach for decentralized multi-project scheduling

In industry, many problems are considered as the decentralized resource-constrained multi-project scheduling problem (DRCMPSP). Existing approaches encounter difficulties in dealing with large DRCMPSP cases while respecting the information privacy requirements of the project agents. In this paper, we tackle DRCMPSP by formulating it as a multi-unit combinatorial auction (Wellman et al. in Games Econ Behav 35(1):271–303, 2001), which does not require sensitive private project information. To handle the hardness of bidder valuation, we introduce the capacity query which uses different item capacity profiles to efficiently elicit valuation information from bidders. Based on the capacity query, we adopt two existing strategies (Gonen and Lehmann in Proceedings of the 2nd ACM conference on electronic commerce, pp 13–20, 2000) for solving multi-unit winner determination problems to find good allocations of the DRCMPSP auctions. The first strategy employs a greedy allocation process, which can rapidly find good allocations by allocating the bidder with the best answer after each query. The second strategy is based on a branch-and-bound process to improve the results of the first strategy, by searching for a better sequence of granting the bids from the bidders. Empirical results indicate that the two strategies can find good solutions with higher quality than state-of-the-art decentralized approaches, and scale well to large-scale problems with thousands of activities from tens of projects.

Winner Determination in Huge Elections with MapReduce

In computational social choice, we are concerned with the development of methods for joint decision making. A central problem in this field is the winner determination problem, which aims at identifying the most preferred alternative(s). With the rise of modern e-business platforms, processing of huge amounts of preference data has become an issue. In this work, we apply the MapReduce framework - which has been specifically designed for dealing with big data - to various versions of the winner determination problem. We obtain efficient and highly parallel algorithms and provide a theoretical analysis and experimental evaluation.

Probably Approximately Efficient Combinatorial Auctions via Machine Learning

A well-known problem in combinatorial auctions (CAs) is that the value space grows exponentially in the number of goods, which often puts a large burden on the bidders and on the auctioneer. In this paper, we introduce a new design paradigm for CAs based on machine learning (ML). Bidders report their values (bids) to a proxy agent by answering a small number of value queries. The proxy agent then uses an ML algorithm to generalize from those bids to the whole value space, and the efficient allocation is computed based on the generalized valuations. We introduce the concept of "probably approximate efficiency (PAE)" to measure the efficiency of the new ML-based auctions, and we formally show how the generelizability of an ML algorithm relates to the efficiency loss incurred by the corresponding ML-based auction. To instantiate our paradigm, we use support vector regression (SVR) as our ML algorithm, which enables us to keep the winner determination problem of the CA tractable. Different parameters of the SVR algorithm allow us to trade off the expressiveness, economic efficiency, and computational efficiency of the CA. Finally, we demonstrate experimentally that, even with a small number of bids, our ML-based auctions are highly efficient with high probability.

Design and modeling of a crowdsource-enabled system for urban parcel relay and delivery

This paper proposes a crowdsource-enabled system for urban parcel relay and delivery. We consider cyclists and pedestrians as crowdsources who are close to customers and interested in relaying parcels with a truck carrier and undertaking jobs for the last-leg parcel delivery and the first-leg parcel pickup. The crowdsources express their interests in doing so by submitting bids to the truck carrier. The truck carrier then selects bids and coordinates crowdsources’ last-leg delivery (first-leg pickup) with its truck operations. The truck carrier's problem is formulated as a mixed integer non-linear program which simultaneously i) selects crowdsources to complete the last-leg delivery (first-leg pickup) between customers and selected points for crowdsource-truck relay; and ii) determines the relay points and truck routes and schedule. To solve the truck carrier problem, we first decompose the problem into a winner determination problem and a simultaneous pickup and delivery problem with soft time windows, and propose a Tabu Search based algorithm to iteratively solve the two subproblems. Numerical results show that this solution approach is able to yield close-to-optimum solutions with much less time than using off-the-shelf solvers. By adopting this new system, truck vehicle miles traveled (VMT) and total cost can be reduced compared to pure-truck delivery. The advantage of the system over pure-truck delivery is sensitive to factors such as penalty for servicing outside customers’ desired time windows, truck unit operating cost, time value of crowdsources, and the crowdsource mode.

Winner determination problem with loss-averse buyers in reverse auctions

Winner determination problem with loss-averse buyers in reverse auctions

A Multi-Agent based Hyper-Heuristic Algorithm for the Winner Determination Problem

In this paper, we propose a Multi-Agent based Hyper-Heuristic algorithm for the Winner Determination Problem named MAH2-WDP. This algorithm explores a set of cooperating agents to select the appropriate operation using learning techniques. MAH2-WDP is specialized for local search methods and evolutionary methods where the following agents are seeking to improve the search within reinforcement learning: the mediator agent, two local search agents, the perturbation agent and two recombination agents. Our computational study shows that the proposed algorithm performs well on the tested benchmark instances in terms of solution quality.

Virtualization of 5G Cellular Networks as a Hierarchical Combinatorial Auction

Virtualization has been seen as one of the main evolution trends in the forthcoming fifth generation (5G) cellular networks which enables the decoupling of infrastructure from the services it provides. In this case, the roles of infrastructure providers (InPs) and mobile virtual network operators (MVNOs) can be logically separated and the resources (e.g., subchannels, power, and antennas) of a base station owned by an InP can be transparently shared by multiple MVNOs, while each MVNO virtually owns the entire BS. Naturally, the issue of resource allocation arises. In particular, the InP is required to abstract the physical resources into isolated slices for each MVNO who then allocates the resources within the slice to its subscribed users. In this paper, we aim to address this two-level hierarchical resource allocation problem while satisfying the requirements of efficient resource allocation, strict inter-slice isolation, and the ability of intra-slice customization. To this end, we design a hierarchical combinatorial auction mechanism, based on which a truthful and sub-efficient resource allocation framework is provided. Specifically, winner determination problems (WDPs) are formulated for the InP and MVNOs, and computationally tractable algorithms are proposed to solve these WDPs. Also, pricing schemes are designed to ensure incentive compatibility. The designed mechanism can achieve social efficiency in each level even if each party involved acts selfishly. Numerical results show the effectiveness of the proposed scheme.

Achieving Economic and Environmental Sustainabilities in Urban Consolidation Center With Bicriteria Auction

Consolidation lies at the heart of the last-mile logistics problem. Urban consolidation centers (UCCs) have been set up to facilitate such consolidation all over the world. To the best of our knowledge, most—if not all—of the UCCs operate on volume-based fixed-rate charges. To achieve environmental sustainability while ensuring economic sustainability in urban logistics, we propose, in this paper, a bicriteria auction mechanism for the automated assignment of last-mile delivery orders to transport resources. We formulate and solve the winner determination problem of the auction as a biobjective programming model. We then present a systematic way to generate the Pareto frontier to characterize the tradeoff between achieving economic and environmental sustainabilities in urban logistics. Finally, we demonstrate that our proposed bicriteria auction produces the solutions that significantly dominate those obtained from the fixed-rate mechanisms. Our sensitivity analysis on the willingness of carriers to participate in the UCC operation reveals that higher willingness is favorable toward achieving greater good for all, if UCC is designed to be nonprofit and self-sustaining.

A Variable bandwidth spectrum auction mechanism with performance guarantee

Spectrum resource is experiencing a rapid growth, which cannot meet the demand of the ever-increasing wireless communications technologies in recent years. Spectrum auctions in the secondary market have been considered as a prominent way to solve this challenge due to its fairness and effectiveness. However, most of the existing studies mainly focus on allocating spectrum in units of channels without considering allocate spectrum with variable bandwidths to the secondary users, which has been supported by the software-defined radio technologies. Variable bandwidth trading can make the usage of spectrum more flexible and efficient. Thus, we study the spectrum auction problem where the primary user wants to share a continuous spectrum with the secondary users, and each secondary user has a fixed transmission demand. The target of this work is to design a truthful auction mechanism, which can allocate spectrum with variable bandwidths to the secondary users and maximize the social efficiency at the same time. We first propose a bid-monotone winner determination mechanism to decide the winning secondary users in the auction. Since the optimal winner determination problem is NP-hard, we prove that the proposed mechanism has an approximation factor of 10. Then, a channel allocation mechanism is proposed, which can allocate spectrum to winners without interference. Finally, we compute the critical value for each winner to ensure truthfulness. We can demonstrate that the proposed auction mechanism is truthful through theoretical analysis. We also perform extensive simulations to study the performance of the proposed auction mechanism, and the simulation results corroborate our theoretical analysis.

Winner determination in geometrical combinatorial auctions

We consider auctions of items that can be arranged in rows. Examples of such a setting appear in allocating pieces of land for real estate development, or seats in a theater or stadium. The objective is, given bids on subsets of items, to find a subset of bids that maximizes auction revenue (often referred to as the winner determination problem). We describe a dynamic programing algorithm which, for a k-row problem with connected and gap-free bids, solves the winner determination problem in polynomial time. We study the complexity for bids in a grid, complementing known results in literature. Additionally, we study variants of the geometrical winner determination setting. We provide a NP-hardness proof for the 2-row setting with gap-free bids. Finally, we extend this dynamic programing algorithm to solve the case where bidders submit connected, but not necessarily gap-free bids in a 2-row and a 3-row problem.

PUSH: A generalized operator for the Maximum Vertex Weight Clique Problem

The Maximum Vertex Weight Clique Problem (MVWCP) is an important generalization of the well-known NP-hard Maximum Clique Problem. In this paper, we introduce a generalized move operator called PUSH, which generalizes the conventional ADD and SWAP operators commonly used in the literature and can be integrated in a local search algorithm for MVWCP. The PUSH operator also offers opportunities to define new search operators by considering dedicated candidate push sets. To demonstrate the usefulness of the proposed operator, we implement two simple tabu search algorithms which use PUSH to explore different candidate push sets. The computational results on 142 benchmark instances from different sources (DIMACS, BHOSLIB, and Winner Determination Problem) indicate that these algorithms compete favorably with the leading MVWCP algorithms.

An Exact Algorithm Based on MaxSAT Reasoning for the Maximum Weight Clique Problem

Recently, MaxSAT reasoning is shown very effective in computing a tight upper bound for a Maximum Clique (MC) of a (unweighted) graph. In this paper, we apply MaxSAT reasoning to compute a tight upper bound for a Maximum Weight Clique (MWC) of a wighted graph. We first study three usual encodings of MWC into weighted partial MaxSAT dealing with hard clauses, which must be satisfied in all solutions, and soft clauses, which are weighted and can be falsified. The drawbacks of these encodings motivate us to propose an encoding of MWC into a special weighted partial MaxSAT formalism, called LW (Literal-Weighted) encoding and dedicated for upper bounding an MWC, in which both soft clauses and literals in soft clauses are weighted. An optimal solution of the LW MaxSAT instance gives an upper bound for an MWC, instead of an optimal solution for MWC. We then introduce two notions called the Top-k literal failed clause and the Top-k empty clause to extend classical MaxSAT reasoning techniques, as well as two sound transformation rules to transform an LW MaxSAT instance. Successive transformations of an LW MaxSAT instance driven by MaxSAT reasoning give a tight upper bound for the encoded MWC. The approach is implemented in a branch-and-bound algorithm called MWCLQ. Experimental evaluations on the broadly used DIMACS benchmark, BHOSLIB benchmark, random graphs and the benchmark from the winner determination problem show that our approach allows MWCLQ to reduce the search space significantly and to solve MWC instances effectively. Consequently, MWCLQ outperforms state-of-the-art exact algorithms on the vast majority of instances. Moreover, it is surprisingly effective in solving hard and dense instances.

An asymmetric multi-item auction with quantity discounts applied to Internet service procurement in Buenos Aires public schools

This article studies a multi-item auction characterized by asymmetric bidders and quantity discounts. We report a practical application of this type of auction in the procurement of Internet services to the 709 public schools of Buenos Aires. The asymmetry in this application is due to firms’ existing technology infrastructures, which affect their ability to provide the service in certain areas of the city. A single round first-price sealed-bid auction, it required each participating firm to bid a supply curve specifying a price on predetermined graduated quantity intervals and to identify the individual schools it would supply. The maximal intersections of the sets of schools each participant has bid on define regions we call competition units. A single unit price must be quoted for all schools supplied within the same quantity interval, so that firms cannot bid a high price where competition is weak and a lower one where it is strong. Quantity discounts are allowed so that the bids can reflect returns-to-scale of the suppliers and the auctioneer may benefit of awarding bundles of units instead of separate units. The winner determination problem in this auction poses a challenge to the auctioneer. We present an exponential formulation and a polynomial formulation for this problem, both based on integer linear programming. The polynomial formulation proves to find the optimal set of bids in a matter of seconds. Results of the real-world implementation are reported.

Winner Determination in Geometrical Combinatorial Auctions

We consider auctions of items that can be arranged in rows. Examples of such a setting appear in allocating pieces of land for real estate development, or seats in a theater or stadium. The objective is, given bids on subsets of items, to find a subset of bids that maximizes auction revenue (often referred to as the winner determination problem). We describe a dynamic programming algorithm which, for a k-row problem with connected and gap-free bids, solves the winner determination problem in polynomial time. We study the complexity for bids in a grid, complementing known results in literature. Additionally, we study variants of the geometrical winner determination setting. We provide a NP-hardness proof for the 2-row setting with gap-free bids. Finally, we extend this dynamic programming algorithm to solve the case where bidders submit connected, but not necessarily gap-free bids in a 2-row and a 3-row problem.

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.

Determining winner in multi-attribute procurement auction: A method based on technical and business experts' evaluation information

A method for solving the winner determination problem(WDP) in multi-attribute procurement auctions is proposed, based on technical and business experts’ evaluation information. Firstly,on the background of procurements in China, a multi-attribute procurement auction mechanism is presented, where technical and business experts participate in the bid evaluation. Then, the concept of TOPSIS is used to determine the positive and negative ideal points of the WDP according to bid prices, the technical and business experts’ evaluation information. Further, the closeness coefficient of each bidder(candidate supplier) is obtained by calculating the distances to the positive and negative ideal points. Thus,the winning supplier can be determined according to the closeness coefficients. Finally, a numerical example is used to illustrate the use of the proposed method.

A hybrid exact algorithm for complete set partitioning

In the Complete Set Partitioning problem we are given a finite set of elements where every subset is associated with a value, and the goal is to partition this set into disjoint subsets so as to maximise the sum of subset values. This abstract problem captures the Coalition Structure Generation problem in cooperative games in characteristic function form, where each subset, or coalition, of agents can make a profit when working together, and the goal is to partition the set of agents into coalitions to maximise the total profit. It also captures the special case of the Winner Determination problem in combinatorial auctions, where bidders place bids on every possible bundle of goods, and the goal is to find an allocation of goods to bidders that maximises the profit of the auctioneer.The main contribution of this article is an extensive theoretical analysis of the search space of the Complete Set Partitioning problem, which reveals that two fundamentally different exact algorithms can be significantly improved upon in terms of actual runtime. These are (1) a dynamic programming algorithm called “DP” [48,36] and (2) a tree-search algorithm called “IP” [32]. We start by drawing a link between DP and a certain graph describing the structure of the search space. This link reveals that many of DP's operations are in fact redundant. Consequently, we develop ODP—an optimal version of DP that avoids all of its redundant operations. Since ODP and IP are based on different design paradigms, each has its own strengths and weaknesses compared to the other. Thus, one has to trade off the advantages of one algorithm for the advantages of the other. This raises the following question: Is this trade-off inevitable? To answer this question, we develop a new representation of the search space, which links both algorithms, and allows for contrasting the workings of the two. This reveals that ODP and IP can actually be combined, leading to the development of ODP-IP—a hybrid algorithm that avoids the limitations of its constituent parts, while retaining and significantly improving upon the advantages of each part.We benchmark our algorithm against that of Björklund et al. (2009) [8], which runs in O(2n) time given n agents. We observe that the algorithm of Björklund et al. relies on performing arithmetic operations with very large integers, and assumes that any such operation has unit cost. In practice, however, working with large integers on a modern PC is costly. Consequently, when implemented, our O(3n) algorithm outperforms that of Björklund et al. by several orders of magnitude on every problem instance, making ours the fastest exact algorithm for complete set partitioning to date in practice.

An Intelligent Economic Approach for Dynamic Resource Allocation in Cloud Services

With Inter-Cloud, distributed cloud and open cloud exchange (OCX) emerging, a comprehensive resource allocation approach is fundamental to highly competitive cloud market. Oriented to infrastructure as a service (IaaS), an intelligent economic approach for dynamic resource allocation (IEDA) is proposed with the improved combinatorial double auction protocol devised to enable various kinds of resources traded among multiple consumers and multiple providers at the same time enable task partitioning among multiple providers. To make bidding and asking reasonable in each round of the auction and determine eligible transaction relationship among providers and consumers, a price formation mechanism is proposed, which is consisted of a back propagation neural network (BPNN) based price prediction algorithm and a price matching algorithm. A reputation system is proposed and integrated to exclude dishonest participants from the cloud market. The winner determination problem (WDP) is solved by the improved paddy field algorithm (PFA). Simulation results have shown that IEDA can not only help maximize market surplus and surplus strength but also encourage participants to be honest.