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Expressive commerce and its application to sourcing: How we conducted $35 billion of generalized combinatorial auctions
"... Sourcing professionals buy several trillion dollars worth of goods and services yearly. We introduced a new paradigm called expressive commerce and applied it to sourcing. It combines the advantages of highly expressive human negotiation with the advantages of electronic reverse auctions. The idea i ..."
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Cited by 48 (7 self)
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Sourcing professionals buy several trillion dollars worth of goods and services yearly. We introduced a new paradigm called expressive commerce and applied it to sourcing. It combines the advantages of highly expressive human negotiation with the advantages of electronic reverse auctions. The idea is that supply and demand are expressed in drastically greater detail than in traditional electronic auctions, and are algorithmically cleared. This creates a Pareto efficiency improvement in the allocation (a win-win between the buyer and the sellers) but the market clearing problem is a highly complex combinatorial optimization problem. We developed the world’s fastest tree search algorithms for solving it. We have hosted $35 billion of sourcing using the technology, and created $4.4 billion of hard-dollar savings plus numerous harder-to-quantify benefits. The suppliers also benefited by being able to express production efficiencies and creativity, and through exposure problem removal. Supply networks were redesigned, with quantitative understanding of the tradeoffs, and implemented in weeks instead of months.
A unified method for handling discrete and continuous uncertainty in bayesian stackelberg games
- In International Conference on Autonomous Agents and Multiagent Systems (AAMAS
, 2012
"... Given their existing and potential real-world security applications, Bayesian Stackelberg games have received significant research interest [3, 12, 8]. In these games, the defender acts as a leader, and the many different follower types model the uncertainty over discrete attacker types. Unfortunate ..."
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Cited by 22 (12 self)
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Given their existing and potential real-world security applications, Bayesian Stackelberg games have received significant research interest [3, 12, 8]. In these games, the defender acts as a leader, and the many different follower types model the uncertainty over discrete attacker types. Unfortunately since solving such games is an NP-hard problem, scale-up has remained a difficult challenge. This paper scales up Bayesian Stackelberg games, providing a novel unified approach to handling uncertainty not only over discrete follower types but also other key continuously distributed real world uncertainty, due to the leader’s execution error, the follower’s observation error, and continuous payoff uncertainty. To that end, this paper provides contributions in two parts. First, we present a new algorithm for Bayesian Stackelberg games, called HUNTER, to scale up the number of types. HUNTER combines the following
Expressive Commerce and Its Application to Sourcing
, 2006
"... Sourcing professionals buy several trillion dollars worth of goods and services yearly. We introduced a new paradigm called expressive commerce and applied it to sourcing. It combines the advantages of highly expressive human negotiation with the advantages of electronic reverse auctions. The idea i ..."
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Cited by 12 (0 self)
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Sourcing professionals buy several trillion dollars worth of goods and services yearly. We introduced a new paradigm called expressive commerce and applied it to sourcing. It combines the advantages of highly expressive human negotiation with the advantages of electronic reverse auctions. The idea is that supply and demand are expressed in drastically greater detail than in traditional electronic auctions, and are algorithmically cleared. This creates a Pareto efficiency improvement in the allocation (a win-win between the buyer and the sellers) but the market clearing problem is a highly complex combinatorial optimization problem. We developed the world’s fastest tree search algorithms for solving it. We have hosted $19 billion of sourcing using the technology, and created $2.1 billion of
Hydra-MIP: Automated Algorithm Configuration and Selection for Mixed Integer Programming
"... Abstract. State-of-the-art mixed integer programming (MIP) solvers are highly parameterized. For heterogeneous and a priori unknown instance distributions, no single parameter configuration generally achieves consistently strong performance, and hence it is useful to select from a portfolio of diffe ..."
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Cited by 12 (6 self)
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Abstract. State-of-the-art mixed integer programming (MIP) solvers are highly parameterized. For heterogeneous and a priori unknown instance distributions, no single parameter configuration generally achieves consistently strong performance, and hence it is useful to select from a portfolio of different configurations. HYDRA is a recent method for using automated algorithm configuration to derive multiple configurations of a single parameterized algorithm for use with portfolio-based selection. This paper shows that, leveraging two key innovations, HYDRA can achieve strong performance for MIP. First, we describe a new algorithm selection approach based on classification with a non-uniform loss function, which significantly improves the performance of algorithm selection for MIP (and SAT). Second, by modifying HYDRA’s method for selecting candidate configurations, we obtain better performance as a function of training time. 1
On the Complexity of Selecting Disjunctions in Integer Programming
- SIAM Journal on Optimization
"... The imposition of general disjunctions of the form “πx ≤ π0 ∨ πx ≥ π0 + 1”, where π,π0 are integer valued, is a fundamental operation in both the branch-and-bound and cuttingplane algorithms for solving mixed integer linear programs. Such disjunctions can be used for branching at each iteration of t ..."
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Cited by 7 (3 self)
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The imposition of general disjunctions of the form “πx ≤ π0 ∨ πx ≥ π0 + 1”, where π,π0 are integer valued, is a fundamental operation in both the branch-and-bound and cuttingplane algorithms for solving mixed integer linear programs. Such disjunctions can be used for branching at each iteration of the branch-and-bound algorithm or to generate split inequalities for the cutting-plane algorithm. We first consider the problem of selecting a general disjunction and show that the problem of selecting an optimal such disjunction, according to specific criteria described herein, is N P-hard. We further show that the problem remains N P-hard even for binary programs or when considering certain restricted classes of disjunctions. We observe that the problem of deciding whether a given inequality is a split inequality can be reduced to one of the above problems, which leads to a proof that the problem is N P-complete. 1
On the Complexity of Selecting Branching Disjunctions in Integer Programming
, 2008
"... Branching is an important component of branch-and-bound algorithms for solving mixed integer linear programs. We consider the problem of selecting, at each iteration of the branchand-bound algorithm, a general branching disjunction of the form “πx ≤ π0∨πx ≥ π0+1”, where π,π0 are integral. We show th ..."
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Branching is an important component of branch-and-bound algorithms for solving mixed integer linear programs. We consider the problem of selecting, at each iteration of the branchand-bound algorithm, a general branching disjunction of the form “πx ≤ π0∨πx ≥ π0+1”, where π,π0 are integral. We show that the problem of selecting an optimal such disjunction, according to specific criteria described herein, is N P-hard. We further show that the problem remains N P-hard even for binary programs or when considering certain restricted classes of disjunctions. We observe that the problem of deciding whether a given inequality is a split inequality can be reduced to one of the above problems, which leads to a proof that this problem is N P-complete. 1
Throwing Darts: Random Sampling Helps Tree Search when the Number of Short Certificates is Moderate
, 2013
"... One typically proves infeasibility in satisfiability/constraint satisfaction (or optimality in integer programming) by constructing a tree certificate. However, deciding how to branch in the search tree is hard, and impacts search time drastically. We explore the power of a simple paradigm, that of ..."
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One typically proves infeasibility in satisfiability/constraint satisfaction (or optimality in integer programming) by constructing a tree certificate. However, deciding how to branch in the search tree is hard, and impacts search time drastically. We explore the power of a simple paradigm, that of throwing random darts into the assignment space and then using information gathered by that dart to guide what to do next. Such guidance is easy to incorporate into state-of-the-art solvers. This method seems to work well when the number of short certificates of infeasibility is moderate, suggesting the overhead of throwing darts can be countered by the information gained by these darts. We explore results supporting this suggestion both on instances from a new generator where the size and number of short certificates can be controlled, and on industral instances from the annual SAT competition.
EXPLOITING STRUCTURE IN INTEGER PROGRAMS
, 2011
"... This dissertation argues the case for exploiting certain structures in integer linear programs. Integer linear programming is a well-known optimisation problem, which seeks the optimum of a linear function of variables, whose values are required to be integral as well as to satisfy certain linear eq ..."
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This dissertation argues the case for exploiting certain structures in integer linear programs. Integer linear programming is a well-known optimisation problem, which seeks the optimum of a linear function of variables, whose values are required to be integral as well as to satisfy certain linear equalities and inequalities. The state of the art in solvers for this problem is the “branch and bound ” approach. The performance of such solvers depends crucially on four types of in-built heuristics: primal, improvement, branching, and cut-separation or, more generally, bounding heuristics. Such heuristics in general-purpose solvers have not, until recently, exploited structure in integer linear programs beyond the recognition of certain types of single-row constraints. Many alternative approaches to integer linear programming can be cast in the following, novel framework. “Structure” in any integer linear program
