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58
Optimal delivery of sponsored search advertisements subject to budget constraints
 In ACM EC
, 2007
"... We discuss an auction framework in which sponsored search advertisements are delivered in response to queries. In practice, the presence of bidder budgets can have a significant impact on the ad delivery process. We propose an approach based on linear programming which takes bidder budgets into acco ..."
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Cited by 28 (3 self)
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We discuss an auction framework in which sponsored search advertisements are delivered in response to queries. In practice, the presence of bidder budgets can have a significant impact on the ad delivery process. We propose an approach based on linear programming which takes bidder budgets into account, and uses them in conjunction with forecasting of query frequencies, and pricing and ranking schemes, to optimize ad delivery. Simulations show significant improvements in revenue and efficiency. Categories and Subject Descriptors G.4 [Mathematics of Computing]: Mathematical Software—Algorithm
DantzigWolfe Decomposition and BranchandPrice Solving in G12
 CONSTRAINTS
"... The date of receipt and acceptance will be inserted by the editor Abstract The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a highlevel model of the problem to an efficient combination of solving methods. Model annotations are used to co ..."
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Cited by 7 (0 self)
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The date of receipt and acceptance will be inserted by the editor Abstract The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a highlevel model of the problem to an efficient combination of solving methods. Model annotations are used to control this process. In this paper we explain the mapping to branchandprice solving. DantzigWolfe decomposition is automatically performed using the additional information given by the model annotations. The obtained models can then be solved using column generation and branchandprice. G12 supports the selection of specialised subproblem solvers, the aggregation of identical subproblems to reduce symmetries, automatic disaggregation when required by branchandbound, the use of specialised subproblem constraintbranching rules, and different master problem solvers including a hybrid solver based on the volume algorithm. We demonstrate the benefits of the G12 framework on three examples: a trucking problem, cutting stock, and twodimensional bin packing.
Automated Channel Abstraction for Advertising Auctions
"... The use of auction mechanisms like the GSP in online advertising can lead to loss of both efficiency and revenue when advertisers have rich preferences: even simple forms of expressiveness like budget constraints can lead to suboptimal outcomes. This has led to the recognition of the value of (seque ..."
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Cited by 5 (2 self)
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The use of auction mechanisms like the GSP in online advertising can lead to loss of both efficiency and revenue when advertisers have rich preferences: even simple forms of expressiveness like budget constraints can lead to suboptimal outcomes. This has led to the recognition of the value of (sequential and/or stochastic) optimization in ad allocation. Unfortunately, natural formulations of such optimization problems fall prey to channel explosion. Specifically, available ad inventory must be partitioned into subsets, or channels, of indistinguishable supply, each channel containing inventory that is interchangeable from the perspective of each active advertiser. The number of such channels grows exponentially in the number of features of interest. We propose a means for automatically abstracting these channels, grouping together channels so that irrelevant distinctions are ignored. Our approach, based on LP/MIP column and constraint generation, dramatically reduces the number of distinct channels over which ads are allocated, thus rendering optimization computationally feasible at practical scales. Our algorithms also allow revenue/efficiency to be sacrificed in a principled fashion by ignoring potentially relevant distinctions, but retaining the most important distinctions, ignoring only those that have low impact on solution quality. This allows tradeoffs to be made between tractability and solution quality. Numerical experiments demonstrate the computational practicality of our approach as well as the quality of the abstractions generated. 1.
Decomposition and Dynamic Cut Generation in Integer Linear Programming
, 2005
"... Decomposition algorithms such as Lagrangian relaxation and DantzigWolfe decomposition are wellknown methods that can be used to generate bounds for mixedinteger linear programming problems. Traditionally, these methods have been viewed as distinct from polyhedral methods, in which bounds are obta ..."
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Cited by 4 (2 self)
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Decomposition algorithms such as Lagrangian relaxation and DantzigWolfe decomposition are wellknown methods that can be used to generate bounds for mixedinteger linear programming problems. Traditionally, these methods have been viewed as distinct from polyhedral methods, in which bounds are obtained by dynamically generating valid inequalities to strengthen an initial linear programming relaxation. Recently, a number of authors have proposed methods for integrating dynamic cut generation with various decomposition methods to yield further improvement in computed bounds. In this paper, we describe a framework within which most of these methods can be viewed from a common theoretical perspective. We then discuss how the framework can be extended to obtain a decompositionbased separation technique we call decompose and cut. As a byproduct, we describe how these methods can take advantage of the fact that solutions with known structure, such as those to a given relaxation, can frequently be separated much more easily than arbitrary real vectors. 1
Combining (integer) linear programming techniques and metaheuristics for combinatorial optimization
 of Studies in Computational Intelligence
, 2008
"... Summary. Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming based methods, and metaheuristic approaches are two highly successful streams for combinatorial problems. These two have been established by d ..."
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Cited by 3 (2 self)
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Summary. Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming based methods, and metaheuristic approaches are two highly successful streams for combinatorial problems. These two have been established by different communities more or less in isolation from each other. Only over the last years a larger number of researchers recognized the advantages and huge potentials of building hybrids of mathematical programming methods and metaheuristics. In fact, many problems can be practically solved much better by exploiting synergies between these different approaches than by “pure ” traditional algorithms. The crucial issue is how mathematical programming methods and metaheuristics should be combined for achieving those benefits. Many approaches have been proposed in the last few years. After giving a brief introduction to the basics of integer linear programming, this chapter surveys existing techniques for such combinations and classifies them into ten methodological categories. 1
H.: Boosting through optimization of margin distributions
 Neural Networks, IEEE Transactions on
, 2010
"... based complexity measure for learning classifiers and developed margin distribution based generalization bounds. Competitive classification results have been shown by optimizing this bound. Another relevant work is [12]. [12] applies a boosting method to optimize the margin distribution based genera ..."
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Cited by 3 (1 self)
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based complexity measure for learning classifiers and developed margin distribution based generalization bounds. Competitive classification results have been shown by optimizing this bound. Another relevant work is [12]. [12] applies a boosting method to optimize the margin distribution based generalization bound obtained by [13]. Experiments show that the new boosting methods achieves considerable improvements over AdaBoost. The optimization of this new boosting method is based on the AnyBoost framework [5]. Aligned with these attempts, we proposed a new boosting algorithm through optimization of margin distribution (termed MDBoost). Instead of minimizing a margin distribution based generalization bound, we directly optimize the margin distribution: maxiarXiv:0904.2037v1
Branch and Price for the Vehicle Routing Problem with Discrete Split Deliveries and Time Windows
, 2009
"... ..."
DantzigWolfe Decomposition for Solving MultiStage Stochastic CapacityPlanning Problems
, 2008
"... We describe a multistage, stochastic, mixedintegerprogramming model for planning discrete capacity expansion of production facilities. A scenario tree represents uncertainty in the model; a general mixedinteger program defines the operational submodel at each scenariotree node; and capacityexp ..."
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Cited by 3 (0 self)
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We describe a multistage, stochastic, mixedintegerprogramming model for planning discrete capacity expansion of production facilities. A scenario tree represents uncertainty in the model; a general mixedinteger program defines the operational submodel at each scenariotree node; and capacityexpansion decisions link the stages. We apply “variable splitting ” to two model variants, and solve those variants using DantzigWolfe decomposition. The DantzigWolfe master problem can have a much stronger linearprogramming relaxation than is possible without variable splitting, over 700 % stronger in one case. The master problem solves easily and tends to yield integer solutions, obviating the need for a full branchandprice solution procedure. For each scenariotree node, the decomposition defines a subproblem that may be viewed as a singleperiod, deterministic, capacityplanning problem. An effective solution procedure results as long as the subproblems solve efficiently, and the procedure incorporates a good “duals stabilization scheme.” We present computational results for a model to plan the capacity expansion of an electricity distribution network in New Zealand, given uncertain future demand. The largest problem we solve to optimality has 6 stages and 243 scenarios, and corresponds to a deterministic equivalent with a quarter of a million binary variables.
Optimal routing and call scheduling in wireless mesh networks with localized information
 the fourth Symposium on Trustworthy Global Computing (TGC 2008), volume 5474 of LNCS:pages 171–185
, 2008
"... Abstract. Wireless mesh network performance issues have been modeled by the Joint Routing and Scheduling Problem (JRSP) in which a maximum perflow throughput is computed. A classical relaxation of JRSP, denoted as the Round Weighting Problem (RWP), consists in assigning enough weight to sets of com ..."
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Cited by 3 (2 self)
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Abstract. Wireless mesh network performance issues have been modeled by the Joint Routing and Scheduling Problem (JRSP) in which a maximum perflow throughput is computed. A classical relaxation of JRSP, denoted as the Round Weighting Problem (RWP), consists in assigning enough weight to sets of compatible simultaneous transmissions (rounds), while minimizing the sum of them, thus maximizing the relative weight of each round, which model the throughput. In this work, we present a new linear formulation of RWP focused on the transport capacity over the network cuts, thus eliminating the routing. We prove its equivalence with existing formulations with flows and formalize a primaldual algorithm that quickly solves this problem using a cross line and column generations process. An asset of this formulation is to point out a bounded region, a ”bottleneck” of the network, that is enough to optimize in order to get the optimal RWP of the whole network. The size and location of this area is experimentally made through simulations, highlighting a few hop distant neighborhood of the mesh gateways. One would then apply approximated methods outside this zone to route the traffic without degrading the achieved capacity. 1
Dual Variable Based Fathoming in Dynamic Programs for Column Generation
 European Journal of Operational Reseach
, 2003
"... In column generation schemes, particularly those proposed for set partitioning type problems, dynamic programming algorithms are applied to solve the respective pricing subproblem. In addition to traditional dominance criteria for state space reduction, we develop a simple generic lower bounding cri ..."
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Cited by 2 (1 self)
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In column generation schemes, particularly those proposed for set partitioning type problems, dynamic programming algorithms are applied to solve the respective pricing subproblem. In addition to traditional dominance criteria for state space reduction, we develop a simple generic lower bounding criterion based on the dual optimal solution of the restricted master problem. Key words: Dynamic programming; Column generation; Linear programming Column generation is a prominentand often the solely applicablemethod to cope with linear programming problems with a colossal number of variables. In recent years we have been witnessing the optimal solution of truly large problems, but still the need for faster algorithms remains, especially in the various practical application areas. The pricing subproblem usually constitutes the crucial part of a column generation scheme, not uncommonly for the reason of being a hard combinatorial optimization problem by itself. Although a dynamic program...