1,516 research outputs found
A Truthful Mechanism for the Generalized Assignment Problem
We propose a truthful-in-expectation, -approximation mechanism for a
strategic variant of the generalized assignment problem (GAP). In GAP, a set of
items has to be optimally assigned to a set of bins without exceeding the
capacity of any singular bin. In the strategic variant of the problem we study,
values for assigning items to bins are the private information of bidders and
the mechanism should provide bidders with incentives to truthfully report their
values. The approximation ratio of the mechanism is a significant improvement
over the approximation ratio of the existing truthful mechanism for GAP.
The proposed mechanism comprises a novel convex optimization program as the
allocation rule as well as an appropriate payment rule. To implement the convex
program in polynomial time, we propose a fractional local search algorithm
which approximates the optimal solution within an arbitrarily small error
leading to an approximately truthful-in-expectation mechanism. The presented
algorithm improves upon the existing optimization algorithms for GAP in terms
of simplicity and runtime while the approximation ratio closely matches the
best approximation ratio given for GAP when all inputs are publicly known.Comment: 18 pages, Earlier version accepted at WINE 201
Adaptive approach heuristics for the generalized assignment problem
The Generalized Assignment Problem consists in assigning a set of tasks to a set of agents with minimum cost. Each agent has a limited amount of a single resource and each task must be assigned to one and only one agent, requiring a certain amount of the resource of the agent. We present new metaheuristics for the generalized assignment problem based on hybrid approaches. One metaheuristic is a MAX-MIN Ant System (MMAS), an improved version of the Ant System, which was recently proposed by Stutzle and Hoos to combinatorial optimization problems, and it can be seen has an adaptive sampling algorithm that takes in consideration the experience gathered in earlier iterations of the algorithm. Moreover, the latter heuristic is combined with local search and tabu search heuristics to improve the search. A greedy randomized adaptive search heuristic (GRASP) is also proposed. Several neighborhoods are studied, including one based on ejection chains that produces good moves without increasing the computational effort. We present computational results of the comparative performance, followed by concluding remarks and ideas on future research in generalized assignment related problems.Metaheuristics, generalized assignment, local search, GRASP, tabu search, ant systems
A polyhedral approach for the generalized assignment problem.
The generalized assignment problem (GAP) consists of finding a maximal profit assignment of n jobs over m capacity constrained agents, whereby each job has to be processed by only one agent. This contribution approaches the GAP from the polyhedral point of view. A good upper bound is obtained by approximating the convex hull of the knapsack constraints in the GAP-polytope using theoretical work of Balas. Based on this result, we propose a procedure for finding close-to-optimal solutions, which gives us a lower bound. Computational results on a set of 60representative and highly capacitated problems indicate that these solutions lie within 0.06% of the optimum. After applying some preprocessing techniques and using the obtained bounds, we solve the generated instances to optimality by branch and bound within reasonable computing time.Assignment;
Mechanism Design without Money via Stable Matching
Mechanism design without money has a rich history in social choice
literature. Due to the strong impossibility theorem by Gibbard and
Satterthwaite, exploring domains in which there exist dominant strategy
mechanisms is one of the central questions in the field. We propose a general
framework, called the generalized packing problem (\gpp), to study the
mechanism design questions without payment. The \gpp\ possesses a rich
structure and comprises a number of well-studied models as special cases,
including, e.g., matroid, matching, knapsack, independent set, and the
generalized assignment problem.
We adopt the agenda of approximate mechanism design where the objective is to
design a truthful (or strategyproof) mechanism without money that can be
implemented in polynomial time and yields a good approximation to the socially
optimal solution. We study several special cases of \gpp, and give constant
approximation mechanisms for matroid, matching, knapsack, and the generalized
assignment problem. Our result for generalized assignment problem solves an
open problem proposed in \cite{DG10}.
Our main technical contribution is in exploitation of the approaches from
stable matching, which is a fundamental solution concept in the context of
matching marketplaces, in application to mechanism design. Stable matching,
while conceptually simple, provides a set of powerful tools to manage and
analyze self-interested behaviors of participating agents. Our mechanism uses a
stable matching algorithm as a critical component and adopts other approaches
like random sampling and online mechanisms. Our work also enriches the stable
matching theory with a new knapsack constrained matching model
Online Multidimensional Packing Problems in the Random-Order Model
We study online multidimensional variants of the generalized assignment problem which are used to model prominent real-world applications, such as the assignment of virtual machines with multiple resource requirements to physical infrastructure in cloud computing. These problems can be seen as an extension of the well known secretary problem and thus the standard online worst-case model cannot provide any performance guarantee. The prevailing model in this case is the random-order model, which provides a useful realistic and robust alternative. Using this model, we study the d-dimensional generalized assignment problem, where we introduce a novel technique that achieves an O(d)-competitive algorithms and prove a matching lower bound of Omega(d). Furthermore, our algorithm improves upon the best-known competitive-ratio for the online (one-dimensional) generalized assignment problem and the online knapsack problem
An approximation algorithm for a generalized assignment problem with small resource requirements.
We investigate a generalized assignment problem where the resource requirements are either 1 or 2. This problem is motivated by a question that arises when data blocks are to be retrieved from parallel disks as efficiently as possible. The resulting problem is to assign jobs to machines with a given capacity, where each job takes either one or two units of machine capacity, and must satisfy certain assignment restrictions, such that total weight of the assigned jobs is maximized. We derive a 2/3-approximation result for this problem based on relaxing a formulation of the problem so that the resulting constraint matrix is totally unimodular. Further, we prove that the LP-relaxation of a special case of the problem is half-integral, and we derive a weak persistency property.Assignment; Constraint; Data; Matrix; Requirements;
Bicriteria multiresource generalized assignment problem
In this study,we consider a bicriteria multiresource generalized assignment problem. Our criteria are the total assignment load and maximum assignment load over all agents. We aim to generate all nondominated objective vectors and the corresponding efficient solutions. We propose several lower and upper bounds and use them in our optimization and heuristic algorithms. The computational results have shown the satisfactory behaviors of our approaches. © 2014 Wiley Periodicals, Inc
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