generalized assignment problem algorithm

The generalized assignment problem is NP-hard, However, there are linear-programming relaxations which give a (/)-approximation. Greedy approximation algorithm. For the problem variant in which not every item must be assigned to a bin, there is a family of algorithms for solving the GAP by using a combinatorial translation of any algorithm for ...

Multiple-Resource Generalized Assignment Problem. Proposed by Gavish and Pirkul [], multi-resource generalized assignment problem (MRGAP) is a special case of the multi-resource weighted assignment model that is previously studied by Ross and Zoltners [].In MRGAP a set of tasks has to be assigned to a set of agents in a way that permits assignment of multiple tasks to an agent subject to a set ...

Components in the algorithms proposed for GAP and MRGAP in [12, 13, 14] are further generalized by Yagiura et al. [15] to make them applicable to wider range of problems. They consider the multi-resource generalized quadratic assignment problem (MR-GQAP), which is a natural generalization of the generalized quadratic assignment problem (GQAP ...

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing job j on machine i requires time pif and incurs a cost of c,f, each machine / is available for 7", time units, and the objective is.t»minimize the total cost incurred.

of problems includes the maximum generalized assignment problem (GAP)1) and a distributed caching problem (DCP) described in this paper. Given a -approximationalgorithmfor nding the high-est value packing of a single bin, we give 1. A polynomial-time LP-rounding based ((1 1 e) )-approximation algorithm. 2. A simple polynomial-time local search ...

We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and its running time is O ( f ( N)), our ...

We consider generalized assignment problems with different objective functions: min-sum, max-sum, min-max, max-min. We review transformations, bounds, approximation algorithms and exact algorithms. The results of extensive computational experiments are given. Download to read the full chapter text.

A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem. The Generalized Assignment Problem (GAP) examines the maximum profit assignment of n jobs to m agents

ABSTRACT. This chapter reviews heuristic and metaheuristic algorithms for generalized assignment problem and explores the problem formally and introduces some related problems and their complexities. It explains basic strategies of greedy method and local search and describes Lagrangian relaxation problems. The chapter provides some basic ideas ...

TLDR. A truthful-in-expectation, (1-1/e)-approximation mechanism for a strategic variant of the generalized assignment problem (GAP), which improves upon the existing optimization algorithms for GAP in terms of simplicity and runtime while the approximation ratio closely matches the best approximation ratio known for G AP when all inputs are ...

Constraint satisfaction problems: Algorithms and applications. Sally C. Brailsford, ... Barbara M. Smith, in European Journal of Operational Research, 1999 Rodosek et al. (to appear) present some empirical results for five specific problems (the progressive party problem, a generalized assignment problem, a packing problem, a set-partitioning problem, and a logical problem to show that it is ...

The generalized assignment problem (GAP), the 0-1 integer programming (IP) problem of assigning a set of n items to a set of m knapsacks, where each item must be assigned to exactly one knapsack and there are constraints on the availability of resources for item assignment, has been further generalized recently to include cases where items may be shared by a pair of adjacent knapsacks. This ...

Abstract. We describe a branch and bound algorithm for the generalized assignment problem in which bounds are obtained from a Lagrangian relaxation with the multipliers set by a heuristic adjustment method. The algorithm was tested on a large sample of small random problems and a number of large problems derived from a vehicle routing application.

A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem. The generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely ...

Instead of using reduction, the unbalanced assignment problem can be solved by directly generalizing existing algorithms for balanced assignment. The Hungarian algorithm can be generalized to solve the problem in O ( m s + s 2 log ⁡ r ) {\displaystyle O(ms+s^{2}\log r)} strongly-polynomial time.

In this paper we present a genetic algorithm (GA)-based heuristic for solving the generalised assignment problem. The generalised assignment problem is the problem of finding the minimum cost assignment of n jobs to m agents such that each job is assigned to exactly one agent, subject to an agent's capacity. In addition to the standard GA procedures, our GA heuristic incorporates a problem ...

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timepij and incurs a cost ofcij; each machinei is available forTi time units, and the objective is to minimize the total cost incurred.

Abstract. The generalized assignment problem (GAP) is an open problem in which an integer is given and one wants to assign agents to jobs such that the sum of the corresponding cost is minimal. Unlike the traditional -cardinality assignment problem, a job can be assigned to many, but different, agents and an agent may undertake several, but different, jobs in our problem.

The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timep ij and incurs a cost ofc ij ; each machinei is available forT i time units, and the objective is to minimize the total cost incurred. Our main result is as follows. There is a ...

A Constructive Genetic Algorithm For The Generalised Assignment Problem Research paper. In this paper an application of the Constructive Genetic Algorithm to the Generalised Assignment Problem (GAP) is presented, which uses a binary representation and an assignment heuristic which allocates items to knapsacks. Expand.

Secondly, the equilibrium generalized assignment problem and the equilibrium constrained generalized assignment problem are proposed in Section 3. To solve the EGAP, a genetic algorithm is designed in Section 4. Finally, the designed GA is tested with some known benchmarks in Section 5. 2. Literature review.

In this paper an application of the Constructive Genetic Algorithm to the Generalised Assignment Problem (GAP) is presented, which uses a binary representation and an assignment heuristic which allocates items to knapsacks. We present in this paper an application of the Constructive Genetic Algorithm (CGA) to the Generalised Assignment Problem (GAP). The GAP can be described as a problem of ...

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A new algorithm for the generalised assignment problem is described in this paper. The algorithm is adapted from a genetic algorithm which has been successfully used on set covering problems, but instead of genetically improving a set of feasible solutions it tries to genetically restore feasibility to a set of near-optimal ones. Thus it may be regarded as operating in a dual sense to the more ...