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A Path Relinking Algorithm for the Generalized Assignment Problem

  • Laurent Alfandari
  • Agnès Plateau
  • Pierre Tolla
Chapter
Part of the Applied Optimization book series (APOP, volume 86)

Abstract

The Generalized Assignment Problem (GAP) consists in finding a maximum-profit assignment of tasks to agents with capacity constraints. In this paper, a path relinking heuristic is proposed for the GAP. The main feature of our path relinking is that both feasible and infeasible solutions are inserted in the reference set of elite solutions, trade-off between feasibility and infeasibility being ruled through a penalty coefficient for infeasibility. Since exploration of the solution space is very sensitive to this penalty coefficient, the coefficient is dynamically updated at each round of combinations so that a balance is kept between feasible and infeasible solutions in the reference set. Numerical experiments reported on classical testbed instances of the OR-library show that the algorithm compares favorably to several other methods in the literature. In particular, more than 95% of the instances in the test-file were solved to optimality with short computation time.

Keywords

Combinatorial optimization Generalized assignment Metaheuristics Path relinking. 

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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Laurent Alfandari
    • 1
  • Agnès Plateau
    • 2
  • Pierre Tolla
    • 3
  1. 1.ESSECCergy-Pontoise CedexFrance
  2. 2.CEDRICCNAMParisFrance
  3. 3.LAMSADEUniversité Paris IX-DauphineParis Cedex 16France

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