Many real life optimization problems do not have accurate estimates of the problem parameters at the optimization phase. For this reason, the min-max regret criteria are widely used to obtain robust solutions. In this paper we consider the generalized assignment problem (GAP) with min-max regret criterion under interval costs. We show that the decision version of this problem is Σp2-complete. We present two heuristic methods: a fixed-scenario approach and a dual substitution algorithm. For the fixed-scenario approach, we show that solving the classical GAP under a median-cost scenario leads to a solution of the min-max regret GAP whose objective function value is within twice the optimal value. We also propose exact algorithms, including a Benders’ decomposition approach and branch-and-cut methods which incorporate various methodologies, including Lagrangian relaxation and variable fixing. The resulting Lagrangian-based branch-and-cut algorithm performs satisfactorily on benchmark instances.
W. Wu, M. Iori, S. Martello, M. Yagiura (2014). Algorithms for the min-max regret generalized assignment problem with interval data. New York : IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA [10.1109/IEEM.2014.7058735].
Algorithms for the min-max regret generalized assignment problem with interval data
MARTELLO, SILVANO;
2014
Abstract
Many real life optimization problems do not have accurate estimates of the problem parameters at the optimization phase. For this reason, the min-max regret criteria are widely used to obtain robust solutions. In this paper we consider the generalized assignment problem (GAP) with min-max regret criterion under interval costs. We show that the decision version of this problem is Σp2-complete. We present two heuristic methods: a fixed-scenario approach and a dual substitution algorithm. For the fixed-scenario approach, we show that solving the classical GAP under a median-cost scenario leads to a solution of the min-max regret GAP whose objective function value is within twice the optimal value. We also propose exact algorithms, including a Benders’ decomposition approach and branch-and-cut methods which incorporate various methodologies, including Lagrangian relaxation and variable fixing. The resulting Lagrangian-based branch-and-cut algorithm performs satisfactorily on benchmark instances.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.