In this paper we present a heuristic approach to two-stage mixed-integer linear stochastic programming models with continuous second stage variables. A common solution approach for these models is Benders decomposition, in which a sequence of (possibly infeasible) solutions is generated, until an optimal solution is eventually found and the method terminates. As convergence may require a large amount of computing time for hard instances, the method may be unsatisfactory from a heuristic point of view. Proximity search is a recently-proposed heuristic paradigm in which the problem at hand is modified and iteratively solved with the aim of producing a sequence of improving feasible solutions. As such, proximity search and Benders decomposition naturally complement each other, in particular when the emphasis is on seeking high-quality, but not necessarily optimal, solutions. In this paper, we investigate the use of proximity search as a tactical tool to drive Benders decomposition, and computationally evaluate its performance as a heuristic on instances of different stochastic programming problems.
Proximity Benders: a decomposition heuristic for stochastic programs / Boland, Natashia; Fischetti, Matteo; Monaci, Michele; Savelsbergh, Martin. - In: JOURNAL OF HEURISTICS. - ISSN 1381-1231. - STAMPA. - 22:2(2016), pp. 181-198. [10.1007/s10732-015-9306-1]
Proximity Benders: a decomposition heuristic for stochastic programs
MONACI, MICHELE;
2016
Abstract
In this paper we present a heuristic approach to two-stage mixed-integer linear stochastic programming models with continuous second stage variables. A common solution approach for these models is Benders decomposition, in which a sequence of (possibly infeasible) solutions is generated, until an optimal solution is eventually found and the method terminates. As convergence may require a large amount of computing time for hard instances, the method may be unsatisfactory from a heuristic point of view. Proximity search is a recently-proposed heuristic paradigm in which the problem at hand is modified and iteratively solved with the aim of producing a sequence of improving feasible solutions. As such, proximity search and Benders decomposition naturally complement each other, in particular when the emphasis is on seeking high-quality, but not necessarily optimal, solutions. In this paper, we investigate the use of proximity search as a tactical tool to drive Benders decomposition, and computationally evaluate its performance as a heuristic on instances of different stochastic programming problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.