Annals of Operations Research 131, 237–257, 2004  2004 Kluwer Academic Publishers. Manufactured in The Netherlands. LSSPER: Solving the Resource-Constrained Project Scheduling Problem with Large Neighbourhood Search MIREILLE PALPANT, CHRISTIAN ARTIGUES and PHILIPPE MICHELON Laboratoire d’Informatique d’Avignon, 339, chemin des meinajariès, Agroparc, BP 1228, 84911 Avignon Cedex 9, France Abstract. This paper presents the Local Search with SubProblem Exact Resolution (LSSPER) method based on large neighbourhood search for solving the resource-constrained project scheduling problem (RCPSP). At each step of the method, a subpart of the current solution is fixed while the other part de- fines a subproblem solved externally by a heuristic or an exact solution approach (using either constraint programming techniques or mathematical programming techniques). Hence, the method can be seen as a hybrid scheme. The key point of the method deals with the choice of the subproblem to be optimized. In this paper, we investigate the application of the method to the RCPSP. Several strategies for generat- ing the subproblem are proposed. In order to evaluate these strategies, and, also, to compare the whole method with current state-of-the-art heuristics, extensive numerical experiments have been performed. The proposed method appears to be very efficient. Keywords: resource-constrained project scheduling problem, large neighbourhood search 1. Introduction The problem of searching a given neighbourhood of an NP-hard problem can be itself defined as a combinatorial optimization problem. In this paper we consider the neigh- bourhood of a solution to an n variables NP-hard problem P as the set of solutions to a p variables subproblem obtained directly from P by fixing n − p variables to their current value. With no restrictive assumption on p, finding the best neighbour is likely to be itself an NP-hard problem and the number of neighbours is exponential in p. When p is small enough, an exhaustive enumeration of the neighbours can be performed but the so-defined neighbourhood is unlikely to contain interesting feasible solutions. In this paper we consider larger values of p, presumably defining a (very) large neighbourhood, and we search for the best neighbour with an implicit enumeration technique or a heuristic. Successful applications of large neighbourhood search (LNS) are available in the literature for various problems. For the quadratic assignment problem (QAP), the MI- MAUSA method designed by Mautor and Michelon (1997) builds at each iteration a re- duced QAP and solves it by branch and bound. For the vehicle routing problem (VRP), Shaw (1998), Gendreau, Pesant, and Rousseau (2002), and recently Bent and Henten- ryck (2001), consider the removal of several customer visits and re-insert them by using limited discrepancy search (LDS). The latter succeeds in improving best published so- lutions of standard VRP instances with time windows. In (Taillard and Voss, 2002),