Annals of Operations Research 131, 305–324, 2004  2004 Kluwer Academic Publishers. Manufactured in The Netherlands. A Population-Based Approach to the Resource-Constrained Project Scheduling Problem ∗ VICENTE VALLS and FRANCISCO BALLESTÍN {Vicente.Valls;Francisco.Ballestin}@uv.es Dpto. de Estadística e Investigación Operativa, Facultad de Matemáticas, Universitat de Valencia, Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain SACRAMENTO QUINTANILLA Maria.Quintanilla@uv.es Dpto. de Economía Financiera y Matemática, Facultad de Económicas y Empresariales, Universitat de Valencia, Avda. de los Naranjos, s/n, Edificio Departamental Oriental, Valencia, Spain Abstract. We present a population-based approach to the RCPSP. The procedure has two phases. The first phase handles the initial construction of a population of schedules and these are then evolved until high quality solutions are obtained. The evolution of the population is driven by the alternative application of an efficient improving procedure for locally improving the use of resources, and a mechanism for combining schedules that blends scatter search and path relinking characteristics. The objective of the second phase is to explore in depth those vicinities near the high quality schedules. Computational experiments on the standard j120 set, generated using ProGen, show that our algorithm produces higher quality solutions than state-of-the-art heuristics for the RCPSP in an average time of less than five seconds. Keywords: population-based algorithms, scatter search, path relinking, hybrid heuristics, resource con- strained project scheduling 1. Introduction The resource-constrained project-scheduling problem (RCPSP) may be stated as fol- lows. A project consists of a set of n activities numbered 1 to n, where each activity has to be processed without interruption to complete the project. The dummy activities 1 and n represent the beginning and end of the project. The duration of an activity j is de- noted by d j where d 1 = d n = 0. There are K renewable resource types. The availability of each resource type k in each time period is R k units, k = 1,...,K . Each activity j requires r jk units of resource k during each period of its duration where r 1k = r nk = 0, k = 1,...,K . All parameters are assumed to be non-negative integer valued. There are precedence relations of the finish-start type with a zero parameter value (i.e., FS = 0) defined between the activities. In other words, activity i precedes activity j – if j cannot start until i has been completed. The structure of a project can be represented by an activity-on-node network G = (V , A), where V is the set of activities and A is the set of precedence relationships. S j (P j ) is the set of successors (predecessors) of activity j . It ∗ This research was partially supported by the CICYT under contract TAP99-1123 and by the Generalitat Valenciana under contract FP 198-CB-12-303.