Multi-objective metaheuristic algorithms for the resource-constrained project scheduling problem with precedence relations

This study addresses the resource-constrained project scheduling problem with precedence relations, and aims at minimizing two criteria: the makespan and the total weighted start time of the activities. To solve the problem, five multi-objective metaheuristic algorithms are analyzed, based on Multi-objective GRASP (MOG), Multi-objective Variable Neighborhood Search (MOVNS) and Pareto Iterated Local Search (PILS) methods. The proposed algorithms use strategies based on the concept of Pareto Dominance to search for solutions and determine the set of non-dominated solutions. The solutions obtained by the algorithms, from a set of instances adapted from the literature, are compared using four multi-objective performance measures: distance metrics, hypervolume indicator, epsilon metric and error ratio. The computational tests have indicated an algorithm based on MOVNS as the most efficient one, compared to the distance metrics; also, a combined feature of MOG and MOVNS appears to be superior compared to the hypervolume and epsilon metrics and one based on PILS compared to the error ratio. Statistical experiments have shown a significant difference between some proposed algorithms compared to the distance metrics, epsilon metric and error ratio. However, significant difference between the proposed algorithms with respect to hypervolume indicator was not observed.