Metaheuristics for the bi-objective resource-constrained project scheduling problem with time-dependent resource costs: An experimental comparison

The bi-objective resource-constrained project scheduling problem with time-dependent resource costs was recently introduced and consists of scheduling a set of activities subject to precedence and resource constraints, minimizing the makespan and the total cost for resource usage. Precisely, costs are determined by the resource being considered together with the time it is used. Although this generalization of the traditional resource-constrained project scheduling problem is rather recent, it has garnered substantial interest as it succeeds in meeting a wide range of real-world demands. In such a multi-objective context, solving the aforementioned problem poses a challenge, as both objectives conflict with each other, giving rise to a set of trade-off optimal solutions, commonly known as the Pareto front (PF). Given that many medium or large-sized instances of this problem cannot be solved by exact methods, the development of metaheuristics to find the PF is necessary. So far, only one metaheuristic had been developed to solve this problem. In this work we have implemented six additional multi-objective evolutionary algorithms (MOEAs), representing different paradigms, and subsequently, an exhaustive comparison of their performance has been carried out. In particular, all the compared MOEAs share the same encoding and main operators, focusing the comparison on the general algorithm framework rather than specific versions. Metaheuristic algorithms typically yield an approximation of the optimal PF, prompting the question of how to assess the quality of the obtained approximations. To this end, a computational and statistically supported study is conducted, choosing a benchmark of bi-criteria resource-constrained project scheduling problems and applying a set of performance measures to the solution sets obtained by each methodology. The results show that there are significant differences among the performance of the metaheuristics evaluated.