Summary: We consider the multi-mode resource-constrained project scheduling problem (MRCPSP), where a task has different execution modes characterized by different resource requirements. Due to the nonrenewable resources and the multiple modes, this problem is NP-hard; therefore, we implement an evolutionary algorithm looking for a feasible solution minimizing the makespan.
In this paper, we propose and investigate two new ideas. On the one hand, we transform the problem of single objective MRCPSP to bi-objective one to cope with the potential violation of nonrenewable resource constraints. Relaxing the latter constraints allows to visit a larger solution set and thus to simplify the evolutionary operators. On the other hand, we build the fitness function not on a priori grid of the bi-objective space, but on an adaptive one relying on clustering techniques. This proposed idea aims at more relevant fitness values. We show that a clustering-based fitness function can be an appealing feature in multi-objective evolutionary algorithms since it may promote diversity and avoid premature convergence of the algorithms. Clustering heuristics require certainly computation time, but they are still competitive with respect to classical niche formation multi-objective genetic algorithm.