Non-dominated Sorting Genetic Algorithm-II to solve bi-objective multi-mode resource-constrained project scheduling problem

In general, the multi-mode resource-constrained project scheduling problem (MRCPSP) is considered as mono-objective problem which aims at finishing the project as soon as possible under resource constraints. Nevertheless, the MRCPSP is multi-objective by nature and the omission of this aspect in its resolution may biases the reality; so we think extend the study of this problem to the bi-objective case. In our knowledge, we are the first to deal with the minimization of both makespan and non-renewable resource cost. The resolution of this Bi-objective MR-CPSP (BMRCPSP) gives more alternatives to the decision maker. In this work, we adapt the Non-dominated Sorting Genetic Algorithm-II technique (NSGA-II) to the BMRCPSP. Results obtained based on expensive experimentations, prove that the NSGA-II algorithm succeeds in solving a bi-objective combinatorial problem.