A Multi-Objective Water Cycle Algorithm for the BI-Objective Multi-Mode Project Resource Renting Problem

. A resource renting problem is a project scheduling problem in which the required resources should be rented, and the goal is to find a schedule and resource renting plan such that the total cost of the resources minimises. Traditionally, the model of a resource renting problem contains single-mode activities and a single objective function. This research aims to present a new mathematical model for a bi-objective multi-mode resource renting problem. The objectives are to minimise the project makespan and also the total cost of resources, including the time-independent resource procurement costs and time-dependent resource renting costs, simultaneously. A novel evolutionary algorithm, namely the Multi-Objective Water Cycle Algorithm (MOWCA), is employed to solve this NP-hard problem. In order to evaluate the proposed algorithm, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) is applied, too. A set of instances is selected from the digital library of project scheduling problems to analyse the performances of evolutionary algorithms. The results of the experimentation are quite satisfactory.