LAUSR

This paper presents a bi-objective mathematical formulation for the multi-skill resource-constrained project scheduling problem (MSRCPSP) with the deterioration effect and financial constraints. The objectives are to optimize the makespan and cost of project, simultaneously. Due to the high NP-hardness of the proposed model, a Pareto-based Grey Wolf Optimizer (P-GWO) algorithm has been developed to solve the problem. A new procedure based on the Weighted Sum Method (WSM) has been designed for the P-GWO to rank the solutions of population in order to find the alpha, beta, delta, and omega wolves. The P-GWO also uses a new procedure based on the Data Envelopment Analysis (DEA) to keep the most efficient newly found solutions and update the archive of non-dominated solutions. Besides, a Multi-Objective Fibonacci-based Algorithm (MOFA) based on the characteristics of the Fibonacci sequence has been proposed to solve the problem. The MOFA utilizes a novel neighborhood operator to generate as many feasible solutions as required in each iteration. For the MOFA, new procedures for finding the best solution of each iteration, elitism and updating archive of non-dominated solutions have been developed as well. To evaluate the proposed algorithms, a series of numerical experiments have been conducted and the outputs of our proposed methods were compared with the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Imperialist Competitive Algorithm (MOICA), and Multi-Objective Fruit-Fly Optimization Algorithm (MOFFOA) in terms of several performance measures. Moreover, a real-life overhaul project in a gas treating company has been studied to demonstrate the practicality of the proposed model. The results of all numerical experiments demonstrate that the P-GWO outperforms other algorithms in terms of most of the metrics. The outputs imply that the MOFA can generate high quality solutions within a reasonable computation time.