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.

本文提出了一种具有恶化效应和财务约束的多技能资源受限项目调度问题（MSRCPSP）的双目标数学公式。目标是同时优化项目的制造周期和成本。由于该模型具有较高的NP硬度，因此开发了基于Pareto的Gray Wolf Optimizer（P-GWO）算法来解决该问题。已为P-GWO设计了一种基于加权和方法（WSM）的新程序，以对种群的解决方案进行排名，以便找到alpha，beta，delta和omega狼。P-GWO还使用基于数据包络分析（DEA）的新过程来保留最有效的新发现解决方案，并更新非主导解决方案的存档。除了，针对该问题，提出了一种基于斐波那契数列特征的基于多目标斐波那契的算法（MOFA）。MOFA利用一种新颖的邻域运算符来生成每次迭代所需的尽可能多的可行解。对于MOFA，还开发了用于查找每次迭代的最佳解决方案，精英主义和更新非主导解决方案存档的新程序。为了评估所提出的算法，我们进行了一系列数值实验，并将我们提出的方法的输出与非主导排序遗传算法II（NSGA-II），多目标帝国主义竞争算法（MOICA）和Multi多种性能指标方面的目标果蝇优化算法（MOFFOA）。此外，研究了一家天然气处理公司的实际大修项目，以证明该模型的实用性。所有数值实验的结果表明，就大多数指标而言，P-GWO的性能优于其他算法。输出表明MOFA可以在合理的计算时间内生成高质量的解决方案。