The problem of integrated project portfolio selection and scheduling (PPSS) is among the most important and highly pursed subjects in project management. In this study, a mathematical model and algorithm are designed specifically to assist decision makers decide which projects are to be chosen and when these projects are to be undertaken. More specifically, the PPSS problem is first formulated as a nonlinear multi-objective model with simultaneous consideration of benefit and risk factors. Due to the complexity and uncertainty involved in most real life situations, fuzzy numbers are incorporated into the model, which can provide decision makers with more flexibility. Then, an inverse modeling based multi-objective evolutionary algorithm using a Gaussian Process is presented to obtain the Pareto set. Finally, an illustrative example is used to demonstrate the high efficacy of the foregoing approach, which can provide decision makers with valuable insights into the PPSS process. The proposed algorithm is found to be more effective compared with two other popular algorithms.

中文翻译：

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模糊环境下的项目组合选择与调度

集成项目组合选择和进度安排（PPSS）问题是项目管理中最重要和高度追求的主题之一。在这项研究中，专门设计了一个数学模型和算法来帮助决策者决定要选择哪些项目以及何时进行这些项目。更具体地说，首先将PPSS问题公式化为非线性多目标模型，同时考虑利益和风险因素。由于大多数现实情况中都涉及复杂性和不确定性，因此将模糊数字合并到模型中，可以为决策者提供更大的灵活性。然后，提出了一种使用高斯过程的基于逆建模的多目标进化算法来获得帕累托集。最后，一个说明性的例子用来证明上述方法的高效率，可以为决策者提供对PPSS流程的宝贵见解。发现该算法比其他两种流行算法更有效。