Abstract In Resource Constrained Project Scheduling Problems (RCPSPs), it is usually assumed that the activity durations are known and integers. This assumption helps to conveniently develop a standard mathematical model, using discrete time steps. However, in reality, activity durations may not only be integer, and they may not be known with certainty at the time of project planning. The consideration of real-valued activity durations would increase the complexity in modelling of RCPSPs. In this paper, we consider that activity duration can be either integer or real-valued or both, and they are uncertain. To solve the optimization problem with uncertainty, scenario-based approaches are a popular choice. However, such a solution method is computationally very expensive. Therefore, in this research, we propose a simulation assisted evolutionary framework, that consists of two multi-operator based EAs and two heuristics to deal with the optimization process, and a simulation approach to deal with the uncertainty components. In the simulation, a range of problem instances is evaluated that are generated based on uncertain durations. The framework also proposes a new strategy to reduce the number of simulation runs. In the approach, the solution representation is different from the one required in the mathematical programming approach for RCPSP, and it does not require any discretization of the time periods. More than 1600 test problems, including some industrial problems, with up to 120 activities, have been solved using this proposed approach and the results have been compared with a set of state-of-the-art algorithms. The results obtained by the proposed approach were found to be of acceptable quality with a significant reduction of computational time.

中文翻译：

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具有不确定变化的资源受限项目调度的进化方法

摘要 在资源约束项目调度问题（RCPSPs）中，通常假设活动持续时间是已知的和整数。该假设有助于使用离散时间步长方便地开发标准数学模型。然而，实际上，活动工期可能不仅是整数，而且在项目规划时可能无法确定。考虑实值活动持续时间会增加 RCPSP 建模的复杂性。在本文中，我们认为活动持续时间可以是整数或实值或两者兼而有之，它们是不确定的。为了解决具有不确定性的优化问题，基于场景的方法是一种流行的选择。然而，这种求解方法在计算上非常昂贵。因此，在本研究中，我们提出了一个模拟辅助进化框架，它由两个基于多算子的 EA 和两个用于处理优化过程的启发式算法组成，以及一种用于处理不确定性分量的模拟方法。在模拟中，评估了一系列基于不确定持续时间生成的问题实例。该框架还提出了一种减少模拟运行次数的新策略。在该方法中，解表示不同于 RCPSP 数学规划方法中所需的解表示，并且不需要对时间段进行任何离散化。使用这种建议的方法已经解决了 1600 多个测试问题，包括一些工业问题，多达 120 个活动，并将结果与​​一组最先进的算法进行了比较。