The problem of optimal sizing and investment timing for a portfolio of gas-fired and photovoltaic (PV) generation is presented and solved using an optimization- classification technique. It is assumed that the demand, the prices of natural gas, and PV technology are stochastic processes. Our methodology takes advantage of decomposing the problem into two sub-problems. First, the optimal sizing problem is solved using dynamic programming and most likely solutions are identified as clusters. Then, the Investment time problem is formulated as a Real Option for each cluster to determine optimal timing. Although the two-step optimization approach can successfully close the loop between operational dynamics and investment decisions, we are also interested in discovering patterns in a multidimensional space of input parameters that make a certain combination of assets optimal among dozens of discrete choices. On that note, by applying Recursive Partitioning algorithm, decision trees are developed to estimate the structure of solutions rendered from optimization models by a rule-based system. Despite the high level of accuracy, the initial model is biased in favor of highly frequent clusters, and discards the optimal clusters resulted from extreme market behaviors. Value at Risk (VaR) is employed as a risk measure to demonstrate the enhancement risk performance. Finally, in order to investigate the robustness of the results, we conduct extensive sensitivity analysis over different parameter settings. The proposed model can be thought of as a statistically optimal summarizer of optimization models that enables decision makers to have an insight into optimal investment strategies according to characteristics of the building and the long-term energy market outlook.

提出并利用优化分类技术解决了燃气和光伏（PV）发电组合的最佳规模和投资时机问题。假定需求，天然气价格和光伏技术是随机过程。我们的方法论利用将问题分解为两个子问题的优势。首先，使用动态规划解决了最佳规模问题，并将最有可能的解决方案识别为集群。然后，将投资时间问题公式化为每个集群的实物期权，以确定最佳时机。尽管两步优化方法可以成功地关闭运营动态和投资决策之间的循环，我们也有兴趣在输入参数的多维空间中发现模式，这些模式可使资产的特定组合在数十个离散选择中达到最佳。关于这一点，通过应用递归分区算法，开发了决策树以估计基于规则的系统从优化模型提供的解决方案的结构。尽管准确性很高，但初始模型偏向于高度频繁的集群，并丢弃了极端市场行为导致的最优集群。风险价值（VaR）被用作一种风险度量，以证明增强的风险绩效。最后，为了调查结果的稳健性，我们对不同的参数设置进行了广泛的灵敏度分析。