Opening range breakout (ORB) is a well-known trading strategy in which predetermined price thresholds are used to characterize price movements. However, some researchers have noted that ORB does not make full use of market characteristics and fails to define a cogent closing strategy. Several modified ORB strategies have been optimized using grid-wise algorithms; however, those methods operate within a discrete limited solution space. In this study, we use the particle swarm optimization algorithm to create a scalable and continuous optimization algorithm, referred to as PORB. We also adopt the Pareto optimal in the creation of a multi-objective optimization algorithm, referred to as MPORB. Experiment results demonstrate that PORB significantly outperformed the benchmark strategies (GAORB and the original ORB) in trading performance and time efficiency. A PORB with stop-loss closing strategy slightly improves profitability and greatly reduces the risk of drawdown. The performance of MPORB is similar to that of PORB; however, in some cases it falls somewhat short. Overall, the scalable and continuous PORB strategy proposed in this study is shown to overcome the limitations of previous solutions. The implementation of Pareto multi-objective optimization in PORB is shown to enhance trading performance without increasing time complexity.

开放范围突破（ORB）是一种众所周知的交易策略，其中使用预定的价格阈值来表征价格走势。但是，一些研究人员指出，ORB并未充分利用市场特征，也未能定义切实可行的关闭策略。几种修改的ORB策略已经使用网格算法进行了优化。但是，这些方法在离散的有限解决方案空间内运行。在这项研究中，我们使用粒子群优化算法来创建可扩展的连续优化算法，称为PORB。在创建称为MPORB的多目标优化算法时，我们还采用了帕累托最优。实验结果表明，PORB在交易性能和时间效率上明显优于基准策略（GAORB和原始ORB）。具有止损平仓策略的PORB略微提高了盈利能力，并大大降低了提款的风险。MPORB的性能类似于PORB；但是，在某些情况下，它有些不足。总体而言，本研究中提出的可扩展且连续的PORB策略可克服先前解决方案的局限性。事实证明，在PORB中实施Pareto多目标优化可以提高交易性能，而不会增加时间复杂度。在某些情况下，它有些不足。总体而言，本研究中提出的可扩展且连续的PORB策略可克服先前解决方案的局限性。结果表明，在PORB中实施Pareto多目标优化可以提高交易性能，而不会增加时间复杂度。在某些情况下，它有些不足。总体而言，本研究中提出的可扩展且连续的PORB策略可克服先前解决方案的局限性。事实证明，在PORB中实施Pareto多目标优化可以提高交易性能，而不会增加时间复杂度。