A financial portfolio contains assets that offer a return with a certain level of risk. To maximise returns or minimise risk, the portfolio must be optimised - the ideal combination of optimal quantities of assets must be found. The number of possible combinations is vast. Furthermore, to make the problem realistic, constraints can be imposed on the number of assets held in the portfolio and the maximum proportion of the portfolio that can be allocated to an asset. This problem is unsolvable using quadratic programming, which means that the optimal solution cannot be calculated. A group of algorithms, called metaheuristics, can find near-optimal solutions in a practical computing time. These algorithms have been successfully used in constrained portfolio optimisation. However, in past studies the computation time of metaheuristics is not limited, which means that the results differ in both quality and computation time, and cannot be easily compared. This study proposes a different way of testing metaheuristics, limiting their computation time to a certain duration, yielding results that differ only in quality. Given that in some use cases the priority is the quality of the solution and in others the speed, time limits of 1, 5 and 25 seconds were tested. Three metaheuristics - simulated annealing, tabu search, and genetic algorithm - were evaluated on five sets of historical market data with different numbers of assets. Although the metaheuristics could not find a competitive solution in 1 second, simulated annealing found a near-optimal solution in 5 seconds in all but one dataset. The lowest quality solutions were obtained by genetic algorithm.

翻译：金融投资组合包含具有特定风险水平的资产，以获取回报。为最大化收益或最小化风险，必须对投资组合进行优化——需找到资产最优数量的理想组合。可能的组合数量极为庞大。此外，为使问题更贴近实际，可对投资组合中持有的资产数量，以及单个资产在投资组合中的最大配置比例施加约束。此问题无法通过二次规划求解，因此无法计算最优解。一类称为元启发式算法的算法能在实际计算时间内找到近优解。这些算法已成功应用于带约束的投资组合优化。然而，过往研究中元启发式算法的计算时间不受限制，导致结果在质量和计算时间上存在差异，且难以直接比较。本研究提出一种不同的元启发式算法测试方法，将其计算时间限制为固定时长，从而仅保留结果的质量差异。鉴于某些应用场景优先考虑解的质量，而另一些则更注重速度，本研究测试了1秒、5秒和25秒的时间限制。三种元启发式算法——模拟退火、禁忌搜索和遗传算法——在五组包含不同数量资产的历史市场数据上进行评估。尽管元启发式算法在1秒内无法找到具有竞争力的解，但模拟退火在除一个数据集外的所有案例中均能在5秒内找到近优解。遗传算法所得到的解质量最低。