Population-based evolutionary algorithms are often considered when approaching computationally expensive black-box optimization problems. They employ a selection mechanism to choose the best solutions from a given population after comparing their objective values, which are then used to generate the next population. This iterative process explores the solution space efficiently, leading to improved solutions over time. However, these algorithms require a large number of evaluations to provide a quality solution, which might be computationally expensive when the evaluation cost is high. In some cases, it is possible to replace the original objective function with a less accurate approximation of lower cost. This introduces a trade-off between the evaluation cost and its accuracy. In this paper, we propose a technique capable of choosing an appropriate approximate function cost during the execution of the optimization algorithm. The proposal finds the minimum evaluation cost at which the solutions are still properly ranked, and consequently, more evaluations can be computed in the same amount of time with minimal accuracy loss. An experimental section on four very different problems reveals that the proposed approach can reach the same objective value in less than half of the time in certain cases.

翻译：基于种群的进化算法常被用于处理计算代价高昂的黑箱优化问题。这类算法通过比较目标值，从给定种群中选择最优解，进而生成下一代种群。这一迭代过程高效地探索解空间，并随时间推移逐步提升解的质量。然而，此类算法需要大量评估才能获得高质量解，当评估代价较高时，计算成本可能十分高昂。在某些情况下，可以用精度较低但成本更低的近似函数替代原始目标函数，这便引入了评估代价与精度之间的权衡。本文提出了一种技术，能够在优化算法执行过程中合理选择近似函数的代价。该技术可找到保证解排序正确的最小评估代价，从而在相同时间内完成更多评估，且精度损失最小。针对四个截然不同问题的实验结果表明，在特定情形下，所提方法可在不到一半的时间内达到相同目标值。