The key challenge of expensive optimization problems (EOP) is that evaluating the true fitness value of the solution is computationally expensive. A common method to deal with this issue is to seek for a less expensive surrogate model to replace the original expensive objective function. However, this method also brings in model approximation error. To efficiently solve the EOP, a novel scale-adaptive fitness evaluation (SAFE) method is proposed in this article to directly evaluate the true fitness value of the solution on the original objective function. To reduce the computational cost, the SAFE method uses a set of evaluation methods (EM) with different accuracy scales to cooperatively complete the fitness evaluation process. The basic idea is to adopt the low-accuracy scale EM to fast locate promising regions and utilize the high-accuracy scale EM to refine the solution accuracy. To this aim, two EM switch strategies are proposed in the SAFE method to adaptively control the multiple EMs according to different evolutionary stages and search requirements. Moreover, a neighbor best-based evaluation (NBE) strategy is also put forward to evaluate the solution according to its nearest high-quality evaluated solution, which can further reduce computational cost. Extensive experiments are carried out on the case study of crowdshipping scheduling problem in the smart city to verify the effectiveness and efficiency of the proposed SAFE method, and to investigate the effects of the two EM switch strategies and the NBE strategy. Experimental results show that the proposed SAFE method achieves better solution quality than some baseline and state-of-the-art algorithms, indicating an efficient method for solving EOP with a better balance between solution accuracy and computational cost.

中文翻译：

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SAFE：针对昂贵优化问题的尺度自适应适应度评估方法

代价高昂的优化问题 (EOP) 的主要挑战是评估解决方案的真实适应度值在计算上是昂贵的。处理这个问题的一个常用方法是寻找一个更便宜的代理模型来代替原来昂贵的目标函数。但是，这种方法也带来了模型逼近误差。为了有效地解决EOP，本文提出了一种新的尺度自适应适应度评估（SAFE）方法，以直接评估解在原始目标函数上的真实适应度值。为了降低计算成本，SAFE 方法使用一组不同精度尺度的评估方法（EM）来协同完成适应度评估过程。基本思想是采用低精度尺度EM快速定位有希望的区域，并利用高精度尺度EM来细化求解精度。为此，在SAFE方法中提出了两种EM切换策略，以根据不同的进化阶段和搜索需求自适应地控制多个EM。此外，还提出了一种基于邻居最佳的评估（NBE）策略，根据其最近的高质量评估解决方案来评估解决方案，这可以进一步降低计算成本。对智慧城市中众包调度问题的案例研究进行了大量实验，以验证所提出的 SAFE 方法的有效性和效率，并研究两种 EM 切换策略和 NBE 策略的效果。