In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ one of the most effective and recently developed criterion space search algorithms, the so-called KSA, during our study. This algorithm computes all nondominated points of a problem with p objectives by searching on a projected criterion space, i.e., a \((p-1)\)-dimensional criterion apace. We present an effective and fast learning approach to identify on which projected space the KSA should work. We also present several generic features/variables that can be used in machine learning techniques for identifying the best projected space. Finally, we present an effective bi-objective optimization-based heuristic for selecting the subset of the features to overcome the issue of overfitting in learning. Through an extensive computational study over 2000 instances of tri-objective knapsack and assignment problems, we demonstrate that an improvement of up to 18% in time can be achieved by the proposed learning method compared to a random selection of the projected space. To show that the performance of our algorithm is not limited to instances of knapsack and assignment problems with three objective functions, we also report similar performance results when the proposed learning approach is used for solving random binary integer program instances with four objective functions.

在本文中，我们研究了使用机器学习技术提高多目标优化解决方案性能的可能性。具体来说，我们专注于多目标二元线性程序，并在我们的研究过程中采用了最有效和最近开发的标准空间搜索算法之一，即所谓的 KSA。该算法通过在投影准则空间（即\((p-1)\)维准则空间）上搜索来计算具有p个目标的问题的所有非支配点。我们提出了一种有效且快速的学习方法来确定 KSA 应该在哪个投影空间上工作。我们还提出了几个通用特征/变量，可用于机器学习技术来识别最佳投影空间。最后，我们提出了一种有效的基于双目标优化的启发式方法，用于选择特征子集，以克服学习中的过度拟合问题。通过对 2000 多个三目标背包和分配问题实例的广泛计算研究，我们证明，与随机选择投影空间相比，所提出的学习方法可以在时间上提高高达 18%。为了表明我们的算法的性能不限于具有三个目标函数的背包实例和分配问题，当所提出的学习方法用于求解具有四个目标函数的随机二进制整数程序实例时，我们还报告了类似的性能结果。