提出新方法统一多目标QUBO尺度，让不同目标可公平比较
Standardization of Multi-Objective QUBOs
- 用方差精确归一化每个目标，使其都具备单位方差
- 在等权重下实现更均衡的优化结果，提升解的质量
- 适合需要自动平衡多目标的科研与工程应用
多目标二次无约束二值优化（QUBO）问题广泛存在于多个领域。其核心挑战在于各目标量级差异大，导致加权融合时难以合理设定权重。本文提出一种新方法，通过精确计算每个QUBO目标的方差，将其缩放至单位方差，使所有目标处于同一量纲。这使得在等权重标量化时能获得更均衡的解，同时有助于权重搜索或选择。我们在多种多目标优化问题上进行了实证评估，结果表明该方法显著降低了人工调参难度，且在缺乏可靠高效解法的情况下表现突出。
原文摘要 · Abstract (English)
Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially operating on very different scales. This imbalance introduces complications such as the selection of appropriate weights when scalarizing multiple objectives into a single objective function. In this paper, we propose a novel technique for scaling QUBO objectives that uses an exact computation of the variance of each individual QUBO objective. By scaling each objective to have unit variance, we align all objectives onto a common scale, thereby allowing for more balanced solutions to be found when scalarizing the objectives with equal weights, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multi-objective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome, and reliable, efficient solutions are scarce.
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