Standardization of Multi-Objective QUBOs

2025-04-16

AI Summary

Multi-objective Quadratic Unconstrained Binary Optimization (QUBO) problems often suffer from imbalanced scalarization due to dimensional disparities among objectives, resulting in high sensitivity to weight selection and poor robustness. To address this, we propose a unit-variance standardization method based on exact analytical variance computation—the first such standardization mechanism integrated into multi-objective QUBO optimization. It enables equal-weight fusion of objectives on a common scale without manual weight tuning. Our framework encompasses QUBO modeling, closed-form variance derivation of objective functions, standardized preprocessing, and scalarization (supporting both equal-weight and weighted variants). Experiments across multiple benchmark multi-objective QUBO instances demonstrate that the proposed method significantly reduces weight sensitivity, improves Pareto front quality, and enhances solution balance and solver stability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Balancing multiple objectives in QUBO problems
• Standardizing scales of different QUBO objectives
• Improving weight selection in multi-objective scalarization

Innovation

• Exact variance computation for QUBO objectives
• Unit variance scaling to align objectives
• Empirical validation on multi-objective problems