Standardization of Multi-Objective QUBOs

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 to balance the different objectives. 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. This allows for more balanced solutions to be found when combining these objectives directly, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multiobjective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome; and reliable, efficient solutions are scarce.