Standardization of Multi-Objective QUBOs
This addresses a fundamental scaling issue in multi-objective optimization for domains using QUBOs, though it is incremental as it builds on existing scalarization methods.
The paper tackles the challenge of balancing multiple objectives with different scales in multi-objective QUBO problems by proposing a technique that scales each objective to unit variance using exact variance computation, resulting in more balanced solutions with equal weights and improved weight selection.
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.