# Standardization of Multi-Objective QUBOs

arXiv: https://arxiv.org/abs/2504.12419 · HTML: https://mlsanity.com/paper/2504.12419/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 16 Apr 2025.

## Builds on (most cited first, 9 of 9)

- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Smooth Tchebycheff Scalarization for Multi-Objective Optimization](https://mlsanity.com/paper/2402.19078/) (2024)
- [Feature Selection on Quantum Computers](https://mlsanity.com/paper/2203.13261/) (2022)
- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [A Study of Scalarisation Techniques for Multi-Objective QUBO Solving](https://mlsanity.com/paper/2210.11321/) (2022)
- [Solving Subset Sum Problems using Quantum Inspired Optimization Algorithms with Applications in Auditing and Financial Data Analysis](https://mlsanity.com/paper/2211.02653/) (2022)
- [Applying Ising Machines to Multi-objective QUBOs](https://mlsanity.com/paper/2305.11648/) (2023)
- [Multicriteria asset allocation in practice](https://mlsanity.com/paper/2103.10958/) (2021)
- [An Efficient Multi-objective Evolutionary Approach for Solving the Operation of Multi-Reservoir System Scheduling in Hydro-Power Plants](https://mlsanity.com/paper/2107.09718/) (2021)

## Abstract (arXiv)

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.