Quantum-Enhanced Multi-Objective Optimization

Multi-objective combinatorial optimization (MOCO) requires finding a set of Pareto-optimal solutions where no objective can be improved without degrading another. While Quantum Approximate Optimization Algorithm (QAOA) has shown promise for single-objective problems, existing multi-objective quantum approaches often rely on fixed scalarization and single-pass sampling. This paper asks whether a multi-round, feedback-driven quantum protocol can better explore the Pareto front without increasing the total quantum sampling budget.

The authors propose QEMOO (Quantum-Enhanced Multi-Objective Optimization), a modular framework that introduces three key innovations:

1. Multi-round feedback: A protocol that redistributes a fixed total shot budget across multiple rounds, allowing the algorithm to learn from intermediate results.
2. Warm-started QAOA: Instead of starting from a uniform superposition, subsequent rounds use elite solutions discovered in previous rounds to bias the initial quantum state.
3. Adaptive scalarization: A set of methods (including PBI-inspired updates) that dynamically adjust the search direction in objective space based on previously found non-dominated solutions.

The framework is tested against a single-pass weighted-sum QAOA baseline across three benchmark stages, including scenarios with strong objective conflicts, using hypervolume (HV) as the primary metric for Pareto-front quality.

QEMOO consistently outperforms the single-pass weighted-sum QAOA baseline under matched shot budgets. The multi-round feedback loop allows the algorithm to refine its search, effectively "zooming in" on promising regions of the objective space. The PBI-inspired adaptive scheme proved particularly effective in strongly conflicting benchmark regimes, where fixed scalarization methods often fail to capture unsupported Pareto-optimal regions. The authors also demonstrate that the quantum sampler provides a genuine advantage beyond the classical feedback logic alone, as evidenced by comparisons with random-sampling controls.