Multiobjective variational quantum optimization for constrained problems: an application to Cash Handling

Abstract Combinatorial optimization problems are ubiquitous in industry. In addition to finding a solution with minimum cost, of high relevance involve number constraints that the must satisfy. Variational quantum algorithms have emerged as promising candidates for solving these noisy intermediate-scale stage. However, often complex enough make their efficient mapping hardware difficult or even infeasible. An alternative standard approach is transform problem include penalty terms, but this method involves additional hyperparameters and does not ensure satisfied due existence local minima. paper, we introduce new combinatorial challenging using variational algorithms. We propose Multi-Objective Constrained Optimizer (MOVCO) classically update parameters by multiobjective performed genetic algorithm. This allows algorithm progressively sample only states within in-constraints space, while optimizing energy states. test our proposal on real-world great finance: Cash Handling problem. novel mathematical formulation problem, compare performance MOVCO versus based optimization. Our empirical results show significant improvement terms cost achieved solutions, especially avoidance minima do satisfy any mandatory constraints.