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International Symposium on Computing and Networking Workshops (CANDARW)

Multi-objective Quantum Optimization based on Bayesian Approach for Computing Resource Assignment Problems

Toyoki Kosuda, Morikazu Nakamura, Shiroma Tadashi, Takayuki Nakachi

Published Nov 26, 2024• 2 citations
Publisher

Abstract

In quantum optimization approaches, such as Quantum Approximate Optimization Algorithms (QAOA) and quantum annealing, the optimal solution is obtained by minimizing an energy function that encapsulates the optimization problem. In the case of multi-objective optimization problems, the trade-offs between competing objective functions are managed by adjusting a set of weight parameters. This paper investigates two parameter-tuning techniques, a grid search and Bayesian optimization, applied to a computational resource allocation problem with multiple objective functions. We compare the performance of these methods by evaluating the efficiency, diversity, and uniformity of the Pareto solutions derived from the optimization results.

DOI
10.1109/candarw64572.2024.00075

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In quantum optimization approaches, such as Quantum Approximate Optimization Algorithms (QAOA) and quantum annealing, the optimal solution is obtained by minimizing an energy function that encapsulates the optimization problem. In the case of multi-objective optimization problems, the trade-offs between competing objective functions are managed by adjusting a set of weight parameters. This paper investigates two parameter-tuning techniques, a grid search and Bayesian optimization, applied to a computational resource allocation problem with multiple objective functions. We compare the performance of these methods by evaluating the efficiency, diversity, and uniformity of the Pareto solutions derived from the optimization results.
An important task in multi-objective optimization is generating the Pareto front -- the set of all Pareto-optimal compromises among multiple objective functions applied to the same set of variables. Since this task can be computationally intensive even for small problems, it is a natural target for quantum optimization. Indeed, this problem was recently approached using the quantum approximate optimization algorithm (QAOA) on an IBM gate-model processor. Here we compare these QAOA results with quantum annealing on the same two input problems, using the same methodology. We find that quantum annealing vastly outperforms not just QAOA run on the IBM processor, but all classical and quantum methods analyzed in the previous study. On the harder problem, quantum annealing improves upon the best known Pareto front. This small study reinforces the promise of quantum annealing in multi-objective optimization.
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches. This study explores the use of quantum computing to address multi-objective optimization challenges. By using a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of multi-objective weighted max-cut problems, the authors demonstrate promising results—both in simulation and on IBM Quantum hardware—surpassing classical approaches.
Materials design is a multi-objective problem, and recent advances in quantum optimization make it possible to bring quantum solvers to bear on such problems. The realistic near-term win, though, is not raw quantum advantage but making an expensive, noisy quantum solver usable by spending its calls wisely. Quantum Approximate Multi-Objective Optimization (QAMOO) traces a Pareto front by solving a family of scalarized Ising problems, one per objective-weight vector, with QAOA --- but chooses those weights \emph{non-adaptively}, sampling them at random, blind to what it has already found. We recast weight selection as \emph{multi-objective Bayesian optimization}: our method, BW-QAMOO (Bayes-Weighted QAMOO), picks each next weight by expected hypervolume improvement (EHVI) under a Gaussian-process (GP) surrogate over the weight-to-objective map. On a frustrated alloy-configuration benchmark across m∈{3,4}m\in\{3,4\}m∈{3,4} objectives and n∈{10,11,12}n\in\{10,11,12\}n∈{10,11,12} sites, BW-QAMOO reaches the same Pareto hypervolume as QAMOO's random sampling with a median 33% fewer scalarized solves across the 90/95\% targets and 60--74\% fewer than a uniform-grid baseline), on a genuine (simulated) QAOA solver; a paired Wilcoxon test confirms the saving is significant, and the advantage grows with the objective count m as the weight simplex expands and blind sampling wastes more of the budget. This is a \emph{query-efficiency} result, and we close with the open challenges on the path to real alloy data and hardware.
The design and operation of renewable energy conversion systems—such as wind turbines, solar photovoltaic arrays, and hybrid storage networks—require balancing multiple, often conflicting objectives, including energy efficiency, cost minimization, environmental impact, and system reliability. Traditional optimization techniques, while effective for isolated parameters, struggle with the combinatorial complexity and nonlinear interdependencies inherent to integrated energy systems. This study explores the application of quantum optimization algorithms in multi-objective renewable energy design, emphasizing how quantum annealing, Quantum Approximate Optimization Algorithm (QAOA), and Variational Quantum Eigensolver (VQE) frameworks can accelerate solution discovery and improve design precision. By leveraging the principles of superposition and entanglement, quantum systems can process vast design spaces in parallel, enabling the rapid evaluation of trade-offs among competing objectives. A hybrid quantum–classical workflow is proposed to integrate quantum solvers into existing computational pipelines for system simulation, control optimization, and energy forecasting. Preliminary modeling results and conceptual simulations indicate that quantum-enhanced optimization not only reduces computation time but also achieves higher Pareto-optimal efficiency compared to conventional multi-objective genetic algorithms and particle swarm optimizers. This interdisciplinary approach demonstrates the transformative potential of quantum computation in sustainable energy system design, supporting the global transition toward carbon neutrality and energy equity. By embedding quantum optimization into renewable infrastructure development, the study provides a foundation for next-generation decision-making frameworks that harmonize performance, sustainability, and scalability.
The quantum approximate optimization algorithm (QAOA) is a leading variational approach to combinatorial optimization, but its practical performance depends strongly on objective design, parameter search, and shot allocation. We present a resource-efficient QAOA framework that uses the cut value of the most probable measured bitstring as the optimization objective, combines it with Bayesian optimization, and adaptively allocates shots using dual criteria based on mode confidence and normalized cut-value variance. Numerical experiments on 3-regular MaxCut show that, for both unweighted and weighted instances, the proposed scheme achieves discrete-solution quality comparable to that of the conventional expectation-based objective while typically requiring fewer total shots to reach the same final mode accuracy. These results indicate that reorganizing QAOA around the maximum-probability bitstring provides an effective route to improving practical performance under limited measurement budgets.
In this work, we present a Bayesian Optimization (BO) approach for tuning the parameters of the Quantum Approximate Optimization Algorithm (QAOA) applied to max-cut problems. Within our black-box optimization framework, BO achieves competitive solutions while requiring significantly fewer quantum circuit evaluations compared to standard non-Bayesian global optimizers. These results highlight the potential of BO to enhance both the efficiency and the overall performance of variational quantum algorithms.