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Soft Computing

A quantum multi-objective optimization algorithm based on harmony search method

Alireza Sadeghi Hesar, Seyed Reza Kamel, Mahboobeh Houshmand

Published Apr 25, 2021• 23 citations
Publisher
DOI
10.1007/s00500-021-05799-x

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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.
Multi-objective optimization is a ubiquitous problem that arises naturally in many scientific and industrial areas. Network routing optimization with multi-objective performance demands falls into this problem class, and finding good quality solutions at large scales is generally challenging. In this work, we develop a scheme with which near-term quantum computers can be applied to solve multi-objective combinatorial optimization problems. We study the application of this scheme to the network routing problem in detail, by first mapping it to the multi-objective shortest path problem. Focusing on an implementation based on the quantum approximate optimization algorithm (QAOA) – the go-to approach for tackling optimization problems on near-term quantum computers – we examine the Pareto plot that results from the scheme, and qualitatively analyze its ability to produce Pareto-optimal solutions. We further provide theoretical and numerical scaling analyses of the resource requirements and performance of QAOA, and identify key challenges associated with this approach. Finally, through Amazon Braket we execute small-scale implementations of our scheme on the IonQ Harmony 11-qubit quantum computer.
Since the mention of the Fourth Industrial Revolution in 2016, quantum computers and quantum computing (QC) have emerged as key technologies. Many researchers are trying to realize quantum computers and quantum computing. In particular, most of the development and application of metaheuristics algorithms using quantum computing is focused on computer engineering fields. Cases in which the developed algorithm is applied to the optimal design of a building or the optimal design results presented by expanding the algorithm in various directions are very insufficient. Therefore, in this paper, we proposed four methods of adopting qubits to perform pitch adjusting in the optimization process of the QbHS (quantum-based harmony search) algorithm and applied it to TTO (truss topology optimization) using four methods to compare the results. The four methods of adopting qubits have the same or decreased number of qubits adopted as the number of iterations changes. As a result of applying TTO using four methods, convergence performance differed depending on the adoption method, and convergence performance was superior to conventional HS (harmony search) algorithms in all methods. The optimal design of structural engineering using such QC is expected to contribute to the revitalization of future technologies in the architectural field and the field of computer information systems.