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Híradástechnika/Infocommunications journal

Quantum Genetic Algorithm for Highly Constrained Optimization Problems

Abdulbasit M. A. Sabaawi, Mohammed Rabeea Almasaoodi, Sara El Gaily, Sándor Imre

Published Jan 1, 2023• 6 citations
Publisher

Abstract

Quantum computing appears as an alternative solution for solving computationally intractable problems. This paper presents a new constrained quantum genetic algorithm designed specifically for identifying the extreme value of a highly constrained optimization problem, where the search space size _database is massive and unsorted_ cannot be handled by the currently available classical or quantum processor, called the highly constrained quantum genetic algorithm (HCQGA). To validate the efficiency of the suggested quantum method, maximizing the energy efficiency with respect to the target user bit rate of an uplink multi-cell massive multiple-input and multiple- output (MIMO) system is considered as an application. Simulation results demonstrate that the proposed HCQGA converges rapidly to the optimum solution compared with its classical benchmark.

DOI
10.36244/icj.2023.3.7

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Quantum computing appears as an alternative solution for solving computationally intractable problems. This paper presents a new constrained quantum genetic algorithm designed specifically for identifying the extreme value of a highly constrained optimization problem, where the search space size database is massive and unsorted cannot be handled by the currently available classical or quantum processor, called the highly constrained quantum genetic algorithm (HCQGA). To validate the efficiency of the suggested quantum method, maximizing the energy efficiency with respect to the target user bit rate of an uplink multi-cell massive multiple-input and multiple- output (MIMO) system is considered as an application. Simulation results demonstrate that the proposed HCQGA converges rapidly to the optimum solution compared with its classical benchmark.
In the past decades, many quantum algorithms have been developed. The main obstacle that prevents the widespread implementation of these algorithms is the small size of the available quantum computer in terms of qubits. Blind Quantum Computation (BQC) holds the promise of handling this issue by delegating computation to quantum remote devices. Here, we introduce a novel Constrained Quantum Genetic Algorithm (CQGA) that selects the optimum extreme (minimum or maximum) value of a constrained goal function (or a vast unsorted database) with very low computational complexity. Since the convergence speed to the optimal solution for the Constrained Classical Genetic Algorithm (CCGA) is highly dependent on the level of quality of the initially selected potential solutions, the CCGA's heuristic initialization stage is replaced by a quantum one. This is achieved by exploiting the strengths of the Constrained Quantum Optimization Algorithm (CQOA) and the BQC. The proposed CQGA is applied as an embedded computational infrastructure for the uplink multi-cell massive MIMO system. The algorithm maximizes the energy efficiency (EE) of the uplink massive MIMO while considering different users target bit rate classes. Simulation results show that the suggested CQGA maximizes energy efficiency through careful computation of the optimal transmit power for each active user using fewer computational steps than the CCGA. We demonstrated that when the overall transmit power set or the overall number of active users increases, the CQGA keeps executing a smaller number of generation steps compared to the CCGA. For instance, if we consider a scenario where the overall number of active users () is set to 18, the CQGA finds the optimal solution with a smaller number of generation steps equal to 6, while the CCGA takes a larger number of generation steps, reaching 65.
There are plenty of real-world applications that require finding extreme value in an unsorted database. This database can be enormously large, such that there is no available quantum computer or classical supercomputer that can execute the search process. We proposed a new unconstrained quantum genetic algorithm (QGA) in order to increase the probability of finding the global solution and escaping from local minima. This algorithm exploits the features provided by blind quantum computation (BQC), which holds the promise to handle this computation issue by delegating computation to quantum remote devices. Massive multiple-input multiple-output (MIMO) systems are used as a toy example for demonstrating the effectiveness of the developed quantum genetic method.
Abstract Devising efficient optimisation methods has been a subject of great research attention since current evolving trends in communication networks, machine learning, and other cutting‐edge systems that need a fast and accurate optimised computational model. Classical computers became incapable of handling new optimisation problems posed by newly emerging trends. Quantum optimisation algorithms appear as alternative solutions. The existing bottleneck that restricts the use of the newly developed quantum strategies is the limited qubit size of the available quantum computers (the size of the most recent universal quantum computer is 433 qubits). A new quantum genetic algorithm (QGA) is proposed that handles the presented problem. A quantum extreme value searching algorithm and quantum blind computing framework are utilised to extend the search capabilities of the GA. The quantum genetic strategy is exploited to maximise energy efficiency at full spectral efficiency of massive multiple‐input, multiple‐output (M‐MIMO) technology as a toy example for pointing out the efficiency of the presented quantum strategy. The authors run extensive simulations and prove how the presented quantum method outperforms the existing classical genetic algorithm.
This paper presents a novel approach to complex optimization problems utilizing a hybrid Genetic Algorithm (GA) enhanced with quantum computing techniques. Classical GAs often struggle with slow convergence rates in high-dimensional search spaces. This research addresses this limitation by integrating quantum superposition and interference into the core operations of the GA, specifically crossover and mutation. The proposed method, termed Quantum-Enhanced Genetic Algorithm (Q-GA), aims to significantly accelerate the optimization process by exploring the solution space more efficiently. The core idea is to represent potential solutions within a quantum state, allowing for parallel exploration facilitated by superposition. We detail the architecture of the Q-GA, outlining the integration of classical GA components with quantum algorithms. The performance of the Q-GA is theoretically analyzed, focusing on the potential speedup achievable through quantum computation. The results presented demonstrate the promise of this hybrid approach for tackling computationally intensive optimization problems where classical GAs fall short.
Classical computing still suffers from the high computational complexity of finding the extreme value of a constrained goal function or an unordered database with respect to a certain constraint. Quantum computing offers new possibilities and solutions due to its quantum nature to surmount this problem. In this paper, we extended a new version of quantum existence testing (QET) _we call it a constrained quantum relation testing (CQRT)_ we also investigate analytically its classical and quantum certainty. Furthermore, we show how the CQRT can be applied for extending the quantum extreme value searching algorithm (QEVSA) version to a constrained quantum optimization algorithm (CQOA). And we gave an extensive explanation of how the CQOA works and how it finds the extreme constrained optimum value solution with high complexity reduction, maximum exponential speed, and high certainty.
Abstract Quantum computers promise to revolutionize the world of computing thanks to some features of quantum mechanics that can enable massive parallelism in computation. This benefit may be particularly relevant in the design of evolutionary algorithms, where the quantum paradigm could support the exploration of multiple regions of the search space in a concurrent way. Although some efforts in this research field are ongoing, the potential of quantum computing is not yet fully expressed due to the limited number of qubits of current quantum processors. This limitation is even more acute when one wants to deal with continuous optimization problems, where the search space is potentially infinite. The goal of this paper is to address this limitation by introducing a hybrid and granular approach to quantum algorithm design, specifically designed for genetic optimization. This approach is defined as hybrid, because it uses a digital computer to evaluate fitness functions, and a quantum processor to evolve the genetic population; moreover, it uses granular computing to hierarchically reduce the size of the search space of a problem, so that good near-optimal solutions can be identified even on small quantum computers. As shown in the experiments, where IBM Q family processors are used, the usage of a granular computation scheme statistically enhances the performance of the state-of-the-art evolutionary algorithm implemented on quantum computers, when it is run to optimize well-known benchmark continuous functions.