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Granular Computing

Improving quantum genetic optimization through granular computing

Giovanni Acampora, Autilia Vitiello

Published Oct 8, 2022• 8 citations
Publisher

Abstract

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.

DOI
10.1007/s41066-022-00348-9

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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.
Recently, quantum computing has emerged as a new paradigm that promises to improve artificial intelligence techniques. One of the research fields that is certainly benefiting from this new computational paradigm is evolutionary optimization. In literature, efforts have been already made to run evolutionary algorithms on quantum computers using quantum effects such as superposition and entanglement to converge towards sub-optimal solutions of hard problems. However, the performance of these quantum evolutionary approaches is limited by the number of qubits available on current quantum devices. This limitation is more noticeable in the case of continuous optimization problems, where the search space is potentially infinite. This paper presents a recursive algorithmic structure that embodies a quantum evolutionary algorithm to overcome the limitations mentioned above. The result is an innovative and efficient approach in the context of quantum evolutionary optimization.
Quantum Genetic Algorithms (QGA) integrate genetic programming and quantum computing to address search and optimization problems. The standard strategy of the hybrid QGA approach is to add quantum resources to classical genetic algorithms (GA), thus improving their efficacy (i.e., quantum optimization of a classical algorithm). However, the extent of such improvements is still unclear. Conversely, Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that reduces the GA search for the best fitness in a population of potential solutions to running Grover's algorithm. Unfortunately, RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions of the problem) in exponential runtime, [[EQUATION]], where [[EQUATION]] is the number of qubits in the individuals' quantum register. This paper introduces a novel QGA optimization strategy, namely a classical optimization of a fully quantum algorithm, to address the Reduced Quantum Genetic Algorithm (RQGA) complexity problem. Accordingly, we control the complexity of theReduced Quantum Genetic Algorithm (RQGA) algorithm by selecting a limited number of qubits in the individuals' register and fixing the remaining ones as classical values of '0' and '1' with a genetic algorithm. We also improve the performance of RQGA by discarding unfit solutions and bounding the search only in the area of valid individuals. As a result, our Hybrid Quantum Algorithm with Genetic Optimization (HQAGO) solves search problems in [[EQUATION]] oracle queries, where [[EQUATION]] is the number of fixed classical bits in the individuals' register.
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.
Abstract Quantum Genetic Algorithms (QGAs) integrate genetic programming and quantum computing to address search and optimization problems. Most QGA approaches add quantum features to genetic algorithm operators, such as selection, crossover, or mutation. Oppositely, the Reduced Quantum Genetic Algorithm (RQGA) is a fully quantum algorithm that encodes the entire search space (i.e., population) as a superposition of all possible solutions (chromosomes) using the individuals’ quantum register; the fitness function takes the individuals’ quantum register as input to generate corresponding fitness values within the chromosomes’ superposition. RQGA finds the best fitness value and its corresponding chromosome (i.e., the solution or one of the solutions) using Grover’s algorithm. The complexity of Grover’s algorithm is O(2N⁄2), where N is the number of superposed individual chromosomes. However, RQGA operates on an exponentially-big search space (N = 2n, where n is the number of qubits in the individuals’ quantum register), which entails an exponential runtime of O(2n⁄2). This paper introduces an optimization solution for RQGA that controls the algorithm complexity by selecting a limited number of qubits in the individuals’ register and fixing the remaining ones as classical values of ’0’ and ’1’ with a genetic algorithm. We also improve the performance of the RQGA by discarding unfit solutions and bounding the search only in the valid individuals’ area. Putting it all together, we introduce a novel quantum genetic algorithm—Hybrid Quantum Algorithm with Genetic Optimization (HQAGO)—that solves search problems in O(2(n-k)⁄2) oracle queries, where k is the number of fixed classical bits in the individuals’ register. We illustrate instantiations of HQAGO that solve the NP-hard knapsack and graph coloring problems, analyze the complexity of the new algorithm, and study the convergence of its heuristic part.
Quantum computing is a promising and emerging field of computer science with the potential to improve artificial intelligence techniques, particularly those related to optimization. However, current quantum devices operate in the Noisy Intermediate-Scale Quantum era, in which quantum noise can significantly compromise computational reliability. Evolutionary algorithms are inherently stochastic and may therefore be less sensitive to such noise, or even benefit from it. This study evaluates the performance of a hybrid quantum genetic algorithm on a set of combinatorial and continuous optimization problems under various realistic noise models. The findings demonstrate that quantum noise does not hinder the algorithm's performance and can even enhance its exploratory capabilities in some cases. This suggests that noise-aware quantum evolutionary strategies have the potential to be effective even with today's imperfect quantum hardware.
Genetic algorithms are widely used for solving optimization problems. As the search space of the problem is augmented, the probability of falling into local minima will be augmented as well. Previous works showed that the adjusted phase (i.e. required modification per generation), may enhance badly the optimality reaching. Moreover, the search for suitable probabilities on crossover and mutation results in huge computational complexity. Recent developments in quantum technology have shown that quantum computers can provide a dramatic advantage over classical computers. This paper will be oriented toward computer scientists interested in the quantum genetic algorithm (QGA). Therefore, we will present a discussion, of the pros, and cons of classical GA. We survey the “state of the art” of the most known techniques for evolving evolutionary algorithms and quantum computing. We intend in this work to help researchers and application developers in gaining insights into the power of quantum computing mechanisms. This science can inherently treat the balance between exploration and exploitation of the search space. This property is due to the use of Q-bits. The orientation toward the best solution is due to the use of Q-gates.