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IEEE Congress on Evolutionary Computation (CEC)

Quantum Mating Operator: A New Approach to Evolve Chromosomes in Genetic Algorithms

Giovanni Acampora, Roberto Schiattarella, Autilia Vitiello

Published Jul 18, 2022• 7 citations
Publisher

Abstract

Genetic Algorithms (GAs) are optimization methods that search near-optimal solutions by applying well-known operations such as selection, crossover and mutation. In particular, crossover and mutation are aimed at creating new solutions from selected parents with the goal of discovering better and better solutions in the search space. In literature, several approaches have been defined to create new solutions from the mating pool to try to improve the performance of genetic optimization. In this paper, the literature is enriched by introducing a new mating operator that harnesses the stochastic nature of quantum computation to evolve individuals in a classical genetic workflow. This new approach, named Quantum Mating Operator, acts as a multi-parent operator that identifies alleles' frequency patterns from a collection of individuals selected by means of conventional selection operators, and encodes them through a quantum state. This state is successively mutated and measured to generate a new classical chromosome. As shown by experimental results, GAs equipped with the proposed operator outperform those equipped with traditional crossover and mutation operators when used to solve well-known benchmark functions.

DOI
10.1109/cec55065.2022.9870425

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Genetic Algorithms (GAs) are optimization methods that search near-optimal solutions by applying well-known operations such as selection, crossover and mutation. In particular, crossover and mutation are aimed at creating new solutions from selected parents with the goal of discovering better and better solutions in the search space. In literature, several approaches have been defined to create new solutions from the mating pool to try to improve the performance of genetic optimization. In this paper, the literature is enriched by introducing a new mating operator that harnesses the stochastic nature of quantum computation to evolve individuals in a classical genetic workflow. This new approach, named Quantum Mating Operator, acts as a multi-parent operator that identifies alleles' frequency patterns from a collection of individuals selected by means of conventional selection operators, and encodes them through a quantum state. This state is successively mutated and measured to generate a new classical chromosome. As shown by experimental results, GAs equipped with the proposed operator outperform those equipped with traditional crossover and mutation operators when used to solve well-known benchmark functions.
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 Genetic Algorithms (QGAs) are emerging as a new class of algorithms that exploit the peculiarities of quantum computers to outperform classical evolutionary approaches in solving complex optimization problems. Despite the theoretical promises, their applicability has been strongly affected by the limitation of current noise-prone quantum hardware. It has only recently been demonstrated that acceptable levels of quantum noise can enhance the exploration capability of QGA in constrained optimization problems. The research corroborates the initial findings, providing further evidence of the efficacy of these algorithms by successfully resolving the NP-hard Ising Problem through the utilization of a QGA equipped with a quantum mating operator. The experimental results show that noisy simulations of QGA are capable of identifying better solutions than genetic algorithms that are equipped with state-of-the-art classical mating operators.
This paper presents a novel approach to optimization design leveraging the principles of quantum mechanics, specifically superposition and entanglement, through a Quantum Genetic Algorithm (QGA). Traditional Genetic Algorithms (GAs) face challenges in complex, high-dimensional optimization problems due to the exponential growth of the search space. The QGA aims to mitigate these limitations by encoding genetic information into quantum states and utilizing quantum operations for selection, crossover, and mutation. This approach theoretically utilizes quantum superposition to explore multiple solution possibilities simultaneously and quantum entanglement to correlate solutions, potentially leading to faster convergence and improved optimization performance. The paper outlines the theoretical framework, the algorithmic steps of the QGA, and discusses potential applications. The primary contribution is the conceptual framework and the proposed method, recognizing the nascent stage of QGA research and presenting a novel exploration of its potential.
This paper proposes a novel approach to optimization problems by integrating quantum entanglement with the Genetic Algorithm (GA). The core idea is to leverage the inherent parallelism and enhanced information transfer capabilities of quantum entanglement to significantly improve the search performance of the GA. We represent genetic algorithm chromosomes as quantum states and employ quantum entanglement to facilitate rapid information exchange and crossover operations across multiple qubits. This mechanism allows for parallel exploration of the search space, mitigating the limitations of traditional GA's tendency towards local optima. The theoretical framework and the underlying principles are presented, demonstrating the potential for the Quantum Entanglement Genetic Algorithm (QGA) to accelerate the solution of complex optimization problems. The algorithm's effectiveness is discussed through a mathematical formulation, focusing on the key components of the QGA and its advantages over conventional GA. The ultimate goal is to demonstrate a robust and efficient method for tackling challenging optimization tasks.
A genetic algorithm (GA) is a search-based optimization technique based on the principles of Genetics and Natural Selection. We present an algorithm which enhances the classical GA with input from quantum annealers. As in a classical GA, the algorithm works by breeding a population of possible solutions based on their fitness. However, the population of individuals is defined by the continuous couplings on the quantum annealer, which then give rise via quantum annealing to the set of corresponding phenotypes that represent attempted solutions. This introduces a form of directed mutation into the algorithm that can enhance its performance in various ways. Two crucial enhancements come from the continuous couplings having strengths that are inherited from the fitness of the parents (so-called nepotism) and from the annealer couplings allowing the entire population to be influenced by the fittest individuals (so-called quantum-polyandry). We find our algorithm to be significantly more powerful on several simple problems than a classical GA.
Genetic algorithms (GAs) are a class of evolutionary algorithms inspired by Darwinian natural selection. They are popular heuristic optimisation methods based on simulated genetic mechanisms, i.e., mutation, crossover, etc. and population dynamical processes such as reproduction, selection, etc. Over the last decade, the possibility to emulate a quantum computer (a computer using quantum-mechanical phenomena to perform operations on data) has led to a new class of GAs known as “Quantum Genetic Algorithms” (QGAs). In this review, we present a discussion, future potential, pros and cons of this new class of GAs. The review will be oriented towards computer scientists interested in QGAs “avoiding” the possible difficulties of quantum-mechanical phenomena.