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A Modified Quantum-Inspired Genetic Algorithm Using Lengthening Chromosome Size and an Adaptive Look-Up Table to Avoid Local Optima

Shahin Hakemi, Mahboobeh Houshmand, Seyyed Abed Hosseini, Xujuan Zhou

Published Oct 17, 2023• 13 citations
Publisher

Abstract

The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). The proposed algorithm utilizes a lengthening chromosome strategy for a balanced and smooth transition between exploration and exploitation phases to avoid local optima and premature convergence. Apart from that, a novel adaptive look-up table for rotation gates is presented to boost the algorithm’s optimization abilities. To evaluate the effectiveness of these ideas, DQGA is tested by various mathematical benchmark functions as well as real-world constrained engineering problems against several well-known and state-of-the-art algorithms. The obtained results indicate the merits of the proposed algorithm and its superiority for solving multimodal benchmark functions and real-world constrained engineering problems.

DOI
10.3390/axioms12100978

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The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). The proposed algorithm utilizes a lengthening chromosome strategy for a balanced and smooth transition between exploration and exploitation phases to avoid local optima and premature convergence. Apart from that, a novel adaptive look-up table for rotation gates is presented to boost the algorithm’s optimization abilities. To evaluate the effectiveness of these ideas, DQGA is tested by various mathematical benchmark functions as well as real-world constrained engineering problems against several well-known and state-of-the-art algorithms. The obtained results indicate the merits of the proposed algorithm and its superiority for solving multimodal benchmark functions and real-world constrained engineering problems.
Abstract This paper proposes a Dynamic Quantum-inspired Genetic Algorithm (DQGA), which combines the quantum mechanics concepts with metaheuristics principles to enhance the search capability of the genetic algorithm. The proposed algorithm also introduces the lengthening chromosome strategy for a balanced and smooth transition between exploration and exploitation phases. Apart from that, a novel adaptive look-up table for rotation gates is presented to boost the algorithm's optimization abilities. To evaluate the effectiveness of these ideas, the DQGA is tested by various mathematical benchmark functions as well as real-world constrained engineering problems against several well-known and state-of-the-art algorithms. The obtained results indicate the merits of the proposed algorithm.
Qubit-inspired Genetic Algorithm (QGA) is an extension of genetic algorithm in which quantum mechanics and its representations are introduced. A chromosome in our QGA is concretized as a series of quantum-bit (qubit) described by its complex-valued representation, and phase-rotation gates are embedded into the selection process over generations. In our previous work, it has been shown that this scheme has better performances than the classical ones in several problems such as N-K landscape problem, Knapsack Problem, Maximum Search, and Construction of image filters. In this paper, we make clear the effectiveness of the QGA by comparing QGA with GA through minimum solution problem on De Jong's functions.
This paper explores the application of a quantum-inspired genetic algorithm (QIGA) for solving complex optimization problems. Traditional genetic algorithms (GAs) can struggle with the intricacies of high-dimensional and non-linear problems, often encountering issues with premature convergence and local optima. This research proposes a novel approach where a standard GA is modified to incorporate principles inspired by quantum mechanics, specifically utilizing quantum-inspired concepts such as superposition and interference, to enhance the exploration and exploitation phases. The core claim is that QIGA can effectively tackle complex optimization scenarios. The mechanism involves mapping the original problem into the fitness function of the GA, and subsequently using the QIGA to perform the optimization. The results demonstrate the potential of this hybrid approach to improve solution quality and speed, particularly in problems with challenging characteristics. The research highlights a promising direction for combining classical optimization techniques with quantum-inspired ideas, offering a new tool for tackling computationally intensive optimization tasks. ---
This paper proposes a new parallel evolutionary algorithm called parallel quantum-inspired genetic algorithm (PQGA). Quantum-inspired genetic algorithm (QGA) is based on the concept and principles of quantum computing such as qubits and superposition of states. Instead of binary, numeric, or symbolic representation, by adopting the qubit chromosome as a representation, QGA can represent a linear superposition of solutions due to its probabilistic representation. QGA is suitable for parallel structures because of rapid convergence and good global search capability. That is, QGA is able to possess the two characteristics of exploration and exploitation simultaneously. The effectiveness and the applicability of PQGA are demonstrated by experimental results on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that PQGA is superior to QGA as well as other conventional genetic algorithms.
Quantum genetic algorithms(QGA) typically construct traditional quantum chromosomes as independent quantum bit systems, which has facilitated the enhancement of search speed and precision in genetic algorithms, demonstrating powerful problem-solving capabilities in optimization issues. Although traditional QGA have enriched population diversity, they still tend to fall into local optima, and the evolutionary update operations require rotation directions to be determined by lookup tables, a process involving multiple conditional judgments that affect algorithm efficiency. To address these issues, an improved method has been proposed to further enhance the performance of QGA. In the initial population selection, a population grouping evolution method based on microhabitat coevolution strategy is used to prevent the algorithm from getting trapped in local optima when solving complex function problems. Additionally, quantum entanglement is introduced on top of quantum super-position by implementing quantum entanglement using quantum registers, and higher-order quantum rotation gates are employed that do not involve multiple conditional judgments of lookup tables, thus improving the efficiency of quantum chromosome measurement and evolutionary updates. Finally, traditional QGA and higher-order quantum genetic algorithms were applied to test functions in multiple experiments. The results indicate that, compared to traditional QGA, the higher-order quantum genetic algorithms have achieved an increase in convergence speed, an approximate 14.3% improvement in convergence precision, and possess enhanced global search capabilities.
The development in the field of quantum computing gives us a significant edge over classical computing in terms of time and efficiency.This is particularly useful for NP-hard problems such as graph layout problems.Since many real world problems are effectively solved by genetic algorithm (GA) and the performance of GA highly depends upon the setting of its parameters, therefore this paper focuses on a Quantum Inspired Genetic Algorithm (QIGA) and develops and evaluates adaptive strategies for the same.QIGA adapts ideas of Q-bits, superposition of Q-bits from quantum computing.The effectiveness and the applicability of adaptive QIGA is demonstrated by experimental results on the benchmark Knapsack, Maxcut and Onemax combinatorial optimization problems.The results show that adaptive QIGA is superior to QIGAs.