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International Conference of the Chilean Computer Science Society (SCCC)

Toward a more Generalized Quantum-Inspired Evolutionary Algorithm for Combinatorial Optimization Problems

Julio Manuel Alegria Reymer, Yván Jesús Túpac Valdivia

Published Nov 1, 2013• 0 citations
Publisher

Abstract

In this paper, a generalization of the original Quantum-Inspired Evolutionary Algorithm (QIEA): the Generalized Quantum-Inspired Evolutionary Algorithm (GQIEA) is proposed. Like QIEA, GQIEA is also based on the quantum computing principle of superposition of states, but extending it not only to be used for binary values {0, 1}, but for any finite set of values {1, n}. GQIEA, as any other quantum inspired evolutionary algorithm, defines an own quantum individual, an evaluation function and population operators. As in QIEA, GQIEA also defines a generalized Q-gate operator, which is a variation operator to drive the individuals toward better solutions. To demonstrate its effectiveness and applicability, the proposal will be applied to the Knapsack Problem (KP), a classic combinatorial optimization problem. Results show that GQIEA has a good performance even with a small population.

DOI
10.1109/sccc.2013.30

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Quantum-inspired evolutionary algorithms (QIEAs), as a subset of evolutionary computation, are based on the principles of quantum computing such as quantum bits and quantum superposition. In this paper, we propose a multi-start quantum-inspired evolutionary algorithm, called MSQIEA. To improve the performance of the algorithm, a multi-measurement operator and a new strategy for updating the rotation angle is proposed. When Q-bit individuals start to converge to their final states, the best solution is stored and all Q-bits in each Q-bit individual are reinitialized. We compare the effectiveness of MSQIEA with a popular quantum-inspired evolutionary algorithm, called QEA, for solving 0-1 knapsack problem. The experimental results show that MSQIEA outperforms QEA and finds a solution with higher profit.
Quantum-Inspired Evolutionary Algorithms (QIEAs) represent a novel fusion of quantum computing principles and classical evolutionary strategies, offering a powerful approach to solving complex optimization problems. This chapter provides a comprehensive overview, detailing foundational concepts, implementation techniques, and potential applications of QIEAs. By leveraging quantum phenomena such as superposition and entanglement, QIEAs enhance the exploitation and exploration capabilities of traditional evolutionary algorithms (EAs), thus enabling an efficient search of vast solution spaces. The study examines key components of QIEA, including quantum encoding, rotation gates, and entanglement operations, and compares its performance with classical EAs. By analyzing real-life examples of combinatorial optimization problems (COPs) such as the minimum spanning tree (MST), traveling salesman problem (TSP), and graph coloring, the chapter demonstrates QIEA’s superior efficiency and solution quality. Despite implementation challenges, QIEA shows promise in various domains, including machine learning, finance, healthcare, telecommunications, and e-commerce. Future research directions are outlined, emphasizing the need for simplified quantum-inspired operators, hybrid quantum-classical systems, and interdisciplinary collaboration. This chapter highlights the transformative potential of QIEA, setting the stage for further advancements and applications in optimization and computational efficiency.
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This paper proposes a novel type of quantum-inspired evolutionary algorithm (QiEA) for numerical optimization inspired by the multiple universes principle of quantum computing, which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Numerical optimization problems are an important field of research with several applications in several areas: industrial plant optimization, data mining and many others, and although being successfully used for solving several optimization problems, evolutionary algorithms still present issues that can reduce their performances when faced with task where the evaluation function is computationally intensive. In order to address those issues the QiEA represent the most recent advance in the field of evolutionary computation. This work present some application about combinatorial and numerical optimization problems.
Quantum-Inspired Evolutionary Algorithm (QEA) has been shown to be better performing than classical Genetic Algorithm based evolutionary techniques for combinatorial optimization problems like 0/1 knapsack problem. QEA uses quantum computing-inspired representation of solution called Q-bit individual consisting of Q-bits. The probability amplitudes of the Q-bits are changed by application of Q-gate operator, which is classical analogous of quantum rotation operator. The Q-gate operator is the only variation operator used in QEA, which along with some problem specific heuristic provides exploitation of the properties of the best solutions. In this paper, we analyzed the characteristics of the QEA for 0/1 knapsack problem and showed that a probability in the range 0.3 to 0.4 for the application of the Q-gate variation operator has the greatest likelihood of making a good balance between exploration and exploitation. Experimental results agree with the analytical finding.
Genetic Quantum Algorithm (GQA) is an evolutionary algorithm in the class of quantum inspired evolutionary algorithms inspired by the principles of quantum computing such as Q-bits, super position, quantum gates, interference and coherence. GQA adopts Q-bit representation and applies quantum rotation gate (QR gate) as genetic operator. The performance of the quantum inspired evolutionary algorithms largely depends upon the effectiveness of quantum gates applied as the genetic operator. Researchers have attempted to improve the performance of quantum inspired evolutionary algorithms by designing various quantum evolutionary operators using different strategies. In this paper, an effort is made to study the impact of Random search based QR gate strategy in GQA, and subsequently a Random search and greedy selection based Genetic Quantum Algorithm (RSGS-GQA) is proposed. The performance of RSGS-GQA algorithm is compared with the standard quantum inspired evolutionary algorithms (QIEA) on knapsack problem. The results indicate that, the RSGS-GQA algorithm performs better than the standard QIEA variants in terms of the quality of the solution and convergence.