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Introduction of Quantum-inspired Evolutionary Algorithm

Kuk-Hyun Han, Jong-Hwan Kim

Published Jan 1, 2002• 9 citations
OpenAlex

Abstract

Abstract: This paper introduces quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, the evaluation function and the population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits.

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This paper proposes a novel evolutionary algorithm inspired by quantum computing, called a quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, evaluation function, and population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits. A Q-gate is introduced as a variation operator to drive the individuals toward better solutions. To demonstrate its effectiveness and applicability, experiments were carried out on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that QEA performs well, even with a small population, without premature convergence as compared to the conventional genetic algorithm.

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Abstract: This paper introduces quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, the evaluation function and the population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits.
This paper proposes a novel evolutionary algorithm inspired by quantum computing, called a quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, evaluation function, and population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits. A Q-gate is introduced as a variation operator to drive the individuals toward better solutions. To demonstrate its effectiveness and applicability, experiments were carried out on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that QEA performs well, even with a small population, without premature convergence as compared to the conventional genetic algorithm.
In this paper, some guidelines for setting the parameters of quantum-inspired evolutionary algorithm (QEA) are presented. QEA is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. However, QEA is not a quantum algorithm, but a novel evolutionary algorithm. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, the evaluation function, and the population dynamics. From recent research on the knapsack problem, the results of QEA are better than those of CGA (conventional GA). Although the performance of QEA is excellent, there is relatively little or no research on the effects of different settings for its parameters. This paper describes some guidelines for setting these parameters. The guidelines are drawn up based on extensive experiments carried out for a class of combinatorial and numerical optimization problems. Through the guidelines, the performance of QEA can be maximized.
A novel evolutionary algorithm called Probability Evolutionary Algorithm (PEA) is proposed, which is inspired by the Quantum computation and Quantum-inspired Evolutionary Algorithm (QEA). The individual in PEA is encoded by a probabilistic superposed bit which can represent a linear superposition of the states 0 to k (k ≥ 1). The observing step is used in PEA to obtain the observed individual, and the update method is used to evolve the population. The function optimization and 0-k knapsack problem experiments show that PEA has apparent superior in application area, searching capability and computation time compared with QEA and canonical genetic algorithm (CGA).
Quantum-Inspired Evolutionary Algorithm (QEA), a type of stochastic algorithm for solving combinatorial optimization problems, is evolutionary computation using quantum bits and superposition states in quantum computation. Although coarse-grained parallel, QEA has many parameters that must be adjusted manually. The simpler algorithm, Quantum-inspired Evolutionary Computation with Pair Swap operator (QEAPS), the authors propose involves just one population and a simple genetic operation exchanging best solution information between two individuals chosen randomly, instead of the migration operation used in QEA, and thereby fewer parameters to be adjusted. The authors found in experiments that QEAPS finds highly qualified solutions, is more robust against constraint handling, and has a higher search performance of thanks to diversified best solution information.
In this paper, an advanced quantum-inspired evolutionary optimization algorithm (A-QEOA) is proposed. This algorithm is based on the principle of quantum computing such as quantum bit representation and superposition of states. Like other evolutionary algorithms, the quantum-inspired evolutionary algorithm has characteristics of exploration and exploitation. The quantum-inspired evolutionary algorithm achieves exploration using observation process and exploitation using quantum rotation gate. Exploration helps to find the search space for a parameter that needs to be optimized. However, the observation process needs a random number which may sometimes increase the number of iterations to converge the algorithm or may lead to premature convergence. In this paper, we propose an algorithm with an updated observation process that helps to converge the algorithm optimally and helps to get results faster in comparison to the existing quantum inspired evolutionary algorithm (QEA).
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.