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Lecture notes in computer science

Real-Observation Quantum-Inspired Evolutionary Algorithm for a Class of Numerical Optimization Problems

Gexiang Zhang, Haina Rong

Published Jan 1, 2007• 37 citations
Publisher
DOI
10.1007/978-3-540-72590-9_151

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From recent research on combinatorial optimization of the knapsack problem, quantum-inspired evolutionary algorithm (QEA) was proved to be better than conventional genetic algorithms. To improve the performance of the QEA, this paper proposes research issues on QEA such as a termination criterion, a Q-gate, and a two-phase scheme, for a class of numerical and combinatorial optimization problems. A new termination criterion is proposed which gives a clearer meaning on the convergence of Q-bit individuals. A novel variation operator H/sub /spl epsi// gate, which is a modified version of the rotation gate, is proposed along with a two-phase QEA scheme based on the analysis of the effect of changing the initial conditions of Q-bits of the Q-bit individual in the first phase. To demonstrate the effectiveness and applicability of the updated QEA, several experiments are carried out on a class of numerical and combinatorial optimization problems. The results show that the updated QEA makes QEA more powerful than the previous QEA in terms of convergence speed, fitness, and robustness.
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.