Abstract
Optimization method is important in engineering design and application. Quantum genetic algorithm has the characteristics of good population diversity, rapid convergence and good global search capability and so on. It combines quantum algorithm with genetic algorithm. A novel quantum genetic algorithm is proposed, which is called Variable-boundary-coded Quantum Genetic Algorithm (vbQGA) in which qubit chromosomes are collapsed into variable-boundary-coded chromosomes instead of binary-coded chromosomes. Therefore much shorter chromosome strings can be gained. The method of encoding and decoding of chromosome is first described before a new adaptive selection scheme for angle parameters used for rotation gate is put forward based on the core ideas and principles of quantum computation. Eight typical functions are selected to optimize to evaluate the effectiveness and performance of vbQGA against standard Genetic Algorithm (sGA) and Genetic Quantum Algorithm (GQA). The simulation results show that vbQGA is significantly superior to sGA in all aspects and outperforms GQA in robustness and solving velocity, especially for multidimensional and complicated functions.
Highlights
Quantum computation is a new and developing interdiscipline integrating information science and quantum mechanics. Benioff (1980) and Feyman (1982) proposed the concepts of quantum computing. Shor (1994) presented a quantum algorithm used for factoring very large numbers, Grover (1996) developed a quantum mechanical algorithm to search unsorted database
Based on the Genetic Quantum Algorithm (GQA), we propose a novel quantum genetic algorithm called variableboundary-coded quantum genetic algorithm, Variable-boundary-coded Quantum Genetic Algorithm (vbQGA), which we will introduce
In vbQGA, we represent the state of a qubit as follow:
Summary
Quantum computation is a new and developing interdiscipline integrating information science and quantum mechanics. Benioff (1980) and Feyman (1982) proposed the concepts of quantum computing. Shor (1994) presented a quantum algorithm used for factoring very large numbers, Grover (1996) developed a quantum mechanical algorithm to search unsorted database. Shor (1994) presented a quantum algorithm used for factoring very large numbers, Grover (1996) developed a quantum mechanical algorithm to search unsorted database. Narayanan and Moore (1996) and Han (2000) proposed respectively quantum inspired genetic algorithm and genetic quantum algorithm. These algorithms are inspired by certain concept and principles of quantum computing such as qubits and superposition of states. Chromosomes in these algorithms are probabilistically represented by qubits and so can represent a linear superposition of solutions. Many researchers have found that these algorithms have excellent performance such as population diversity, rapid convergence and global search capability. Wang et al (2005) have put effective applications in shop scheduling
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