Quantum Clonal Multiobjective Evolutionary Algorithms

Many optimization problems in science and engineering practice can be attributed to multiobjective optimization problem (MOP) and these objectives often compete or conflict with each other and unable to compare directly. However, the current multi-objective optimization algorithms (MOA) have local convergence, poor population diversity, high time complexity, the sensitivity of parameter and other problems. Therefore, the study of a more efficient MOA has scientific and practical significance.Artificial immune system (AIS) is an intelligent method which imitates biological immune system and has a strong ability to recognize, learn, memory and be self-adaptive. Quantum evolutionary algorithm (QEA) is a kind of probability search algorithm based on the theory of quantum computing, which has better population diversity and global optimization, small population but with the same performance of the algorithm.Aftering analysing the advantages and disadvantages of multiobjective evolutionary algorithm, artificial immune system and quantum evolutionary algorithm, two Quantum Clonal Algorithms for solving MOP and a theoretical framework of Quantum Clonal Multiobjective Evolutionary Algorithm (QCMEA) were proposed in this paper based on the ergodicity of chaotic search, the efficiency of quantum computing and antibody clonal selection theory of AIS. The main contents of this paper are summarized as follows:(1)A novel MOA—Chaos Quantum Clonal Multi-objective Evolutionary Algorithm (CQCMEA) is proposed in this paper, which introduces a new quantum coding method, designs the corresponding quantum rotation gate mutation operator to improve the converg- ence of the algorithm, clones the immunodominant antibody proportionally and uses crowding distance to maintain the distribution and diversity of solutions. The performance and complexity of this algorithm are analyzed. Theoretical analysis and numerical simulation proved the effectiveness of this algorithm.(2)This paper proposes Quantum Clonal Multiobjective Evolutionary Algorithm based on non-uinform mutation, which designs a new quantm rotation gate mutation—non-uniform chaos quantum rotation gate mutation by combining non-uniform mutation with chaos quantum rotation gate mutation, and uses dynamic chaotic variable to accelerate the speed of convergence and improve the convergence of the algorithm. The performance of this algori- thm is analyzed. Theoretical analysis and experimental results show that the algorithm has better convergence and faster speed of convergence and the optimal solution on the Pareto-front have better uniformity and wider distribution.