A modified immune network optimization algorithm
- Authors: Hong, Lu , Kamruzzaman, Joarder
- Date: 2014
- Type: Text , Journal article
- Relation: IAENG International Journal of Computer Science Vol. 41, no. 4 (2014), p. 231-236
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- Description: This study proposes a modified artificial immune network algorithm for function optimization problems based on idiotypic immune network theory. A hyper-cubic mutation operator was introduced to reduce the heavy computational cost of the traditional opt-AINet algorithm. Moreover, the new symmetrical mutation can effectively improve local search. To maintain population diversity, we also devised an immune selection mechanism based on density and fitness. The global convergence of the algorithm was deduced through the method of pure probability and iterative formula. Simulation results of benchmark function optimization show that the modified algorithm converges more effectively than other immune network algorithms.
A new convergence rate estimation of general artificial immune algorithm
- Authors: Hong, Lu , Kamruzzaman, Joarder
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Intelligent and Fuzzy Systems Vol. 28, no. 6 (2015), p. 2793-2800
- Full Text: false
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- Description: Artificial immune algorithm has been used widely and successfully in many computational optimization areas, but the theoretical research exploring the convergence rate characteristics of artificial immune algorithm is yet inadequate. In this paper, instead of the traditional eigenvalue estimation of state transition matrix, stochastic processes theory is introduced to study the convergence rate of general artificial immune algorithm. The method begins by analyzing the necessary condition for convergence of artificial immune algorithm and takes it as the sufficient condition for a class of general artificial immune algorithm. Through the definition of Markov chain convergence rate, a probability strong convergence rate estimation method of general artificial immune algorithm is proposed. This method is judged by the final convergence of the best antibody, which overcomes the conservative defect of traditional estimation methods. The simulation results show the correctness of the proposed estimation method, and the estimation method can be used to judge the convergence and convergence rate of a class of artificial immune algorithms. This research has a certain theoretical reference value to optimize the convergence rate in the practical application of artificial immune algorithm.
Convergence of elitist clonal selection algorithm based on martingale theory
- Authors: Hong, Lu , Kamruzzaman, Joarder
- Date: 2013
- Type: Text , Journal article
- Relation: Engineering Letters Vol. 21, no. 4 (2013), p. 181-184
- Full Text: false
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- Description: In recent years, progress has been made in the analysis of global convergence of clonal selection algorithms (CSA), but most analyses are based on the theory of Markov chain, which depend on the description of the transition matrix and eigenvalues. However, such analyses are very complicated, especially when the population size is large, and are presented for particular implementations of CSA. In this paper, instead of the traditional Markov chain theory, we introduce martingale theory to prove the convergence of a class of CSA, called elitist clonal selection algorithm (ECSA). Using the submartingale convergence theorem, the best individual affinity evolutionary sequence is described as a submartingale, and the almost everywhere convergence of ECSA is derived. Particularly, the algorithm is proved convergent with probability 1 in finite steps when the state space of population is finite. This new proof of global convergence analysis of ECSA is more simplified and effective, and not implementation specific.