Search

Abstract: This paper presents a novel Constrained Optimization based on Modified Differential Evolution algorithm (COMDE). In the new algorithm, a new directed mutation rule, based on the weighted difference vector between the best and the worst individuals at a particular generation, is introduced. The new directed mutation rule is combined with the modified basic mutation strategy DE/rand/1/bin, where only one of the two mutation rules is applied with the probability of 0.5. The proposed mutation rule is shown to enhance the local search ability of the basic Differential Evolution (DE) and to get a better trade-off between convergence rate and robustness. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability is utilized to balance the global exploration and local exploitation. COMDE also includes a modified constraint handling technique based on feasibility and the sum of constraints violations. A new dynamic tolerance technique to handle equality constraints is also adopted. The effectiveness and benefits of the new directed mutation strategy and modified basic strategy used in COMDE has been experimentally investigated. The effect of the parameters of the crossover probability function and the parameters of the dynamic tolerance equation on the performance of COMDE have been analyzed and evaluated by different experiments. Numerical experiments on 13 well-known benchmark test functions and five engineering design problems have shown that the new approach is efficient, effective and robust. The comparison results between the COMDE and the other 28 state-of-the-art evolutionary algorithms indicate that the proposed COMDE algorithm is competitive with, and in some cases superior to, other existing algorithms in terms of the quality, efficiency, convergence rate, and robustness of the final solution. [Copyright &y& Elsevier]

Abstract: In evolutionary multi-objective optimization (EMO), the convergence to the Pareto set of a multi-objective optimization problem (MOP) and the diversity of the final approximation of the Pareto front are two important issues. In the existing definitions and analyses of convergence in multi-objective evolutionary algorithms (MOEAs), convergence with probability is easily obtained because diversity is not considered. However, diversity cannot be guaranteed. By combining the convergence with diversity, this paper presents a new definition for the finite representation of a Pareto set, the B-Pareto set, and a convergence metric for MOEAs. Based on a new archive-updating strategy, the convergence of one such MOEA to the B-Pareto sets of MOPs is proved. Numerical results show that the obtained B-Pareto front is uniformly distributed along the Pareto front when, according to the new definition of convergence, the algorithm is convergent. [Copyright &y& Elsevier]

Abstract: Neuro-fuzzy approach is known to provide an adaptive method to generate or tune fuzzy rules for fuzzy systems. In this paper, a modified gradient-based neuro-fuzzy learning algorithm is proposed for zero-order Takagi–Sugeno inference systems. This modified algorithm, compared with conventional gradient-based neuro-fuzzy learning algorithm, reduces the cost of calculating the gradient of the error function and improves the learning efficiency. Some weak and strong convergence results for this algorithm are proved, indicating that the gradient of the error function goes to zero and the fuzzy parameter sequence goes to a fixed value, respectively. A constant learning rate is used. Some conditions for the constant learning rate to guarantee the convergence are specified. Numerical examples are provided to support the theoretical findings. [Copyright &y& Elsevier]