Nonlinear constrained optimization using the flexible tolerance method hybridized with different unconstrained methods

This paper proposes the use of the flexible tolerance method(FTM) modified with scaling of variables and hybridized with different unconstrained optimization methods to solve real constrained optimization problems.The benchmark problems used to analyze the performance of the methods were taken from G-Suite functions.The original method(FTM) and other four proposed methods:(i) FTM with scaling of variables(FTMS),(ii) FTMS hybridized with BFGS(FTMS-BFGS),(iii) FTMS hybridized with modified Powell's method(FTMS-Powell)and(iv) FTMS hybridized with PSO(FTMS-PSO), were implemented. The success rates of the methods were 80%,100%, 75%, 95% and 85%, for FTM, FTMS, FTMS-BFGS, FTMS-Powell and FTMS-PSO, respectively. Numerical experiments including real constrained problems indicated that FTMS gave the best performance, followed by FTMSPowell and FTMS-PSO. Despite the inferior performance compared to FTMS and FTMS-Powell, the FTMS-PSO method presented some advantages since good different initial points could be obtained, which allow exploring different routes through the solution space and to escape from local optima. The proposed methods proved to be an effective way of improving the performance of the original FTM.

Improved cat swarm optimization for parameter estimation of mixed additive and multiplicative random error model

To estimate the parameters of the mixed additive and multiplicative(MAM)random error model using the weighted least squares iterative algorithm that requires derivation of the complex weight array,we introduce a derivative-free cat swarm optimization for parameter estimation.We embed the Powell method,which uses conjugate direction acceleration and does not need to derive the objective function,into the original cat swarm optimization to accelerate its convergence speed and search accuracy.We use the ordinary least squares,weighted least squares,original cat swarm optimization,particle swarm algorithm and improved cat swarm optimization to estimate the parameters of the straight-line fitting MAM model with lower nonlinearity and the DEM MAM model with higher nonlinearity,respectively.The experimental results show that the improved cat swarm optimization has faster convergence speed,higher search accuracy,and better stability than the original cat swarm optimization and the particle swarm algorithm.At the same time,the improved cat swarm optimization can obtain results consistent with the weighted least squares method based on the objective function only while avoiding multiple complex weight array derivations.The method in this paper provides a new idea for theoretical research on parameter estimation of MAM error models.