Tranditionally the problems of parameter estimation of soft sensing model are solved by using the traditional gradient methods to optimize the nonlinear least squares models. However

there exist the disadvantages of the dependence on the initial solution

the requirement of additional trend analysis to verify model correctness and the insufficiency in solving complex problems. Therefore

a new idea of transforming the original parameter estimation problem into a constrained optimization problem and using a hybrid optimization algorithm to solve it is developed. An adaptive hybrid particle swarm optimization algorithm for constrained optimization problems (AHPSO-C) is proposed. In AHPSO-C

an update strategy of maximum function evaluations for the interior-point method (IPM) is imported to balance the global search (chaotic particle swarm optimization) and local search (IPM). The simulation results for the 12 classic benchmark functions indicate that AHPSO-C is an effective algorithm for solving constrained optimization problems. The feasibility and superiority of the method is illustrated with the challenging parameter estimation of soft sensing model for melt index in a cascade slurry HDPE reaction process.