Modified quantum-behaved particle swarm optimization for parameters estimation of generalized nonlinear multi-regressions model based on Choquet integral with outliers

In this paper, a generalized nonlinear multi-regression model based on Choquet integral (NMRCI) is proposed and applied for estimation of non-additive systems that include outliers under inherent interaction among inputs. The parameters estimation for the proposed model is also performed via a modified algorithm based on particle swarm optimization with quantum-behavior (QPSO), named MQPSO. From the proposed model, the high breakdown regression estimator, a least trimmed squares (LTS) is applied to eliminate the influence caused by these observations that contain outliers. Besides, elitist crossover of genetic algorithm (GA) and adaptive decay of simulated annealing (SA) are used for conquering premature and controlling search policy, respectively. Hence, the proposed MQPSO algorithm which combines the mechanisms of GA, SA and LTS within the QPSO algorithm can deal with the proposed model with outliers. From simulation results, the proposed MQPSO readily corrects the deviation caused by outliers without losing precisions and swiftly achieves convergences on estimating the parameters of the proposed generalized NMRCI model for the non-additive systems with outliers.