Evolutionary heuristic algorithms attempt to biologically emulate the adaptive evolutionary nature of living beings via different procedures. This work proposes new mechanisms for improving the performance-complexity tradeoff of the evolutionary Particle Swarm Optimization (PSO) algorithm applied to parameter estimation of a three-phase induction motor problem subject to the operational changing of motor parameters during its operation. The proposed variant, namely the Halton-Chaos-$\beta$-PSO algorithm, resolves the parameter estimation problem faster and with minor errors than the conventional PSO. An analytical-iterative-heuristic variant combining the augmented Lagrangian method (ALM) and PSO (ALPSO) demonstrated good performance-complexity trade-off, particularly under online operation, with instantaneous (on-fly) modification of the motor parameters. Additionally, the ALM combined with a quasi-Newton method and the PSO hybridization with the gravitational search algorithm (PSOGSA) was evaluated. The efficiency and effectiveness of the proposed hybrid analytical-iterative-heuristic methods are corroborated by extensive numerical simulation results, considering heuristic input parameters tuning, which have revealed a remarkable reduction in the error estimation values when the estimation procedure is deployed dynamically in real-time applications.