A Class Of Improved Whale Optimization Algorithms And Their Applications On Parameter Estimation Problems Of Nonlinear Systems

Swarm intelligent optimization algorithm is a class of optimization algorithms which are based on the intelligent behaviors of animals in the nature.Compared with conventional optimization algorithms,swarm intelligent optimization algorithms have high self-adaptivity and high versatility.Since they have no specific requirements on the optimization problems,such as the differentiability,the convexity and the linearity,it can be widely used to solve various sophisticated problems.But the balance between the exploration and the exploitation is a milestone for such algorithms,the algorithms with high exploration capacity are prone to have a low accuracy,while the algorithms with high exploitation capacity are more likely to stagnate into local optima.Therefore,it is always necessary to adapt the algorithms according to specific problems.Meanwhile,according to No-Free-Lunch Theorems:there is no omnipotent algorithm for all systems.Therefore,it is of great interest to deign appropriate algorithms for different systems,in pursuit of improving the performance of algorithms.Whale Optimization Algorithm(WOA)is a type of swarm intelligent optimization algorithms.It mimics the foraging behavior of whales,and it has proved its efficiency in solving multi-modal and uni-modal problems.In order to further ameliorate the optimization capacity of this algorithm,in this thesis,a series of improved WOAs were developed,their performance was validated via solving the parameter estimation problems of various integral nonlinear systems and fractional nonlinear systems,their superior performance was proved by rigorous numerical experiments and statistical analysis.The main contents of this thesis include:1.A Hybrid Whale Optimization Algorithm(HWOA)based on performance learning and its application on the parameter estimation problemsSince WOA is more likely to choose exploitation operator during its last few iterations,leading to its premature,and its updating mechanism is relatively simple,we proposed a Hybrid Whale Optimization Algorithm(HWOA)which was integrated with a general normal distribution optimization algorithm and a performance-learning mechanism.In order to prove the efficiency of HWOA,it was applied to solve the parameter estimation problem of integral and fractional photovoltaic systems.The results showed that HWOA had high robustness and accuracy,and it had a high convergence speed.2.A Q-Learning based Whale Optimization Algorithm(QWOA)and its application on the parameter estimation problemsThough HWOA has shown certain improvement on accuracy,its adaptive mechanism is relatively simple，which is not flexible enough to adapt to systems with frequent changes.In order to improve the adaptivity of WOA on the parameter identification problems of such systems,in this thesis,reinforcement learning method is considered to ameliorate the overall performance of WOA,a Q-learning based Whale Optimization Algorithm(QWOA)was developed to solve the calibration of car-following models.Based on the analysis of the results obtained by numerical experiments on nonlinear car following models,it could be found that QWOA not only had a high accuracy but also had the capacity to learn the optimal strategy via interacting with the testing environment,it demonstrated a high adaptivity.3.An Improved Surrogate-assisted Whale Optimization Algorithm(ISAWOA)and its application on the parameter estimation problemsBased on previous results of HWOA and QWOA，it was found that these two algorithms have relatively high computational complexity when it came to the parameter optimization problems of fractional nonlinear systems.In this study,aiming to design an algorithm which is not only efficient but also requires less CPU time，an Improved Surrogate-Assisted Whale Optimization Algorithm(ISAWOA)was developed.Levy flight and a quadratic interpolation operator were integrated to the designation of this algorithm.Then,a surrogate model was combined with WOA,with the purpose of reducing the evaluation time on the real simulator,resulting in the reduction of CPU time.Via tests on benchmark functions and several fractional chaotic systems,ISAWOA not only showed a high accuracy and a high convergence speed，it also reduced the CPU time significantly in comparison with other algorithms.ISAWOA was a promising swarm intelligent algorithm in coping with the problems requiring high computational budget.The innovation of this thesis is:it integrated different modification strategies into the design of WOA and extended the application of such algorithm to the parameter estimation problems of different nonlinear systems in various fields.On the one hand,this research enhanced the overall performance of WOA,meanwhile it improved the adaptivity，the practicability and the efficiency of this optimization algorithm,which could provide a reference for the design of swarm intelligent algorithms.On the other hand,the study provided several efficient approaches for the parameter estimation problems of nonlinear systems,facilitating the modeling and optimal management of nonlinear systems.