This research is based on the determination of the parameters of the PID and fractional-order PID controllers designed for quarter-car suspension system. Initially, without considering the active suspension structure, the performance of the passive suspension system under different wheel load index is presented by using the transfer function of the system. Then, by adding a wheel-load, the classical PID controller is designed and applied to the current controlled hydraulic actuator as a part of active suspension system. The parameters of this controller are determined by three heuristic optimization algorithms; Particle Swarm Optimization (PSO), Differential Evolution (DE) and Gravitational Search Algorithm (GSA). As the second part of this study after evaluating the performance of classical PID controller, fractional-order PID controller is designed and applied to the problem to improve the performance of the classical PID controller. Similarly, the parameters of this controller are also obtained by using the same optimization algorithms. In the paper, for modeling the road, instead of sinusoidal (road with hill) or random changes, a saw tooth signal is preferred as a relatively harder condition. Implementation results are showed that the performance of the fractional-order PID controller is much better that PID controller and also instead of relatively complex and expensive controller, it is possible to use fractional-order PID controller for the problem.

Multimodal problems are related to locating multiple, redundant global optima, as opposed to single solution. In practice, generally in engineering problems it is desired to obtain many redundant solutions instead of single global optima since the available resources cannot be enough or not possible to implement the solution in real-life. Hence, as a toolbox for finding multimodal solutions, modified single objective algorithms can able to use. As one of the fundamental modification, from one of the niching schemes, crowding method was applied to Differential Evolution (DE) algorithm to solve multimodal problems and frequently preferred to compared with developed methods. Therefore, in this study, eight different DE are considered/evaluated on ten benchmark problems to provide best possible DE algorithm for crowding operation. In conclusion, the results show that the time varying scale mutation DE algorithm outperforms against other DE algorithms on benchmark problems.