Comparative Study of Derivative Free Optimization Algorithms

Stable Iterative Correlation-based Tuning algorithm for servo systems

“…The stable iterative CbT algorithm presented in the previous section is applied to a class of servo systems defmed by the state-space model of the process { 0, iflu(t)l:S;ua, The actuator of this setup controls the DC motor by PWM, and it is modeled by the static nonlinearity according to (25).…”

“…for the processes modeled by (25) and (26). The step scaling parameters were chosen according to (22) with the initial step Yo = 8.10-23 [20].…”

“…and the step scaling parameter but it can also include a Gauss-Newton approximation of the Hessian. Other expressions of c.f.s can be defined [22]- [25] in terms of several models [26]- [29] .…”

Mathematical models for efficient medical electromagnetic tomography

“…the diffraction effect and the presence of evanescent waves at UHF and S bands are unavoidable limitations, the long computational time of EMT is due to the numerical formulation of the gradient-based optimization procedure utilized in every EMT system [27]- [28], discussed in Chapter I, II, and III. As these optimizations find the optimum values of "variables", rather than "parameters" [58], a moderate or high computational time is typically required to find these optimums. More precisely, if the shape, and dielectric properties of the stroke across the brain are unknown, they are considered as variables whose optimum values must be retrieved at every "pixel" of the image shown in Fig.…”

“…As far as the computational time is the main concern in the optimization procedure in comparison with accuracy, the NM optimization is usually the fastest method with respect to the other gradient-free optimizations [58]. Indeed, "This algorithm shows very promising results compared with other well-known evolutionary algorithms independent of gradients as the GA and PSO, where it outperforms these algorithms with much higher success rate and at least 10 to 100 times faster convergence" [58]. Regarding the stroke monitoring during CRP where time is life, NM optimization best suits the monitoring requirements.…”