For the fitting curve without penalty function
in Figure 5(a), a serious overfitting problem occurs due to great data fluctuation.
where [phi](t) := [|t|.sup.p] is a penalty function
with p [member of] (0, 2], sparsity-inducing for p < 1, and [beta] := [beta](x), [beta] : [OMEGA] [right arrow] [0,1], is an adaptive function which approaches zero at the high curvature points of [OMEGA].
Valve point effect and a penalty function
for generator active power violations are added to quadratic cost function in order to provide the more appropriate simulation of fuel cost.
Keywords: derivative free methods, penalty function
, structural optimization, truss structure, unconstrained optimization.
We design penalty function
for constrained optimization problems by following the guidelines suggested by Richard Sen et al.
is one of the most effective methods to solve the evolutionary constraint optimization problem [21-25].
To take into account constraints on intermediate coordinates value of the following penalty function
In addition, the standard LSO employed a penalty function
to preserve feasibility of the encountered solutions.
as the penalty function
, where A e Rsxm is a weighting matrix with full column rank and satisfies [lambda]([[LAMBDA].sup.T][LAMBDA]) < 1, where [lambda](*) denotes the eigenvalue of a matrix.
In this work, to solve our formulated constrained optimization problem we have converted it into an unconstrained optimization problem by penalty function
In the course of settlement about model constraints, adopting penalty function
to reduce the fitness ability of individuals that don't not satisfy constraints, then their reproducing can be controlled.