```python
import numpy as np
from simsopt.geo.surfacerzfourier import SurfaceRZFourier
from simsopt.field.biotsavart import BiotSavart
from simsopt.field.coil import Current, Coil, ScaledCurrent
from simsopt.geo.curve import curves_to_vtk
from simsopt.objectives.fluxobjective import SquaredFlux
from simsopt.optimize.objectives import LeastSquaresProblem
from scipy.optimize import minimize
from simsopt.geo.curvecorrected import CurveCorrected
from simsopt.geo.curve import curves_to_multifilaments, create_equally_spaced_curves

# Initialize the boundary magnetic surface
nfp = 1  # Number of field periods
nphi = 16
nzeta = 16
surface = SurfaceRZFourier(nphi=nphi, nzeta=nzeta, nfp=nfp, mpol=3, ntor=3)
surface.set_coeffs(np.random.randn(*surface.coeffs.shape))

# Create equally spaced curves and multifilament grid
num_curves = 3
num_filaments_per_curve = 10
curves = create_equally_spaced_curves(surface, num_curves, num_filaments_per_curve)
multifilament_curves = curves_to_multifilaments(curves, num_filaments_per_curve)

# Apply stellarator and rotation symmetries
for curve in multifilament_curves:
    curve.kappa = 1.0
    curve.tau = 0.0

# Define the Biot-Savart law
coils = [Coil(curve, current=Current(1e6)) for curve in multifilament_curves]
bs = BiotSavart(coils)
bs.set_points(surface.gamma().reshape((-1, 3)))

# Define the objective function
flux_obj = SquaredFlux(surface, bs)
length_penalty = sum([c.length() for c in multifilament_curves])
coil_distance_penalty = sum([np.linalg.norm(c1.X - c2.X) for c1 in multifilament_curves for c2 in multifilament_curves if c1 != c2])

def objective(x):
    for curve, xi in zip(multifilament_curves, np.array_split(x, len(multifilament_curves))):
        curve.x = xi
    bs.clear_cached_properties()
    return flux_obj.J() + 1e-4 * length_penalty + 1e-5 * coil_distance_penalty

# Perform a Taylor test
x0 = np.concatenate([c.x for c in multifilament_curves])
problem = LeastSquaresProblem(objective, x0)
problem.taylor_test()

# Run the optimization
res = minimize(problem.fun, x0, method='L-BFGS-B', jac=problem.jac, options={'disp': True})

# Update the coil positions based on optimization results
for curve, xi in zip(multifilament_curves, np.array_split(res.x, len(multifilament_curves))):
    curve.x = xi

# Save the output in VTK format
curves_to_vtk(multifilament_curves, "optimized_coils.vtk")
```