I feel like the resulting shape is more of a fluke here.
> The performance of the wheel was based on the final speed achieved by an accelerating imaginary car, vf. The wheel was driven with a constant torque, τ, and no slipping.
There is nothing in this fitness value that defines the shape of the wheel. As described here, there's no clear reason why the shape of the wheel would affect the speed of a car (no slip, no taking into account up/down movement of the car, etc.) Rather this algorithm seems to optimize for a certain radius and the circular shape is the result of the fact that all points converge to the same optimum.
I also find the fact that it converges at a finite radius using this model suspicious. If you look at this optimization problem analytically, the optimum is obviously a wheel with a zero radius: Force on car is torque over wheel radius. If radius goes to zero, then force goes to infinity and acceleration goes to infinity and car speed goes to infinity.
It doesn't take the vertical movement of the car into account directly, but that cosine term in the force does mean that having to raise the car (or lower the car) saps it of effective torque.
Also, the wheel spoke lengths are normalized, so the wheel can't grow or shrink overall.
I feel the same thing. It's basically optimizing the "gear ratio" to get maximum speed. The wheel isn't centered because it doesn't complete an integer number of revolutions during the simulation.
I'm still scratching my head while trying to figure out what's the mechanism that prevents the solution blowing up to infinity by setting the radius to zero and therefore achieving huge accelerations from a constant torque.
> The performance of the wheel was based on the final speed achieved by an accelerating imaginary car, vf. The wheel was driven with a constant torque, τ, and no slipping.
There is nothing in this fitness value that defines the shape of the wheel. As described here, there's no clear reason why the shape of the wheel would affect the speed of a car (no slip, no taking into account up/down movement of the car, etc.) Rather this algorithm seems to optimize for a certain radius and the circular shape is the result of the fact that all points converge to the same optimum.
I also find the fact that it converges at a finite radius using this model suspicious. If you look at this optimization problem analytically, the optimum is obviously a wheel with a zero radius: Force on car is torque over wheel radius. If radius goes to zero, then force goes to infinity and acceleration goes to infinity and car speed goes to infinity.