Slow being a little less than half the speed of light, thanks to getting a very large boost as they start their journey.
Slow down there!
At that speed it's not really a generation ship since you can get to many other stars within the original crews lifetime.
And there are hazards to going that fast.
Lets assume the ship is, say, 10X the mass of the worlds largest supertanker, that's very conservative for the numbers you talk about but it's a number to work with.
How do you slow down at all?
At 0.5 c that ship would have 7.197×10^25 joules of kinetic energy you'd need to get rid of if you want to slow down.
That's about 1800 times as much energy as the energy from entire worlds fossile fuel reserves. You need some kind of fuel and some plan for slowing down.
Hitting things in your path
If there's something the size and mass of a sugar cube in your path it hits the front of your ship with the energy of the nuclear bomb dropped on Hiroshima with all the energy pretty well focused to rip through any sane quantity of armor.
And that's not the only problem.
The atoms between the stars
using the figures for a cold neutral interstellar medium from wikipedia: 20—50 atoms/cm3
So let's go with 25 atoms/cm3
25000000 atoms per cubic meter.
Lets imagine the ship is a nice neat cylinder. We can treat the volume of space that the ship passes through as a cylinder with a cross section equal to that of the front of the ship.
Now lets look at how much it hits while traveling, say, 10 light years.
Treat it as a cylinder 10 light years long with the diameter of the ship, again, lets guesstimate that the ship has a radius of 100 meters.
This lets us estimate the total number of (almost all hydrogen) atoms in the path of the ship, lets assume they all hit and there's no shockwave effects:
946073047258080000000 π m^3 (cubic meters)
Multiply by 25000000 atoms per cubic meter.
mass of (946073047258080000000 * π *25000000 ) hydrogen atoms = 124.4 kilograms
so over the course of 10 light years it will impact with 124.4 kg kilograms of gas atoms. For simplicity I'm assuming all hydrogen.
Those atoms are hitting at .5c so the front of your ship (assuming it's a big round shield with radius 100m).
kinetic energy of 124.4 kilograms at .5c is 1.73×10^18 joules
I'm going to ignore time dilation because it's hard and I need to maintain my sanity.
so at .5 C it takes us 20 years to travel those 10 light years
So lets convert that into the energy of the gas hitting the front of the ship each hour.
1/24 (1/365 (1/20×1.73×10^18 J (joules))) = 9.8748×10^12 joules/h = 2.743 GW h (gigawatt hours) per hour
has to cope with 2.743 GW hours worth of energy hitting it every hour. It's like having a large nuclear power plant at the front of your ship producing heat. you have no way of getting rid of that much heat with your ship in a vacuum and it will be melting your heat shield.
So just slow down
It's really common for writers to throw around large fractions of light speed but without magitech shields there's massive practical problems with going that fast at all. At those speeds the fine mist of interstellar gas is enough to cook an astronaut to death just from being outside the ship unshielded and enough to destroy any shielding made of matter within a short time.
Since your ships are generation ships anyway you almost certainly want to slow your ships down to something sane like 0.05 C (or probably even lower if your crew want to continue to live)
At least then you have some chance of stopping and some chance of surviving if you hit some grains of sand in deep space.
Putting more ice or rock on the front of the ship does not help.
Lets imagine that we put a cylinder of solid ice 100 meters thick at the front of the ship as a shield.
it's an idea, I'll give you that, but lets work out how long it's likely to last at 0.5C ....
cylinder | radius 100 meters, height 100 meters = 3.14159×10^6 cubic meters
That's 3,141,590 cubic meters of ice, millions of cubic meters of ice.
Wolfram alpha gives a helpful table for this
Phase change energies for 3.14159×106 m3 of water from 25 °C:
energy required to heat to boiling point | 9.85×10^11 kJ (kilojoules)
energy required to convert to vapor | 7.01×10^12 kJ (kilojoules)
energy required to heat to boiling point and convert to vapor | 8×10^12 kJ (kilojoules)
energy released from cooling to freezing point | 3.28×10^11 kJ (kilojoules)
energy released from converting to solid | 1.05×10^12 kJ (kilojoules)
energy released from cooling to freezing point and converting to solid | 1.38×10^12 kJ (kilojoules)
It's annoying that it calculates from 25 degrees C but the energy released from cooling and energy needed to heat can just be added together.
Practically speaking I'm being very very forgiving by assuming that the energy needed is the same as at sea level.
To melt that much ice we could need 1.05×10^15 J (joules)
To turn that much ice into steam we would need about 7.01×10^15 J (joules)
Unfortunately the front of our ship would be receiving 1.975×10^13 J (joules) every hour while traveling at 0.5 C from impacts with the fine mist of atoms in interstellar space.
From there's it's just a matter of multiplying.
it would shield you for a little while....
Within 5 days your 3 million cubic meters of ice has melted.
after 34 days your ice has all turned into steam.
But what if we use something stronger than ice!
Lets imagine that instead of 3 million cubic meters of ice we make that shield out of 3 million cubic meters of solid iron!
It takes 6.11×10^15 J to melt 3 million cubic meters of solid iron.
Within 26 days enough energy has hit the front of your ship to melt 3 million cubic meters of iron.
This is not exactly how long your shield will last, some energy will be radiated away, some will be lost to cooking your crew and iron may ablate in a less simplistic manner but it's a rough ballpark figure.
At 0.5 C shields are not enough. Asteroids traveling at 0.5 C would melt and turn into a gas in short order.
I cannot stress enough how poor natural intuition is when it comes to the rigors put on anything traveling at large fractions of the speed of light.