Roach traps work pretty well.

 

Stop squawkin, call Owkin!

 

Roaches are vastly more robust than flies and mosquitoes, and so the circuit shown will only give tjhem a tingle. And the problem with zapping them is that they can sense the electric field and stay clear of it. So the zapping scheme needs to have off times to allow them to enter an array that then switches on every so often to zap them. But then there is the problem of burning roaches, which is a fire hazard.

 

From the internet:

• One way to kill cockroaches is to use a mixture of sugar and boric acid. Mix three parts boric acid with one part sugar, and sprinkle it behind your appliances, under the sink, and into cracks along the edges of counters. The sugar will lure the cockroaches and the boric acid will kill them. You can also do this with equal parts sugar and baking soda.
• If you see a cockroach, and can quickly get to it, you can spray it with a mixture of soap and water. The soap will suffocate the roach.
• Put bay leaves in the areas where you’ve seen cockroaches. They hate the smell and will steer clear.
• Use a brush or empty ketchup bottle to apply diatomaceous earth around your baseboards. While safe for humans, the substance is lethal to cockroaches (and ants).
• Use a mixture of one tablespoon cayenne pepper powder, one crushed garlic clove, and one tablespoon of onion paste. Put it all in a spray bottle filled with water, let it sit for an hour before using, and then spray wherever you’ve seen cockroaches.
• Put a half-full jar of water in the areas where you know you have a roach problem. They’ll climb in, but won’t be able to get out.