I don’t live in a Publix area and I have never had a roach. Carpenter ants, on the other hand abound in my area. I have to pay the exterminator every spring and fall to keep them away from my home.
I get them in my kitchen window every spring, I put out the little ant baits in between the inside and outside window, and with in a few days no more ants. For outside I use 10% 7 Dust is the best product to use. I use it on my green bean plants, when I notice holes in the leaves.
They climb up the columns of the house to get into the gutters. So I dust the base of the columns with the 7 dust.
We have more of a problem with the saw palmento bugs flying into the house. Find them belly up in the morning.