There are various pest risks in kitchens, for instance ants, flies and cockroaches. Many countermeasures include killing the animals. What vegan methods of pest control are there?
Keep everything clean of food and water, to prevent them from moving in where there is sustenance. Make sure that openings to outdoors are sealed. For flies and bigger bugs like cockroaches, you can transport them outside (maybe a ways away so they don't just come back), near some shelter/food, so they'll remain where you leave them.
I don't mind house spiders (they'll eat the flies). Centipedes can be scary, but they also do a great job of pest control - eating ants for example, so I usually try to put them in my garden if I find them in my house; although if you have ants in your house, a centipede might be a solution! (Centipedes can sting humans, but usually don't, and it's not a dangerous sting).
Ants - the small "sugar ants" you will see are usually a symptom of having food sources accessible to them. Of course removing (or killing) those little ants won't do much, since they have a colony centered elsewhere. Key is removing their sustenance, and another trick is to thoroughly wipe clean their trails. Since they use scent to navigate back to food sources, if you clean the surfaces, it will slow them down if the trail is gone. You can also use something with capsaicin (spicy peppers) and coat certain key areas where you want them "not to walk" but I've only had mixed success with that technique.
Keeping dry goods (flour, grains, sugar...), especially those that are only infrequently accessed, in truly airtight containers (bail lock jars, clip lock plastic boxes etc.), will make sure that such foods are not infested by eg moths or ants, and that infestations can be easily kept from spreading to other containers. Also, in case there is a pest problem that needs major cleaning, these can be washed from the outside without damaging the contents.