http://www.verticalfarm.com/moreIs it even feasible in terms of soil availability, and all the nutrients you need in the soil to be able to produce crops? As for putting farms in buildings, the main reason they're outside is because doing it without walls and a roof makes it dirt cheap. Unless people can put up with a major spike in staple foods it's not economically viable.
An average western family needs around 5000 square feet (I have the source if someone wants it) of garden to feed themselves solely on vegetables all year round. You could decrease this amount of space considerably with advanced but highly time intensive agricultural techniques, but the land needed to feed a small neighborhood is still beyond the scope of some of the largest buildings in most cities.
Even as food prices as they are, it's unlikely that this would be even feasible in terms of how costly making a multi-level automated building can be. The difference of maintenance costs between a standard outdoor farm and one that needs to be supported within a building is going to be significant. I find one of the boasts in the web sit: "VF creates sustainable environments for urban centers " to be exceedingly expensive to the tasks they are trying to perform. I don't think they have considered just how expensive land in urban centres are, and even land in towns compared to the sparsely populated country side. The amount of room you need, and the amount of buildings required to feed the a city entirely would likely take up a vast portion of the city itself. Then we have to consider that the website states that this should be a viable alternative when 80% of the earth's population is living in the cities themselves, can you imagine the property taxes alone, let alone the competition for the land inside of these cities.
Green houses do exist, and their yield per feet of ground is more than the average farm, but not astronomically more that on can take up the production of two or more normal farms. They're also usually one level due to the costs of building a multistory buildings. They're also built in the country side or away from agricultural centres due to the cost of land there.
You'd probably have more success relying on the techniques being developed right now, bioengineered crops will likely play a big role in the future. Improvement of aquaculture and already existing farming facilities would likely be a much cheaper and more feasible choice rather than devoting entire multistory buildings to this purpose. There are vast fields of parks that can be converted to farmland if need be. A great deal of the nations on this earth are also surrounded by vast coastlines, and though not every area is going to be suitable to aquaculture, there is a great deal of area that can be exploited here.