[xaedes]

The problem you describe is known as "multi objective optimization".

Normalizing the input data to similar ranges usually helps, but there is no single golden rule how to weight. It depends on what you want to accomplish.

But regardless of any weighting in multi objective optimization problems there is a subset of all items (apartments in your case) that is better then all the items not in this set. This set is called the "pareto front". There are methods to compute this set.

You can't decide which item of the pareto front is better than another; it is a rock, scissors, paper situation. But the pareto front can exclude a lot of items, that you then don't need to consider. These items are worse in every aspect (optimization objective) than any item from the pareto front.

As a computer science student we often used population based optimization methods for dealing with multi objective optimization. For example ant colony optimization or evolutionary algorithms.