Metaheuristics (for example, genetic algorithms) are applicable for any type of optimization problem, but especially those which are non-linear in nature. Modern mixed integer linear program solvers are impressively good, but the less linear a problem is, the harder it is to model as a MIP.

One practical consideration often ignored is difficulty of implementation. To make a MIP model, you only have the tools of linear programming: equations and linear inequalities, like mx >= y. If you want a MIP, you need to write down ALL aspects of your problem as a list of inequalities, which can be difficult for some real world domains. There is a real art to MIP modeling.

On the other hand, metaheuristics are like an interface where you only need to implement a few functions in plain old code and you can get good answers.

It’s not quite that simple, since there is still an art to modeling a problem in a suitable input format for a meta heuristic (for example in genetic algorithm, how do I write my delivery schedule as a genome?), but the upshot is that it doesn’t have to be a mathematically precise formulation to work correctly.