Many metrics are used to assess the quality of approximation found by metaheuristics. Two of them are used really often: distance to the true optimum according to its position and to its value.
Unfortunately, the objective function's shape can vary a lot in real-world problem, making these metrics difficult to interpret. For example, if the optimum is in a very deep valley (in value), a solution close to it in position may not signifiate that the algorithm have well learn the shape of it. Inversely, a solution close to an optimum in value may not signifiate that it is in the same valley.
One metric that can counter thse drawbacks is a distance taking into account the parameters of the problem as well as the value dimension.
Anyway, the question of the type of distance to use is dependent of the problem.