# How to normalize the objective functions of multi-objective optimization into uniform form?

In my bi-objective model, the range of solution value for the first objective is large than the second objective. I decide to obtain a single solution by the weighted sum approach and solve it using metaheuristics. How can I do that?

There is another approach which is similar but might produce a different solution. It involves first optimizing each objective separately, again scaling them as needed to make their magnitudes comparable. If $$z_1^*$$ and $$z_2^*$$ are the optimal values of the two scaled objectives, we refer to the point $$z^* = (z_1^*, z_2^*)\in \mathbb{R}^2$$ as the "utopia point". The objective function for the metaheuristics is then to minimize the norm of the distance of the scaled objective values $$(z_1, z_2)$$ from the utopia point, using your favorite norm (1-norm, 2-norm, infinity-norm).