# Can I combine two objective functions if they have a relation between them?

I will use a meta-heuristic algorithm, to maximize the following objective functions:

• Objective function 1 $$=\sum\limits_{r=1}^{M} \sum\limits_{s=r+1}^{M} \sum\limits_{j=r+1}^{N} (r_{rj}w_j - r_{sj}w_j)$$

• Objective function 2 $$= \sum\limits_{j=r+1}^{N} [(2w_1r_{1j} ) + (0.5w_2r_{2j})+(1w_3r_{3j}) ]$$

subject to:

• $$0 \le w_1, w_2, w_3 \le 10$$
• $$w_1+ w_2+ w_3 = 10$$

Can I combine two objective functions if they have a relation between them? Or consider the problem as a multi-objective optimization problem?

• What have you tried? Did you review any textbook, tutorial, class notes or similar examples? What do you think - based on intuition - the answer should be? And why? – dhasson Nov 12 '20 at 11:29