Integer or mix integer objective function

Question

I'm a beginner in the maths field, however, I have read the classification of optimization problems yet I have a quick question regarding the problem type, so I have the following objectives

`obj_1=power * price * states; (states mean on and Off: binary variable)

obj_2= buying_energy - selling_energy; (all values are integer, with if-else conditions)

obj_3= char * cost+ dischar * cost; (all values are integer, with if-else conditions)

Objective function= obj_1+obj_2+obj_3

Minimize Objective function; obj_1,2, and 3 are related to 24-hour household energy consumption ` comment: I'm aiming to solve the problem through heuristic algorithms, however, still have some kind of doubts about the problem type due to my colleagues, I think it's an integer programming, non-linear convex problem, however, my colleagues question related to non-linearity and convexity of the problem. Can you help me to sort out this?

Answer 1

The easiest way is to use the "Solution Search" from MS Excel. The function is located on the "data" tab in the "Analysis" block (if you don't have this there, then you need to enable this function through the settings). Enter variables there (power,price, status, buying_energy, etc.), all restrictions on them (integers, bool, >0, <0, etc.), write down the target function, choose the solution method "Search for a solution by the GDG (generalized downward gradient) method" (your case).

P.S.:Is it true that the function sums a Boolean variable with integers?

Answer 2

If there are exists no multiplicative relation between 2 or more decision variables either in the objective or constraints or conditions your problem remains linear & convex. Else it's non-linear and depending upon if the constraints/objective or booth are nonlinear you may have models like quadratic programming, nonlinear models, quadratically constrained models etc.
Also some nonlinear relations can also be linearized & problem can be turned linear.