Genetic algorithm, transformation methods for the different objective function

I am using a genetic algorithm for the optimization of a thermodynamic cycle. The problem has no analytical solution and the solution space is computationally large. The question is the following: How can i combine 2 or more objective functions with different value range and dimensions into a single multi-objective function that has to be maximized or minimized? The usual methods involve some kind of normalization using minimum and maximum values of the single-objective functions. The problem is that it would take a significant amount of time to explore the solution space. Is there an alternative?

• What criteria do you have for the combination? What do you mean by a "multi-objective function"?
– D.W.
Apr 24, 2022 at 5:58
• Do you mean that the solution space is much smaller if there is only one objective function? Or do you mean it is much faster to find the solution if there is only one objective function? Apr 24, 2022 at 6:28
• @John L. It has to do with the way the values of the functions are calculates. It is time-consuming. What i want is to somehow bypass the calculation of min and max within a very large solution space. Apr 24, 2022 at 9:16
• @D.W. The following function is to be maximized: F(X)=w1*nth+w2*nex-w3*At, where nth is the thermal efficiency, nex the exergy efficiency and At the total heat exchanger surface respectively. w1,w2,w3 are the weight coefficients (weighted sum method). nth and nex are dimensionless and receive values between 0 and 1. At ranges roughly between 5 and 15 m^2. My question is how to combine single objective functions without having to calculate their min and max within the solution space. Some methods take into consideration the deviation from target values, which are unknown. Apr 24, 2022 at 9:21
• Please don't put clarifications in the comments. Instead, edit the question so it is self-contained and contains all information needed, and so it reads well for someone who encounters it for the first time. Thank you!
– D.W.
Apr 24, 2022 at 23:17