Ranking and sorting the Pareto front in optimal shell structure design: integration of the AHP method

Here is a spreadsheet that formulates the AHP method for a three-by-three matrix. The inputs are DM’s preferences over the objective functions (only three elements should be determined, and the other elements are determined based on the relation between elements, as mentioned in the method section). This spreadsheet calculates the CR, CI, λ_max, the maximum eigenvalue, M_i, and w_i for the matrix and performs the required checks. Additionally, this spreadsheet will calculate the normalized weight coefficient (w_i-norm.)

Additionally, in another spreadsheet, the result (Pareto front) of Case Study I of the published paper at the Journal of Frontier of Architectural Research is reported. The users can construct a judgment matrix and calculate the weights using the first spreadsheet, then utilize it to rank and sort the Pareto front (with the second spreadsheet) based on their preferences. (There are 125 unique matrices feasible for this case study.) Moreover, this spreadsheet allows users to choose between three different methods of normalizing the values (objective functions), as discussed in Section 4.5.

In addition, the pseudocode for the integration of multi-objective optimization and the AHP method (the proposed methodology in this journal paper) is provided.

Any other data related to this research will be available upon request.