Ranking and sorting the Pareto front in optimal shell structure design

The Pareto front is a collection of optimal solutions and trade-offs between objective functions without hierarchy. The challenge lies in selecting a single solution from this set for design development. This research utilizes a unique method that integrates multi-objective optimization (MOO) with the Analytic Hierarchy Process (AHP) method to score, rank, and sort the solutions of the Pareto front. First, a judgment matrix is created and evaluated based on the decision-maker's (DM) preferences over objective functions. Then, weight coefficients are derived from the judgment matrix to score and rank each solution in the Pareto front, allowing the sorting. The efficiency of this method was evaluated and discussed in two case studies of a complex, lightweight, continuous concrete shell structure, considering various design criteria that encompassed structural, acoustic, and energy performance. Additionally, the proposed method is compared with the weighted sum method. Combining MOO with the AHP enhances optimization and facilitates more effective interaction between the decision-maker and the optimal solution-finding process. This method enables a trade-off among criteria to solve a complex design problem. The DM's preferences guide the ranking process, and their active involvement ensures that the final solution aligns with the project's requirements and preferences.