Integrated multiple criteria decision-making framework for ranking Pareto optimal solutions of the multiobjective optimization problem of tuned mass dampers

Abstract

Tuned mass dampers (TMD) have demonstrated effectiveness and robustness in controlling vibrations in marine structures. Solutions to the TMD's Multi-objectives optimization problem (MOOP) always yield a set of Pareto compromise solutions for different conflicting objectives. However, because all the Pareto solutions are non-dominated, the solution of the MOOP still needs to be completed since a single Pareto solution must be selected from a large set of Pareto solutions. Researchers in the literature concentrated on obtaining the Pareto front by solving the MOOP of the TMD for different objective functions. Nonetheless, no effort has been put into selecting the best solution from the Pareto set. Therefore, this paper presents the novel application of the multiple-criteria decision-making (MCDM) techniques in the solution of the MOOP of the TMD applied to a marine structure. The presented framework ensures that the decision-makers (DMs) obtain the most optimal solution from the Pareto set of solutions of the TMD. In this paper, the problem of the TMD applied to a jacket platform is formulated as a MOOP, which comprises conflicting objectives related to TMD cost and performance. NSGA-II is utilized to find a large set of non-dominated TMD tuning parameters from which the DMs must select only one solution. Then, the DMs' preferences are prioritized using the Analytical Hierarchy Process (AHP). Meanwhile, the reasonableness of the DMs' preferences is assessed. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is utilized for ranking the non-dominated set of solutions by assessing the relative closeness of each solution to the ideal solution and farness away from the negative ideal solution. A Finite Element (FE) model of a fixed offshore platform under the dynamic disturbance of irregular waves is numerically solved using COMSOL multiphysics to assess the goals mentioned earlier. A TMD is applied to the marine structure to mitigate wave-induced vibrations. The hydrodynamic forces affecting the structure are computed using Morison's equation, and the irregular waves are characterized using the Joint North Sea Wave Project (JONSWAP) wave spectrum. The presented framework will be used for ranking the Pareto solutions of the TMD applied to the deck of the FE model. The TMD tuning parameters considered in this regard are the TMD mass ratio μ, damping ratio ξopt, and frequency ratio fopt. The findings indicate that the framework presented provides an efficient decision-making methodology for selecting the best solution in various design scenarios. These scenarios can be presented in 2D, 3D, or high-dimensional objective space. Meanwhile, the DMs will be able to select the best compromise among the objectives without the need for numerical judgments. As a result, an efficient TMD that provides valuable response mitigation in a low-cost and effective space was presented.