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Optimal design of stiffened plate subjected to combined stochastic loads
Published in C. Guedes Soares, Y. Garbatov, Progress in the Analysis and Design of Marine Structures, 2017
A three-step approach for design of stiffened plate that couples the reliability methods and structural optimization techniques is presented. Once the structural topology is defined, the scantling of the structural components of the stiffened plate is performed and optimized, in which the design variables, objective functions related to the minimum net sectional area, which leads to a minimum weight and minimum displacement and constraints, including the ultimate compressive strength are defined in a purely deterministic manner. Then the Pareto frontier is used to define the most suitable design solutions in minimizing both objective functions, satisfying all constraints. The design solutions at the Pareto frontier is then used as a basis for the reliability-based optimization regarding the target reliability level that is required to guarantee the structural integrity in which the limit state function is composed by the selected stochastically described design variables. This step accommodates the uncertainties related to the design variables and involved computational models.
The complex approach to optimization of composite bridges
Published in Jaap Bakker, Dan M. Frangopol, Klaas van Breugel, Life-Cycle of Engineering Systems, 2017
In addition to sensitivity analysis, the Pareto frontier was obtained from the calculated results. Pareto frontier is a surface formed by optimal solutions in accordance to Pareto optimality state. It is defined as a trade-off between non-dominant solutions in which it is impossible to make any individual cost function better without making at least one individual cost function worse off. It was defined by V. Pareto (1848–1923).
Integrated LCA and LCCA network level pavement maintenance model
Published in Maurizio Crispino, Pavement and Asset Management, 2019
J. Cirilovic, G. Mladenovic, C. Queiroz
The Pareto frontier, as shown in Figure 7, represents the set of “optimal” solutions which provides a clearer outlook on the trade-off between the two solutions based on cost and CO2 emissions, as a relative distance between solutions.
Multi-objective optimisation for sustainable few-to-many pickup and delivery vehicle routing problem
Published in International Journal of Production Research, 2023
Francesco Pilati, Riccardo Tronconi
Since the analysis of this frontier is non-trivial, the three bi-dimensional views are also shown, in which two objective functions are represented in the axes while the third one is represented through a colour bar (Figure 7). Pareto frontier is a support for practitioners in the decisions-making process and, thus, the selection of the trade-off solution depends on the importance that they assign to each objective function. Indeed, managers can undergo the right decision on the solution to adopt according to the importance they assign to each sustainability aspect. As sake of exemplification, Figure 7(a,b) shows that, if it is supposed to assign the same relevance to each objective function, it is possible to improve drastically the social performance with a limited worsening in the economic and environmental ones by moving from the solution in the circle to the solution in the square. In detail, through a worsening of 0.04% in economic and 0.36% in environmental objective functions, practitioners can improve the social performance of their e-commerce platform by 18.3%. Figure 7(c), instead, clearly shows the relation between the economic and the environmental objective functions.
Multi-objective spur gear design using teaching learning-based optimization and decision-making techniques
Published in Cogent Engineering, 2019
Edmund S. Maputi, Rajesh Arora
A Pareto frontier is a curve of points representing a range of possible solutions whose optimality is based on the designer’s preference (Messac, 2015). In multi-objective design optimization, the articulation of objective weights or preferences may be done prior to optimization, during or after the optimization process. Respectively, these methods are defined as “a priori”, progressive and “posteriori” articulation (Messac, 1996). “A priori” articulation assumes a particular weighting ratio which could be biased towards a particular solution which may not be the true optimal value. Similarly, progressive articulation adjusts the weighting during the optimization stage so as to approach a specific value. The bias associated with the previously mentioned methods is eliminated by posteriori articulation which investigates a range of optimal solutions to determine the optimum values.
Multi-objective optimal computer-aided engineering of hydraulic brake systems for electrified road vehicles
Published in Vehicle System Dynamics, 2022
Pier Giuseppe Anselma, Giovanni Belingardi
A multi-target optimisation framework is then considered in overall down-sizing the hydraulic brake system while maximising the energy recovery capability of the BEV in everyday driving conditions. The brake system layout is particularly optimised to enhance the energy recovery potential in WLTP as representative of a common driving environment. A PSO algorithm is adopted for selecting the right sizes of components, while the simulation of safety standard braking maneuvers ensures that only sizing candidates capable of complying with regulatory requirements are considered. The optimal Pareto frontier can then be obtained by repeating the optimisation workflow while sweeping different weights for size cost term and energy cost term.