Single-objective and Multi-objective Robust Optimization of Airfoils using Adjoint Solutions

2014 ◽  
Author(s):  
Giovanni Petrone ◽  
Chris Hill
Keyword(s):  
Robust Optimization ◽  
Multi Objective ◽  
Adjoint Solutions ◽  
Single Objective

An Efficient Multi-Objective Robust Optimization Method by Sequentially Searching From Nominal Pareto Solutions

2021 ◽  
Vol 21 (4) ◽  
Author(s):  
Tingting Xia ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Computational Time ◽  
Pareto Solutions ◽  
Worst Case ◽  
Multi Objective ◽  
Pareto Points ◽  
Single Objective

Abstract Multi-objective optimization problems (MOOPs) with uncertainties are common in engineering design. To find robust Pareto fronts, multi-objective robust optimization (MORO) methods with inner–outer optimization structures usually have high computational complexity, which is a critical issue. Generally, in design problems, robust Pareto solutions lie somewhere closer to nominal Pareto points compared with randomly initialized points. The searching process for robust solutions could be more efficient if starting from nominal Pareto points. We propose a new method sequentially approaching to the robust Pareto front (SARPF) from the nominal Pareto points where MOOPs with uncertainties are solved in two stages. The deterministic optimization problem and robustness metric optimization are solved in the first stage, where nominal Pareto solutions and the robust-most solutions are identified, respectively. In the second stage, a new single-objective robust optimization problem is formulated to find the robust Pareto solutions starting from the nominal Pareto points in the region between the nominal Pareto front and robust-most points. The proposed SARPF method can reduce a significant amount of computational time since the optimization process can be performed in parallel at each stage. Vertex estimation is also applied to approximate the worst-case uncertain parameter values, which can reduce computational efforts further. The global solvers, NSGA-II for multi-objective cases and genetic algorithm (GA) for single-objective cases, are used in corresponding optimization processes. Three examples with the comparison with results from the previous method are presented to demonstrate the applicability and efficiency of the proposed method.

Multi-Objective Robust Optimization Formulations With Operational Flexibility and Discretized Uncertainty

2016 ◽  
Author(s):  
Shapour Azarm ◽  
Yu-Tai Lee
Keyword(s):  
Robust Optimization ◽  
Black Box ◽  
Optimized Design ◽  
Operational Flexibility ◽  
Deterministic Optimization ◽  
Numerical Examples ◽  
Multi Objective ◽  
Operational Variables ◽  
Single Objective

Traditional robust optimization formulations can be considered to be “passive” in the sense that they can obtain optimized design and operational solutions for a system for all realizations of uncertainty. However, flexibility in the system’s operation can be used to devise formulations that obtain solutions that are optimum for all realizations of uncertainty while operational variables are used to mitigate or eliminate the effects of uncertainty. The objective of this paper is to extend existing formulations in single-objective robust optimization to multi-objective robust optimization with or without operational flexibility under discretized uncertainty. The formulations with operational flexibility are referred to as flexible optimization. The flexible optimization formulations and corresponding solutions are demonstrated and compared with those from robust and deterministic optimization formulations using numerical examples, and an engineering example with black-box objective and constraint functions.

An Efficient Multi-Objective Robust Optimization Method by Sequentially Searching From Nominal Pareto Solutions

2020 ◽  
Author(s):  
Tingting Xia ◽  
Mian Li
Keyword(s):  
Robust Optimization ◽  
Pareto Front ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Pareto Solutions ◽  
Worst Case ◽  
Multi Objective ◽  
Pareto Points ◽  
Engineering Design Problems ◽  
Single Objective

Abstract Multi-objective optimization problems (MOOPs) with uncertainties are common in engineering design problems. To find the robust Pareto fronts, multi-objective robust optimization methods with inner-outer optimization structures generally have high computational complexity, which is always an important issue to address. Based on the general experience, robust Pareto solutions usually lie somewhere near the nominal Pareto points. Starting from the obtained nominal Pareto points, the search process for robust solutions could be more efficient. In this paper, we propose a method that sequentially approaching to the robust Pareto front (SARPF) from the nominal Pareto points. MOOPs are solved by the SARPF in two optimization stages. The deterministic optimization problem and the robustness metric optimization problem are solved in the first stage, and nominal Pareto solutions and the robust-most solutions can be found respectively. In the second stage, a new single-objective robust optimization problem is formulated to find the robust Pareto solutions starting from the nominal Pareto points in the region between the nominal Pareto front and the robust-most points. The proposed SARPF method can save a significant amount of computation time since the optimization process can be performed in parallel at each stage. Vertex estimation is also applied to approximate the worst-case uncertain parameter values which can save computational efforts further. The global solvers, NSGA-II for the multi-objective case and genetic algorithm (GA) for the single-objective case, are used in corresponding optimization processes. Two examples with comparison to a previous method are presented for the applicability and efficiency demonstration.

Introducing Robustness in Multi-Objective Optimization

2006 ◽  
Vol 14 (4) ◽  
pp. 463-494 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Himanshu Gupta
Keyword(s):  
Robust Optimization ◽  
Global Optimum ◽  
Test Problems ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Small Perturbations ◽  
Multi Objective ◽  
Engineering Design Problem ◽  
Second Procedure ◽  
Single Objective

In optimization studies including multi-objective optimization, the main focus is placed on finding the global optimum or global Pareto-optimal solutions, representing the best possible objective values. However, in practice, users may not always be interested in finding the so-called global best solutions, particularly when these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the robust solutions which are less sensitive to small perturbations in variables. Although robust optimization is dealt with in detail in single-objective evolutionary optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find a robust frontier, instead of the global Pareto-optimal frontier in a problem. The first procedure is a straightforward extension of a technique used for single-objective optimization and the second procedure is a more practical approach enabling a user to set the extent of robustness desired in a problem. To demonstrate the differences between global and robust multi-objective optimization principles and the differences between the two robust optimization procedures suggested here, we develop a number of constrained and unconstrained test problems having two and three objectives and show simulation results using an evolutionary multi-objective optimization (EMO) algorithm. Finally, we also apply both robust optimization methodologies to an engineering design problem.

scholarly journals Study on coloring method of airport flight-gate allocation problem

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Hongyan Li ◽  
Xianfeng Ding ◽  
Jiang Lin ◽  
Jingyu Zhou
Keyword(s):  
Graph Coloring ◽  
Programming Model ◽  
Weight Vector ◽  
Multi Objective ◽  
Average Value ◽  
Two Factors ◽  
Minimum Number ◽  
First Come First Serve ◽  
Airport Terminals ◽  
Single Objective

Abstract With the development of economy, more and more people travel by plane. Many airports have added satellite halls to relieve the pressure of insufficient boarding gates in airport terminals. However, the addition of satellite halls will have a certain impact on connecting flights of transit passengers and increase the difficulty of reasonable allocation of flight and gate in airports. Based on the requirements and data of question F of the 2018 postgraduate mathematical contest in modeling, this paper studies the flight-gate allocation of additional satellite halls at airports. Firstly, match the seven types of flights with the ten types of gates. Secondly, considering the number of gates used and the least number of flights not allocated to the gate, and adding the two factors of the overall tension of passengers and the minimum number of passengers who failed to transfer, the multi-objective 0–1 programming model was established. Determine the weight vector $w=(0.112,0.097,0.496,0.395)$ w = ( 0.112 , 0.097 , 0.496 , 0.395 ) of objective function by entropy value method based on personal preference, then the multi-objective 0–1 programming model is transformed into single-objective 0–1 programming model. Finally, a graph coloring algorithm based on parameter adjustment is used to solve the transformed model. The concept of time slice was used to determine the set of time conflicts of flight slots, and the vertex sequences were colored by applying the principle of “first come first serve”. Applying the model and algorithm proposed in this paper, it can be obtained that the average value of the overall tension degree of passengers minimized in question F is 35.179%, the number of flights successfully allocated to the gate maximized is 262, and the number of gates used is minimized to be 60. The corresponding flight-gate difficulty allocation weight is $\alpha =0.32$ α = 0.32 and $\beta =0.40$ β = 0.40 , and the proportion of flights successfully assigned to the gate is 86.469%. The number of passengers who failed to transfer was 642, with a failure rate of 23.337%.

A two-sided matching decision-making approach based on regret theory under intuitionistic fuzzy environment

2021 ◽  
pp. 1-18
Author(s):  
Xiang Jia ◽  
Xinfan Wang ◽  
Yuanfang Zhu ◽  
Lang Zhou ◽  
Huan Zhou
Keyword(s):  
Decision Making ◽  
Hamming Distance ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Sets ◽  
Regret Theory ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Objective Model ◽  
Single Objective

This study proposes a two-sided matching decision-making (TSMDM) approach by combining the regret theory under the intuitionistic fuzzy environment. At first, according to the Hamming distance of intuitionistic fuzzy sets and regret theory, superior and inferior flows are defined to describe the comparative preference of subjects. Hereafter, the satisfaction degrees are obtained by integrating the superior and inferior flows of the subjects. The comprehensive satisfaction degrees are calculated by aggregating the satisfaction degrees, based on which, a multi-objective TSMDM model is built. Furthermore, the multi-objective TSMDM model is converted to a single-objective model, the optimal solution of the latter is derived. Finally, an illustrative example and several analyses are provided to verify the feasibility and the effectiveness of the proposed approach.

The Position of ADME Predictions in Multi-Objective QSAR

2021 ◽  
Vol 6 (1) ◽  
pp. 1-8
Author(s):  
Anna Tsantili-Kakoulidou
Keyword(s):  
Drug Efficacy ◽  
Clinical Development ◽  
Efficacy And Safety ◽  
Huge Amount ◽  
Multi Objective ◽  
Drug Candidates ◽  
Drug Molecules ◽  
Qsar Models ◽  
Adme Properties ◽  
Single Objective

ADME properties and toxicity predictions play an essential role in prioritization and optimization of drug molecules. According to recent statistics, drug efficacy and safety are principal reasons for drug failure. In this perspective, the position of ADME predictions in the evolution of traditional QSAR from the single objective of biological activity to a multi-task concept is discussed. The essential features of ADME and toxicity QSAR models are highlighted. Since such models are applied to prioritize existing or virtual project compounds with already established or predicted target affinity, a mechanistic interpretation, although desirable, is not a primary goal. However, a broad applicability domain is crucial. A future challenge with multi-objective QSAR is to adapt to the realm of big data by integrating techniques for the exploitation of the continuously increasing number of ADME data and the huge amount of clinical development endpoints for the sake of efficacy and safety of new drug candidates.

Multi-Objective Robust Optimization for Planning of Mineral Processing under Uncertainty

2021 ◽  
Author(s):  
Quan Xu ◽  
Kesheng Zhang ◽  
Mingyu Li ◽  
Yangang Chu ◽  
Danwei Zhang
Keyword(s):  
Robust Optimization ◽  
Mineral Processing ◽  
Multi Objective
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