Response Surface Approximation of Pareto Optimal Front in Multi-objective Optimization

2004 ◽  
Author(s):  
Tushar Goel ◽  
Rajkumar Vaidyanathan ◽  
Raphael Haftka ◽  
Wei Shyy ◽  
Nestor Queipo ◽  
...  
Keyword(s):  
Response Surface ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Response Surface Approximation ◽  
Surface Approximation ◽  
Pareto Optimal Front ◽  
Multi Objective

Response surface approximation of Pareto optimal front in multi-objective optimization

2007 ◽  
Vol 196 (4-6) ◽  
pp. 879-893 ◽  
Author(s):  
Tushar Goel ◽  
Rajkumar Vaidyanathan ◽  
Raphael T. Haftka ◽  
Wei Shyy ◽  
Nestor V. Queipo ◽  
...  
Keyword(s):  
Response Surface ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Response Surface Approximation ◽  
Surface Approximation ◽  
Pareto Optimal Front ◽  
Multi Objective

scholarly journals Integration of Operability Framework and Pareto Optimal Front to Calculate Optimal Condition of Ethane Cracking Process

2020 ◽  
pp. 105-113
Author(s):  
M. Farsi
Keyword(s):  
Pareto Front ◽  
Optimal Solution ◽  
Optimization Procedure ◽  
Operating Conditions ◽  
Base Case ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Cracking Process

The main aim of this research is to present an optimization procedure based on the integration of operability framework and multi-objective optimization concepts to find the single optimal solution of processes. In this regard, the Desired Pareto Index is defined as the ratio of desired Pareto front to the Pareto optimal front as a quantitative criterion to analyze the performance of chemical processes. The Desired Pareto Front is defined as a part of the Pareto front that all outputs are improved compared to the conventional operating condition. To prove the efficiency of proposed optimization method, the operating conditions of ethane cracking process is optimized as a base case. The ethylene and methane production rates are selected as the objectives in the formulated multi-objective optimization problem. Based on the simulation results, applying the obtained operating conditions by the proposed optimization procedure on the ethane cracking process improve ethylene production by about 3% compared to the conventional condition.  

Pareto-optimal front for multi-objective optimization of the suspension of a full-vehicle model in the frequency domain

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Giovani Gaiardo Fossati ◽  
Letícia Fleck Fadel Miguel ◽  
Walter Jesus Paucar Casas
Keyword(s):  
Frequency Domain ◽  
Computational Time ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Vehicle Model ◽  
Content Type ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Suspension Systems ◽  
Road Profile

PurposeThis study aims to propose a complete and powerful methodology that allows the optimization of the passive suspension system of vehicles, which simultaneously takes comfort and safety into account and provides a set of optimal solutions through a Pareto-optimal front, in a low computational time.Design/methodology/approachUnlike papers that consider simple vehicle models (quarter vehicle model or half car model) and/or simplified road profiles (harmonic excitation, for example) and/or perform a single-objective optimization and/or execute the dynamic analysis in the time domain, this paper presents an effective and fast methodology for the multi-objective optimization of the suspension system of a full-car model (including the driver seat) traveling on an irregular road profile, whose dynamic response is determined in the frequency domain, considerably reducing computational time.FindingsThe results showed that there was a reduction of 28% in the driver seat vertical acceleration weighted root mean square (RMS) value of the proposed model, which is directly related to comfort, and, simultaneously, an improvement or constancy concerning safety, with low computational cost. Hence, the proposed methodology can be indicated as a successful tool for the optimal design of the suspension systems, considering, simultaneously, comfort and safety.Originality/valueDespite the extensive literature on optimizing vehicle passive suspension systems, papers combining multi-objective optimization presenting a Pareto-optimal front as a set of optimal results, a full-vehicle model (including the driver seat), an irregular road profile and the determination of the dynamic response in the frequency domain are not found.

Manufacturer Order Fulfillment Based on Multi-Objective Optimization NSGA II Model

2013 ◽  
Vol 340 ◽  
pp. 136-140
Author(s):  
Liang You Shu ◽  
Ling Xiao Yang
Keyword(s):  
Optimization Model ◽  
Optimization Problems ◽  
Population Based ◽  
Pareto Optimal ◽  
Order Fulfillment ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Pareto Optimal Front ◽  
Multi Objective ◽  
Local Search Procedure

The aim of this paper is to study the production and delivery decision problem in the Manufacturer Order Fulfillment. Owing to the order fulfillment optimization condition of the manufacturer, the multi-objective optimization model of manufacturers' production and delivery has been founded. The solution of the multi-objective optimization model is also very difficult. Fast and Elitist Non-dominated Sorting Genetic Algorithm (NSGA II) have been applied successfully to various test and real-world optimization problems. These population based the algorithm provide a diverse set of non-dominated solutions. The obtained non-dominated set is close to the true Pareto-optimal front. But its convergence to the true Pareto-optimal front is not guaranteed. Hence SBX is used as a local search procedure. The proposed procedure is successfully applied to a special case. The results validate that the algorithm is effective to the multi-objective optimization model.

scholarly journals Robust Multi-Objective Optimization for Response Surface Models Applied to Direct Low-Value Natural Gas Conversion Processes

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 248
Author(s):  
Luiz Célio S. Rocha ◽  
Mariana S. Rocha ◽  
Paulo Rotella Junior ◽  
Giancarlo Aquila ◽  
Rogério S. Peruchi ◽  
...  
Keyword(s):  
Natural Gas ◽  
Response Surface ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Optimal Point ◽  
Natural Gas Conversion ◽  
Multi Objective ◽  
Reactor Temperature ◽  
Entropic Measure ◽  
Gas Conversion

The high proportion of CO2/CH4 in low aggregated value natural gas compositions can be used strategically and intelligently to produce more hydrocarbons through oxidative methane coupling (OCM). The main goal of this study was to optimize direct low-value natural gas conversion via CO2-OCM on metal oxide catalysts using robust multi-objective optimization based on an entropic measure to choose the most preferred Pareto optimal point as the problem’s final solution. The responses of CH4 conversion, C2 selectivity, and C2 yield are modeled using the response surface methodology. In this methodology, decision variables, e.g., the CO2/CH4 ratio, reactor temperature, wt.% CaO and wt.% MnO in ceria catalyst, are all employed. The Pareto optimal solution was obtained via the following combination of process parameters: CO2/CH4 ratio = 2.50, reactor temperature = 1179.5 K, wt.% CaO in ceria catalyst = 17.2%, wt.% MnO in ceria catalyst = 6.0%. By using the optimal weighting strategy w1 = 0.2602, w2 = 0.3203, w3 = 0.4295, the simultaneous optimal values for the objective functions were: CH4 conversion = 8.806%, C2 selectivity = 51.468%, C2 yield = 3.275%. Finally, an entropic measure used as a decision-making criterion was found to be useful in mapping the regions of minimal variation among the Pareto optimal responses and the results obtained, and this demonstrates that the optimization weights exert influence on the forecast variation of the obtained response.

Multi Objective Optimization of a Turbomachinery Blade Using NSGA-II

2007 ◽  
Author(s):  
Abdus Samad ◽  
Kwang-Yong Kim ◽  
Ki-Sang Lee
Keyword(s):  
Total Pressure ◽  
Three Dimensional ◽  
Axial Flow ◽  
Navier Stokes ◽  
Total Efficiency ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Pareto Optimal Front ◽  
Multi Objective

This work presents numerical optimization for design of a blade stacking line of a low speed axial flow fan with a fast and elitist Non-Dominated Sorting of Genetic Algorithm (NSGA-II) of multi-objective optimization using three-dimensional Navier-Stokes analysis. Reynolds-averaged Navier-Stokes (RANS) equations with k-ε turbulence model are discretized with finite volume approximations and solved on unstructured grids. Regression analysis is performed to get second order polynomial response which is used to generate Pareto optimal front with help of NSGA-II and local search strategy with weighted sum approach to refine the result obtained by NSGA-II to get better Pareto optimal front. Four geometric variables related to spanwise distributions of sweep and lean of blade stacking line are chosen as design variables to find higher performed fan blade. The performance is measured in terms of the objectives; total efficiency, total pressure and torque. Hence the motive of the optimization is to enhance total efficiency and total pressure and to reduce torque.

IMPROVING THE PERFORMANCE OF MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS USING THE ISLAND PARALLEL MODEL

2007 ◽  
Vol 17 (02) ◽  
pp. 127-139 ◽  
Author(s):  
A. MÁRQUEZ ◽  
C. GIL ◽  
R. BAÑOS ◽  
J. GÓMEZ
Keyword(s):  
Parallel Processing ◽  
Evolutionary Algorithms ◽  
Population Size ◽  
Test Problems ◽  
Pareto Optimal ◽  
Parallel Model ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective

Recently, the research interest in multi-objective optimization has increased remarkably. Most of the proposed methods use a population of solutions that are simultaneously improved trying to approximate them to the Pareto-optimal front. When the population size increases, the quality of the solutions tends to be better, but the runtime is higher. This paper presents how to apply parallel processing to enhance the convergence to the Pareto-optimal front, without increasing the runtime. In particular, we present an island-based parallelization of five multi-objective evolutionary algorithms: NSGAII, SPEA2, PESA, msPESA, and a new hybrid version we propose. Experimental results in some test problems denote that the quality of the solutions tends to improve when the number of islands increases.

Improved Memetic NSGA-II Using a Deep Neighborhood Search

2021 ◽  
Vol 12 (4) ◽  
pp. 138-154
Author(s):  
Samir Mahdi ◽  
Brahim Nini
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Pareto Front ◽  
Neighborhood Search ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Pareto Optimal Front ◽  
Slow Convergence ◽  
Multi Objective

Elitist non-sorted genetic algorithms as part of Pareto-based multi-objective evolutionary algorithms seems to be one of the most efficient algorithms for multi-objective optimization. However, it has some shortcomings, such as low convergence accuracy, uneven Pareto front distribution, and slow convergence. A number of review papers using memetic technique to improve NSGA-II have been published. Hence, it is imperative to improve memetic NSGA-II by increasing its solving accuracy. In this paper, an improved memetic NSGA-II, called deep memetic non-sorted genetic algorithm (DM-NSGA-II), is proposed, aiming to obtain more non-dominated solutions uniformly distributed and better converged near the true Pareto-optimal front. The proposed algorithm combines the advantages of both exact and heuristic approaches. The effectiveness of DM-NSGA-II is validated using well-known instances taken from the standard literature on multi-objective knapsack problem. As will be shown, the performance of the proposed algorithm is demonstrated by comparing it with M-NSGA-II using hypervolume metric.

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