Solving multi-objective structural optimization problems using GDE3 and NSGA-II with reference points

2021 ◽  
Vol 239 ◽  
pp. 112187
Author(s):  
Dênis E.C. Vargas ◽  
Afonso C.C. Lemonge ◽  
Helio J.C. Barbosa ◽  
Heder S. Bernardino
Keyword(s):  
Structural Optimization ◽  
Optimization Problems ◽  
Reference Points ◽  
Nsga Ii ◽  
Multi Objective

scholarly journals Elite Exploitation: A Combination of Mathematical Concept and EMO Approach for Multi-Objective Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 136
Author(s):  
Wenxiao Li ◽  
Yushui Geng ◽  
Jing Zhao ◽  
Kang Zhang ◽  
Jianxin Liu
Keyword(s):  
Decision Making ◽  
Optimization Problems ◽  
Hybrid Genetic Algorithm ◽  
Decision Makers ◽  
Superior Performance ◽  
Test Problems ◽  
Mathematical Function ◽  
Hyperbolic Tangent ◽  
Nsga Ii ◽  
Multi Objective

This paper explores the combination of a classic mathematical function named “hyperbolic tangent” with a metaheuristic algorithm, and proposes a novel hybrid genetic algorithm called NSGA-II-BnF for multi-objective decision making. Recently, many metaheuristic evolutionary algorithms have been proposed for tackling multi-objective optimization problems (MOPs). These algorithms demonstrate excellent capabilities and offer available solutions to decision makers. However, their convergence performance may be challenged by some MOPs with elaborate Pareto fronts such as CFs, WFGs, and UFs, primarily due to the neglect of diversity. We solve this problem by proposing an algorithm with elite exploitation strategy, which contains two parts: first, we design a biased elite allocation strategy, which allocates computation resources appropriately to elites of the population by crowding distance-based roulette. Second, we propose a self-guided fast individual exploitation approach, which guides elites to generate neighbors by a symmetry exploitation operator, which is based on mathematical hyperbolic tangent function. Furthermore, we designed a mechanism to emphasize the algorithm’s applicability, which allows decision makers to adjust the exploitation intensity with their preferences. We compare our proposed NSGA-II-BnF with four other improved versions of NSGA-II (NSGA-IIconflict, rNSGA-II, RPDNSGA-II, and NSGA-II-SDR) and four competitive and widely-used algorithms (MOEA/D-DE, dMOPSO, SPEA-II, and SMPSO) on 36 test problems (DTLZ1–DTLZ7, WGF1–WFG9, UF1–UF10, and CF1–CF10), and measured using two widely used indicators—inverted generational distance (IGD) and hypervolume (HV). Experiment results demonstrate that NSGA-II-BnF exhibits superior performance to most of the algorithms on all test problems.

Multi-objective structural optimization of a wind turbine blade using NSGA-II algorithm and FSI

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ramazan Özkan ◽  
Mustafa Serdar Genç
Keyword(s):  
Structural Optimization ◽  
Wind Turbine ◽  
Turbine Blade ◽  
Wind Turbine Blade ◽  
Design Parameters ◽  
Aerodynamic Optimization ◽  
Nsga Ii ◽  
Content Type ◽  
Multi Objective ◽  
Optimization Study

Purpose Wind turbines are one of the best candidates to solve the problem of increasing energy demand in the world. The aim of this paper is to apply a multi-objective structural optimization study to a Phase II wind turbine blade produced by the National Renewable Energy Laboratory to obtain a more efficient small-scale wind turbine. Design/methodology/approach To solve this structural optimization problem, a new Non-Dominated Sorting Genetic Algorithm (NSGA-II) was performed. In the optimization study, the objective function was on minimization of mass and cost of the blade, and design parameters were composite material type and spar cap layer number. Design constraints were deformation, strain, stress, natural frequency and failure criteria. ANSYS Composite PrepPost (ACP) module was used to model the composite materials of the blade. Moreover, fluid–structure interaction (FSI) model in ANSYS was used to carry out flow and structural analysis on the blade. Findings As a result, a new original blade was designed using the multi-objective structural optimization study which has been adapted for aerodynamic optimization, the NSGA-II algorithm and FSI. The mass of three selected optimized blades using carbon composite decreased as much as 6.6%, 11.9% and 14.3%, respectively, while their costs increased by 23.1%, 29.9% and 38.3%. This multi-objective structural optimization-based study indicates that the composite configuration of the blade could be altered to reach the desired weight and cost for production. Originality/value ACP module is a novel and advanced composite modeling technique. This study is a novel study to present the NSGA-II algorithm, which has been adapted for aerodynamic optimization, together with the FSI. Unlike other studies, complex composite layup, fiber directions and layer orientations were defined by using the ACP module, and the composite blade analyzed both aerodynamic pressure and structural design using ACP and FSI modules together.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

scholarly journals Multi-objective optimization of solar thermal photovoltaic hybrid power generation system based on NSGA-II algorithm

2021 ◽  
Vol 336 ◽  
pp. 02022
Author(s):  
Liang Meng ◽  
Wen Zhou ◽  
Yang Li ◽  
Zhibin Liu ◽  
Yajing Liu
Keyword(s):  
Power Generation ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Solar Thermal ◽  
Multi Objective Optimization ◽  
Generation System ◽  
Nsga Ii ◽  
Multi Objective ◽  
Hybrid Power ◽  
Power Generation System

In this paper, NSGA-Ⅱ is used to realize the dual-objective optimization and three-objective optimization of the solar-thermal photovoltaic hybrid power generation system; Compared with the optimal solution set of three-objective optimization, optimization based on technical and economic evaluation indicators belongs to the category of multi-objective optimization. It can be considered that NSGA-Ⅱ is very suitable for multi-objective optimization of solar-thermal photovoltaic hybrid power generation system and other similar multi-objective optimization problems.

Multi-Objective Evolutionary Algorithm Based on Two Reference Points Decomposition and Historical Information Prediction

2021 ◽  
Vol 01 ◽  
Author(s):  
Er-chao Li ◽  
Kang-wei Li
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Reference Points ◽  
Multi Objective Optimization ◽  
Test Function ◽  
Historical Information ◽  
Multi Objective ◽  
Nadir Point ◽  
Overall Performance ◽  
Better Than

Aims: The main purpose of this paper is to solve the issues that the poor quality of offspring solutions generated by traditional evolutionary operators, and that the inability of the evolutionary algorithm based on decomposition to better solve the multi-objective optimization problems (MOPs) with complicated Pareto fronts (PFs). Background: For some complicated multi-objective optimization problems, the effect of the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is poor. For specific complicated problems, there is less research on improving the algorithm's performance by setting and adjusting the direction vector in the decomposition-based evolutionary algorithm. And considering that in the existing algorithms, the optimal solutions are selected according to the selection strategy in the selection stage, without considering if it could produce the better solutions in the stage of individual generation to achieve the optimization effect faster. As a result of these, a multi-objective evolutionary algorithm that is based on two reference points decomposition and historical information prediction is proposed. Objective: In order to verify the feasibility of the proposed strategy, the F-series test function with complicated PFs is used as the test function to simulate the proposed strategy. Method: Firstly, the evolutionary operator based on Historical Information Prediction (EHIP) is used to generate better offspring solutions to improve the convergence of the algorithm; secondly, the decomposition strategy based on ideal point and nadir point is used to select solutions to solve the MOPs with complicated PFs, and the decomposition method with augmentation term is used to improve the population diversity when selecting solutions according to the nadir point. Finally, the proposed algorithm is compared to several popular algorithms by the F-series test function, and the comparison is made according to the corresponding performance metrics. Result: The performance of the algorithm is improved obviously compared with the popular algorithms after using the EHIP. When the decomposition method with augmentation term is added, the performance of the proposed algorithm is better than the algorithm with only the EHIP on the whole. However, the overall performance is better than the popular algorithms. Conclusion and Prospect: The experimental results show that the overall performance of the proposed algorithm is superior to the popular algorithms. The EHIP can produce better quality offspring solutions, and the decomposition strategy based on two reference points can well solve the MOPs with complicated PFs. This paper mainly demonstrates the theory without testing the practical problems. The following research mainly focuses on the application of the proposed algorithm to the practical problems such as robot path planning.

Multi-objective Structural Optimization Base on Improved NSGA-II Algorithm

2013 ◽  
Vol 12 (23) ◽  
pp. 7646-7650 ◽  
Author(s):  
M.Z. Lai ◽  
Z.M. Duan ◽  
G.Y Zhang ◽  
B.D .
Keyword(s):  
Structural Optimization ◽  
Nsga Ii ◽  
Multi Objective

An Improved Multi-Objective Particle Swarm Optimization Based on Utopia Point Guided Search

2018 ◽  
Vol 9 (4) ◽  
pp. 71-96 ◽  
Author(s):  
Swapnil Prakash Kapse ◽  
Shankar Krishnapillai
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Particle Swarm ◽  
Nsga Ii ◽  
Swarm Optimization ◽  
Guided Search ◽  
Multi Objective ◽  
Search Approach ◽  
Utopia Point

This article demonstrates the implementation of a novel local search approach based on Utopia point guided search, thus improving the exploration ability of multi- objective Particle Swarm Optimization. This strategy searches for best particles based on the criteria of seeking solutions closer to the Utopia point, thus improving the convergence to the Pareto-optimal front. The elite non-dominated selected particles are stored in an archive and updated at every iteration based on least crowding distance criteria. The leader is chosen among the candidates in the archive using the same guided search. From the simulation results based on many benchmark tests, the new algorithm gives better convergence and diversity when compared to existing several algorithms such as NSGA-II, CMOPSO, SMPSO, PSNS, DE+MOPSO and AMALGAM. Finally, the proposed algorithm is used to solve mechanical design based multi-objective optimization problems from the literature, where it shows the same advantages.

scholarly journals An Effective Couple Method for Reliability-Based Multi-Objective Optimization of Truss Structures with Static and Dynamic Constraints

2019 ◽  
Vol 17 (06) ◽  
pp. 1950016 ◽  
Author(s):  
T. Vo-Duy ◽  
D. Duong-Gia ◽  
V. Ho-Huu ◽  
T. Nguyen-Thoi
Keyword(s):  
Cross Section ◽  
Optimization Problems ◽  
Computational Cost ◽  
Probabilistic Constraints ◽  
Truss Structures ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Dynamic Constraints ◽  
Multi Objective ◽  
Couple Method

This paper proposes an effective couple method for solving reliability-based multi-objective optimization problems of truss structures with static and dynamic constraints. The proposed coupling method integrates a single-loop deterministic method (SLDM) into the nondominated sorting genetic algorithm II (NSGA-II) algorithm to give the so-called SLDM-NSGA-II. Thanks to the advantage of SLDM, the probabilistic constraints are treated as approximating deterministic constraints. And therefore the reliability-based multi-objective optimization problems can be transformed into the deterministic multi-objective optimization problems of which the computational cost is reduced significantly. In these reliability-based multi-objective optimization problems, the conflicting objective functions are to minimize the weight and the displacements of the truss. The design variables are cross-section areas of the bars and contraints include static and dynamic constraints. For reliability analysis, the effect of uncertainty of parameters such as force, added mass in the nodes, material properties and cross-section areas of the bars are taken into account. The effectiveness and reliability of the proposed method are demonstrated through three benchmark-type truss structures including a 10-bar planar truss, a 72-bar spatial truss and a 200-bar planar truss. Moreover, the influence of parameters on the reliability-based Pareto optimal fronts is also carried out.

The Relationship between Metaheuristics Stopping Criteria and Performances

2014 ◽  
Vol 5 (3) ◽  
pp. 44-70 ◽  
Author(s):  
Mohamed-Mahmoud Ould Sidi ◽  
Bénédicte Quilot-Turion ◽  
Abdeslam Kadrani ◽  
Michel Génard ◽  
Françoise Lescourret
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Statistical Tests ◽  
Particle Swarm ◽  
Computational Time ◽  
Plant Management ◽  
Stopping Criterion ◽  
Nsga Ii ◽  
Multi Objective ◽  
Crowding Distance

A major difficulty in the use of metaheuristics (i.e. evolutionary and particle swarm algorithms) to deal with multi-objective optimization problems is the choice of a convenient point at which to stop computation. Indeed, it is difficult to find the best compromise between the stopping criterion and the algorithm performance. This paper addresses this issue using the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Multi-Objective Particle Swarm Optimization with Crowding Distance (MOPSO-CD) for the model-based design of sustainable peach fruits. The optimization problem of interest contains three objectives: maximize fruit fresh mass, maximize fruit sugar content, and minimize the crack density on the fruit skin. This last objective targets a reduction in the use of fungicides and can thus enhance preservation of the environment and human health. Two versions of the NSGA-II and two of the MOPSO-CD were applied to tackle this difficult optimization problem: the original versions with a maximum number of generations used as stopping criterion and modified versions using the stopping criterion proposed by the authors of (Roudenko & Schoenauer, 2004). This second stopping criterion is based on the stabilization of the maximal crowding distance and aims to stop computation when many generations are performed without further improvement in the quality of the solutions. A benchmark consisting of four plant management scenarios has been used to compare the performances of the original versions (OV) and the modified versions (MV) of the NSGA-II and the MOPSO-CD. Twelve independent simulations were performed for each version and for each scenario, and a high number of generations were generated for the OV (e.g., 1500 for the NSGA-II and 200 for the MOPSO-CD). This paper compares the performances of the two versions of both algorithms using four standard metrics and statistical tests. For both algorithms, the MV obtained solutions similar in quality to those of the OV but after significantly fewer generations. The resulting reduction in computational time for the optimization step will provide opportunities for further studies on the sustainability of peach ideotypes.

Optimization of Vehicle-Borne Radar Antenna Pedestal Based on Modified NSGA-II

2014 ◽  
Vol 945-949 ◽  
pp. 2241-2247
Author(s):  
De Gao Zhao ◽  
Qiang Li
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Population Diversity ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Sorting Process ◽  
Definition Of ◽  
Radar Antenna ◽  
Modified Algorithm

This paper deals with application of Non-dominated Sorting Genetic Algorithm with elitism (NSGA-II) to solve multi-objective optimization problems of designing a vehicle-borne radar antenna pedestal. Five technical improvements are proposed due to the disadvantages of NSGA-II. They are as follow: (1) presenting a new method to calculate the fitness of individuals in population; (2) renewing the definition of crowding distance; (3) introducing a threshold for choosing elitist; (4) reducing some redundant sorting process; (5) developing a self-adaptive arithmetic cross and mutation probability. The modified algorithm can lead to better population diversity than the original NSGA-II. Simulation results prove rationality and validity of the modified NSGA-II. A uniformly distributed Pareto front can be obtained by using the modified NSGA-II. Finally, a multi-objective problem of designing a vehicle-borne radar antenna pedestal is settled with the modified algorithm.

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