Optimization of Hood Thickness Based on the Multi-Objective

2012 ◽  
Vol 197 ◽  
pp. 755-759
Author(s):  
Duo Nian Yu ◽  
Lu Yao Zhou ◽  
Li Li ◽  
Zheng Cai Hu
Keyword(s):  
Head Injury ◽  
Optimization Algorithm ◽  
Approximate Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Genetic Optimization ◽  
Optimal Solutions ◽  
Thickness Optimization ◽  
Nsga Ii ◽  
Genetic Optimization Algorithm

Head injury of pedestrian is the most common and fatal cause of mortality in vehicle-to-pedestrian crash. And the engine hood is most likely to cause harm to pedestrian head. Efforts to improve engine hood design, which minimize the head injury of pedestrian in vehicle-to-pedestrian crash, are becoming more and more important. In this study, an approximate model of hood thickness for three targets: HIC, mass and modality, is established. In order to meet the requirements of lightweight and reducing vibration and noise, approximate models iterate by the NSGA-II genetic optimization algorithm, and select the Pareto optimal solutions for thickness optimization. At last the study re-simulates the collision between pedestrian head and hood to verify the reliability of the obtained optimization results.

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

scholarly journals Production Process Optimization of Metal Mines Considering Economic Benefit and Resource Efficiency Using an NSGA-II Model

Processes ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 228 ◽  
Author(s):  
Xunhong Wang ◽  
Xiaowei Gu ◽  
Zaobao Liu ◽  
Qing Wang ◽  
Xiaochuan Xu ◽  
...  
Keyword(s):  
Production Process ◽  
Resource Utilization ◽  
Economic Benefits ◽  
Resource Efficiency ◽  
Utilization Rate ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Metal Mines

The optimization of the production process of metal mines has been traditionally driven only by economic benefits while ignoring resource efficiency. However, it has become increasingly aware of the importance of resource efficiency since mineral resource reserves continue to decrease while the demand continues to grow. To better utilize the mineral resources for sustainable development, this paper proposes a multi-objective optimization model of the production process of metal mines considering both economic benefits and resource efficiency. Specifically, the goals of the proposed model are to maximize the profit and resource utilization rate. Then, the fast and elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) is used to optimize the multi-objective optimization model. The proposed model has been applied to the optimization of the production process of a stage in the Huogeqi Copper Mine. The optimization results provide a set of Pareto-optimal solutions that can meet varying needs of decision makers. Moreover, compared with those of the current production indicators, the profit and resource utilization rate of some points in the optimization results can increase respectively by 2.99% and 2.64%. Additionally, the effects of the decision variables (geological cut-off grade, minimum industrial grade and loss ratio) on objective functions (profit and resource utilization rate) were discussed using variance analysis. The sensitivities of the Pareto-optimal solutions to the unit copper concentrate price were studied. The results show that the Pareto-optimal solutions at higher profits (with lower resource utilization rates) are more sensitive to the unit copper concentrate prices than those obtained in regions with lower profits.

scholarly journals Production Process Optimization of Metal Mines Considering Economic Benefit and Resource Efficiency Using an NSGA-II Model

2018 ◽  
Author(s):  
Xunhong Wang ◽  
Xiaowei Gu ◽  
Zaobao Liu ◽  
Qing Wang ◽  
Xiaochuan Xu ◽  
...  
Keyword(s):  
Production Process ◽  
Resource Utilization ◽  
Economic Benefits ◽  
Resource Efficiency ◽  
Utilization Rate ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Metal Mines

The optimization of the production process of metal mines has been traditionally driven only by economic benefits while ignoring resource efficiency. However, it has become increasingly aware of the importance of resource efficiency since mineral resource reserves continue to decrease while the demand continues to grow. To better utilize the mineral resources for sustainable development, this paper proposes a multi-objective optimization model of the production process of metal mines considering both economic benefits and resource efficiency. Specifically, the goals of the proposed model are to maximize the profit and resource utilization rate. Then, the fast and elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) is used to optimize the multi-objective optimization model. The proposed model has been applied to the optimization of the production process of a stage in the Huogeqi Copper Mine. The optimization results provide a set of Pareto-optimal solutions that can meet varying needs of decision makers. Moreover, compared with those of the current production indicators, the profit and resource utilization rate of some points in the optimization results can increase respectively by 2.99% and 2.64%. Additionally, the effects of the decision variables (geological cut-off grade, minimum industrial grade and loss ratio) on objective functions (profit and resource utilization rate) were discussed using variance analysis. The sensitivities of the Pareto-optimal solutions to the unit copper concentrate price were studied. The results show that the Pareto-optimal solutions at higher profits (with lower resource utilization rates) are more sensitive to the unit copper concentrate prices than those obtained in regions with lower profits.

Adaptive Control of Dominance Area of Solutions in Evolutionary Many-Objective Optimization

2015 ◽  
Vol 11 (02) ◽  
pp. 135-150 ◽  
Author(s):  
Kouhei Tomita ◽  
Minami Miyakawa ◽  
Hiroyuki Sato
Keyword(s):  
Pareto Front ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Pareto Optimal ◽  
Search Performance ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Dominance ◽  
Nsga Ii ◽  
Convergence Of Solutions

Controlling the dominance area of solutions (CDAS) relaxes the concept of Pareto dominance with an user-defined parameter S. CDAS with S < 0.5 expands the dominance area and improves the search performance of multi-objective evolutionary algorithms (MOEAs) especially in many-objective optimization problems (MaOPs) by enhancing convergence of solutions toward the optimal Pareto front. However, there is a problem that CDAS with an expanded dominance area (S < 0.5) generally cannot approximate entire Pareto front. To overcome this problem we propose an adaptive CDAS (A-CDAS) that adaptively controls the dominance area of solutions during the solutions search. Our method improves the search performance in MaOPs by approximating the entire Pareto front while keeping high convergence. In early generations, A-CDAS tries to converge solutions toward the optimal Pareto front by using an expanded dominance area with S < 0.5. When we detect convergence of solutions, we gradually increase S and contract the dominance area of solutions to obtain Pareto optimal solutions (POS) covering the entire optimal Pareto front. We verify the effectiveness and the search performance of the proposed A-CDAS on concave and convex DTLZ3 benchmark problems with 2–8 objectives, and show that the proposed A-CDAS achieves higher search performance than conventional non-dominated sorting genetic algorithm II (NSGA-II) and CDAS with an expanded dominance area.

Analysis of NSGA-II and NSGA-II with CDAS, and Proposal of an Enhanced CDAS Mechanism

2009 ◽  
Vol 13 (4) ◽  
pp. 470-480 ◽  
Author(s):  
Kyoko Tsuchida ◽  
◽  
Hiroyuki Sato ◽  
Hernan Aguirre ◽  
Kiyoshi Tanaka ◽  
...  
Keyword(s):  
Pareto Optimal ◽  
Search Performance ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Degree Of Dominance ◽  
Before And After ◽  
The Relationship ◽  
Best Parameters ◽  
Selection Of

In this work, we analyze the functionality transition in the evolution process of NSGA-II and an enhanced NSGA-II with the method of controlling dominance area of solutions (CDAS) from the viewpoint of front distribution. We examine the relationship between the population of the first front consisting of non-dominated solutions and the values of two metrics, NORM and ANGLE, which measure convergence and diversity of Pareto-optimal solutions (POS), respectively. We also suggest potentials to further improve the search performance of the enhanced NSGA-II with CDAS by emphasizing the parameterS, which controls the degree of dominance by contracting or expanding the dominance area of solutions, before and after the boundary generation of functionality transition. Furthermore, we analyze the behavior of the evolution of the enhanced NSGA-II with CDAS using the best parameters combination and compare its performance with two other algorithms that enhance selection of NSGA-II.

scholarly journals Multiobjective Collective Decision Optimization Algorithm for Economic Emission Dispatch Problem

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Xinlin Xu ◽  
Zhongbo Hu ◽  
Qinghua Su ◽  
Zenggang Xiong
Keyword(s):  
Multiobjective Optimization ◽  
Learning Strategies ◽  
Optimization Algorithm ◽  
Test System ◽  
Collective Decision ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Unit Test ◽  
Decision Optimization

The collective decision optimization algorithm (CDOA) is a new stochastic population-based evolutionary algorithm which simulates the decision behavior of human. In this paper, a multiobjective collective decision optimization algorithm (MOCDOA) is first proposed to solve the environmental/economic dispatch (EED) problem. MOCDOA uses three novel learning strategies, that is, a leader-updating strategy based on the maximum distance of each solution in an external archive, a wise random perturbation strategy based on the sparse mark around a leader, and a geometric center-updating strategy based on an extreme point. The proposed three learning strategies benefit the improvement of the uniformity and the diversity of Pareto optimal solutions. Several experiments have been carried out on the IEEE 30-bus 6-unit test system and 10-unit test system to investigate the performance of MOCDOA. In terms of extreme solutions, compromise solution, and three metrics (SP, HV, and CM), MOCDOA is compared with other existing multiobjective optimization algorithms. It is demonstrated that MOCDOA can generate the well-distributed and the high-quality Pareto optimal solutions for the EED problem and has the potential to solve the multiobjective optimization problems of other power systems.

MULTIOBJECTIVE DESIGN OF EQUIVALENT ACCELERATED LIFE TESTING PLANS

2008 ◽  
Vol 15 (06) ◽  
pp. 515-538 ◽  
Author(s):  
HAITAO LIAO ◽  
ZHAOJUN LI
Keyword(s):  
Solution Set ◽  
Accelerated Life Test ◽  
Test Time ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Solutions ◽  
Nsga Ii ◽  
Accelerated Life ◽  
Multiobjective Design

This paper is focused on the multiobjective design of equivalent accelerated life test (ALT) plans. Equivalent ALT plans are expected to achieve the same statistical performance as a baseline ALT plan yet lead to other desired performance measures such as reduced test time and total cost. Before determining the desired multiobjective equivalent ALT plans, an efficient fast non-dominated sorting genetic algorithm (NSGA-II) is utilized to identify a set of Pareto optimal solutions. To handle a large number of Pareto optimal solutions, a self-organizing map (SOM) and data envelopment analysis (DEA) are sequentially applied to classify the Pareto solutions and reduce the size of the suggested solution set. This integrated approach allows for the tradeoff of information among the Pareto solutions and the reduction in the size of the solution set. It provides a useful tool for practitioners to make meaningful decisions in planning ALT experiments.

scholarly journals A Novel Method of Optimal Capacitor Placement in the Presence of Harmonics for Power Distribution Network Using NSGA-II Multi-Objective Genetic Optimization Algorithm

2020 ◽  
Vol 25 (1) ◽  
pp. 17
Author(s):  
Majid Ebrahimi Moghadam ◽  
Hamid Falaghi ◽  
Mahdi Farhadi
Keyword(s):  
Optimization Algorithm ◽  
Reactive Power ◽  
Reducing Power ◽  
Optimal Placement ◽  
Genetic Optimization ◽  
Nonlinear Loads ◽  
Nsga Ii ◽  
Multi Objective ◽  
Capacitor Banks ◽  
Genetic Optimization Algorithm

One of the effective ways of reducing power system losses is local compensation of part of the reactive power consumption by deploying shunt capacitor banks. Since the capacitor’s impedance is frequency-dependent and it is possible to generate resonances at harmonic frequencies, it is important to provide an efficient method for the placement of capacitor banks in the presence of nonlinear loads which are the main cause of harmonic generation. This paper proposes a solution for a multi-objective optimization problem to address the optimal placement of capacitor banks in the presence of nonlinear loads, and it establishes a reasonable reconciliation between costs, along with improvement of harmonic distortion and a voltage index. In this paper, while using the harmonic power flow method to calculate the electrical quantities of the grid in terms of harmonic effects, the non-dominated sorting genetic (NSGA)-II multi-objective genetic optimization algorithm was used to obtain a set of solutions named the Pareto front for the problem. To evaluate the effectiveness of the proposed method, the problem was tested for an IEEE 18-bus system. The results were compared with the methods used in eight other studies. The simulation results show the considerable efficiency and superiority of the proposed flexible method over other methods.

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