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.

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.

Multi-Objective Design and Selection of One Single Optimal Solution

2004 ◽  
Author(s):  
F. Levi ◽  
M. Gobbi ◽  
M. Farina ◽  
G. Mastinu
Keyword(s):  
Optimal Solution ◽  
Engineering Problem ◽  
Design Solution ◽  
Pareto Optimal ◽  
Large Set ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Optimal Set ◽  
Final Design ◽  
Selection Of

In the paper, the problem of choosing a single final design solution among a large set of Pareto-optimal solutions is addressed. Two methods, the k-optimality approach and the more general k-ε-optimality method will be introduced. These two methods theoretically justify and mathematically define the designer’s tendency to choose solutions which are “in the middle” of the Pareto-optimal set. These two methods have been applied to the solution of a relatively simple engineering problem, i.e. the selection of the stiffness and damping of a passively suspended vehicle in order to get the best compromise between discomfort, road holding and working space. The final design solution, found by means of the k-ε-optimality approach seems consistent with the solution selected by skilled suspensions specialists. Finally the k-optimality method has proved to be very effective also when applied to complex engineering problems. The optimization of the tyre/suspension system of a sports car has been formulated as a design problem with 18 objective functions. A large set of Pareto-optimal solutions have been computed. Again, the k-optimality approach has proved to be a useful tool for the selection of a fully satisfactory final design solution.

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.

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.

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.

scholarly journals Determining a Robust, Pareto Optimal Geometry for a Welded Joint

2014 ◽  
Vol 1016 ◽  
pp. 39-43
Author(s):  
Simon Barrans ◽  
H.E. Radhi
Keyword(s):  
Welded Joint ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Optimal Geometry ◽  
Pareto Optimal Set ◽  
Particular Solution ◽  
Optimal Set ◽  
Selection Of

Multi-criteria optimization problems are known to give rise to a set of Pareto optimal solutions where one solution cannot be regarded as being superior to another. It is often stated that the selection of a particular solution from this set should be based on additional criteria. In this paper a methodology has been proposed that allows a robust design to be selected from the Pareto optimal set. This methodology has been used to determine a robust geometry for a welded joint. It has been shown that the robust geometry is dependent on the variability of the geometric parameters.

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.

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