Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set

2000 ◽  
Author(s):  
Jin Wu ◽  
Shapour Azarm
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Frontier ◽  
Optimization Methods ◽  
Optimization Method ◽  
Solution Set ◽  
Pareto Solution ◽  
Vibrating Platform ◽  
Pareto Solution Sets ◽  
Multiobjective Design

Abstract In this paper, several new set quality metrics are introduced that can be used to evaluate the ‘goodness’ of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include coverage difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer either monitor the quality of an observed Pareto solution set as obtained by a multiobjective optimization method, or compare the quality of observed Pareto solution sets as reported by different multiobjective optimization methods. A vibrating platform example is used to demonstrate the calculation of these metrics for an observed Pareto solution set.

Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set

2000 ◽  
Vol 123 (1) ◽  
pp. 18-25 ◽  
Author(s):  
Jin Wu ◽  
Shapour Azarm
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Frontier ◽  
Optimization Methods ◽  
Optimization Method ◽  
Solution Set ◽  
Pareto Solution ◽  
Vibrating Platform ◽  
Pareto Solution Sets ◽  
Multiobjective Design

In this paper, several new set quality metrics are introduced that can be used to evaluate the “goodness” of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include hyperarea difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer to either monitor the quality of an observed Pareto solution set as obtained by a multiobjective optimization method, or compare the quality of observed Pareto solution sets as reported by different multiobjective optimization methods. A vibrating platform example is used to demonstrate the calculation of these metrics for an observed Pareto solution set.

scholarly journals New multiobjective optimization algorithm using NBI-SASP approaches for mechanical structural problems

2022 ◽  
Vol 13 ◽  
pp. 4
Author(s):  
Samira El Moumen ◽  
Siham Ouhimmou
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Pareto Frontier ◽  
Optimization Method ◽  
Multi Objective Optimization ◽  
Design Problems ◽  
Multi Objective ◽  
Structural Problems ◽  
Engineering Design Problems ◽  
Set Of Points

Various engineering design problems are formulated as constrained multi-objective optimization problems. One of the relevant and popular methods that deals with these problems is the weighted method. However, the major inconvenience with its application is that it does not yield a well distributed set. In this study, the use of the Normal Boundary Intersection approach (NBI) is proposed, which is effective in obtaining an evenly distributed set of points in the Pareto set. Given an evenly distributed set of weights, it can be strictly shown that this approach is absolutely independent of the relative scales of the functions. Moreover, in order to ensure the convergence to the Global Pareto frontier, NBI approach has to be aligned with a global optimization method. Thus, the following paper suggests NBI-Simulated Annealing Simultaneous Perturbation method (NBI-SASP) as a new method for multiobjective optimization problems. The study shall test also the applicability of the NBI-SASP approach using different engineering multi-objective optimization problems and the findings shall be compared to a method of reference (NSGA). Results clearly demonstrate that the suggested method is more efficient when it comes to search ability and it provides a well distributed global Pareto Front.

An Information-Theoretic Entropy Metric for Assessing Multi-Objective Optimization Solution Set Quality

2003 ◽  
Vol 125 (4) ◽  
pp. 655-663 ◽  
Author(s):  
Ali Farhang-Mehr ◽  
Shapour Azarm
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Frontier ◽  
Optimization Techniques ◽  
Solution Set ◽  
Multi Objective Optimization ◽  
Information Theoretic ◽  
Multi Objective ◽  
Speed Reducer ◽  
Quantitative Basis

An entropy-based metric is presented that can be used for assessing the quality of a solution set as obtained from multi-objective optimization techniques. This metric quantifies the “goodness” of a set of solutions in terms of distribution quality over the Pareto frontier. The metric can be used to compare the performance of different multi-objective optimization techniques. In particular, the metric can be used in analysis of multi-objective evolutionary algorithms, wherein the capabilities of such techniques to produce and maintain diversity among different solution points are desired to be compared on a quantitative basis. An engineering test example, the multi-objective design optimization of a speed-reducer, is provided to demonstrate an application of the proposed entropy metric.

scholarly journals Optimized Energy Storage System Configuration for Voltage Regulation of Distribution Network With PV Access

2021 ◽  
Vol 9 ◽  
Author(s):  
Qiang Li ◽  
Feijie Zhou ◽  
Fuyin Guo ◽  
Fulin Fan ◽  
Zhengyong Huang
Keyword(s):  
Renewable Energy ◽  
Energy Storage ◽  
Power Supply ◽  
Pso Algorithm ◽  
Optimization Method ◽  
Voltage Regulation ◽  
Solution Set ◽  
Optimal Solutions ◽  
Voltage Profile ◽  
Pareto Solution

With the large-scale integration of renewable energy such as wind power and PV, it is necessary to maintain the voltage stability of power systems while increasing the use of intermittent renewable energy sources. The rapid development of energy storage technologies permits the deployment of energy storage systems (ESS) for voltage regulation support. This paper develops an ESS optimization method to estimate the optimal capacity and locations of distributed ESS supporting the voltage regulation of a distribution network. The electrical elements of the network integrated with PV and ESS are first modelled to simulate the voltage profile of the network. Then an improved multi-objective particle swarm optimization (PSO) algorithm is employed to minimise a weighted sum of the overall nodal voltage deviation from the nominal level across the network and across the time horizon and the energy capacity of ESS reflecting the associated investment. The improved PSO algorithm adaptively adjusts the inertia weight associated with each particle based on its distance from the best known particle of the population and introduces the cross-mutation operation for a small distance to avoid falling into local optimal solutions. Then the dynamic dense distance arrangement is taken to update the non-inferior solution set and indicate potential global optimal solutions so as to keep the scale and uniformity of the optimal Pareto solution set. To mitigate the impact of decision makers’ preference, the information entropy based technique for order of preference by similarity to ideal solution is used to select the optimal combination of the ESS access scheme and capacity from the Pareto solution set. The proposed ESS optimization method is tested based on the IEEE 24-bus system with additional imports from high-voltage power supply. The voltage profile of the network simulated without the ESS or with the random or optimized ESS placement is compared to illustrate the effectiveness of the optimized ESS in performing voltage regulation under normal operation and supporting emergency power supply during high-voltage transmission failures.

scholarly journals A Comparison of Grid Quality of Optimized Spherical Hexagonal–Pentagonal Geodesic Grids

2005 ◽  
Vol 133 (10) ◽  
pp. 2817-2833 ◽  
Author(s):  
Hiroaki Miura ◽  
Masahide Kimoto
Keyword(s):  
Common Ground ◽  
Optimization Methods ◽  
Optimization Method ◽  
Numerical Schemes ◽  
Optimal Method ◽  
Grid Optimization

Abstract Construction and optimization methods of spherical hexagonal–pentagonal geodesic grids are investigated. The objective is to compare grid structures on common ground. The distinction between two types of hexagonal–pentagonal grids is made. Three conventional grid optimization methods are summarized. In addition, three new optimization methods are proposed. Six desirable conditions for an ideal grid are described, and the grid optimization methods are organized in view of such conditions. Interval uniformity, area uniformity, isotropy, and bisection of cell faces are systematically investigated for optimized grids. There are compensations of preferable grid features in each optimization method, and an optimal method cannot be decided based only on the research of grid features. It is suggested that grid optimization methods should be selected based on research of numerical schemes.

Multiobjective Design Optimization of a Biconcave Mobile-Bearing Lumbar Total Artificial Disk Considering Spinal Kinematics, Facet Joint Loading, and Metal-on-Polyethylene Contact Mechanics

2019 ◽  
Vol 142 (4) ◽  
Author(s):  
Chaochao Zhou ◽  
Ryan Willing
Keyword(s):  
Multiobjective Optimization ◽  
Design Optimization ◽  
Performance Metrics ◽  
Facet Joint ◽  
Pareto Frontier ◽  
Mobile Bearing ◽  
Ultrahigh Molecular Weight Polyethylene ◽  
Joint Force ◽  
Multiobjective Design ◽  
Single Objective

Abstract Total disk arthroplasty (TDA) using an artificial disk (AD) is an attractive surgical technique for the treatment of spinal disorders, since it can maintain or restore spinal motion (unlike interbody fusion). However, adverse surgical outcomes of contemporary lumbar TDAs have been reported. We previously proposed a new mobile-bearing AD design concept featuring a biconcave ultrahigh-molecular-weight polyethylene (UHMWPE) mobile core. The objective of this study was to develop an artificial neural network (NN) based multiobjective optimization framework to refine the biconcave-core AD design considering multiple TDA performance metrics, simultaneously. We hypothesized that there is a tradeoff relationship between the performance metrics in terms of range of motion (ROM), facet joint force (FJF), and polyethylene contact pressure (PCP). By searching the resulting three-dimensional (3D) Pareto frontier after multiobjective optimization, it was found that there was a “best-tradeoff” AD design, which could balance all the three metrics, without excessively sacrificing each metric. However, for each single-objective optimum AD design, only one metric was optimal, and distinct sacrifices were observed in the other two metrics. For a commercially available biconvex-core AD design, the metrics were even worse than the poorest outcomes of the single-objective optimum AD designs. Therefore, multiobjective design optimization could be useful for achieving native lumbar segment biomechanics and minimal PCPs, as well as for improving the existing lumbar motion-preserving surgical treatments.

Multiobjective Design Optimization of B-Screw Series Propellers Using Evolutionary Algorithms

2003 ◽  
Vol 40 (04) ◽  
pp. 229-238
Author(s):  
Ernesto Benini
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Personal Computer ◽  
Optimization Method ◽  
Preliminary Design ◽  
Thrust Coefficient ◽  
Marine Propellers ◽  
Complex Design ◽  
Conflicting Objectives ◽  
Multiobjective Design

Methodical series are still widely used in the preliminary design of light-and moderate-duty marine propellers. If the above series enables standard screws to be designed by simple chart methods, they do not help the designer to deal with a complex design involving multiple and conflicting objectives. In this paper, a multiobjective optimization method of B-screw series propeller is introduced that makes use of an evolutionary algorithm maximizing both efficiency and thrust coefficient with a constraint determined by cavitation. The capabilities of the method are illustrated and discussed in detail. The results following the application of the method are given in the form of diagrams, which can be implemented on a common personal computer and used to derive optimal screw configurations in real time.

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