Pareto-Optimal Solutions Using Kinematic and Dynamic Functions for a Scho¨nflies Parallel Manipulator

2009 ◽  
Author(s):  
Oscar Altuzarra ◽  
Charles Pinto ◽  
Bogdan Sandru ◽  
Enrique Amezua
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Frobenius Norm ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Motion Generation ◽  
Dimensional Parameters

The search of Pareto-optimal solutions for the optimal design of Low-Mobility Parallel Manipulators with Scho¨nflies motion is the subject of this paper. As a working example, a four-degree-of-freedom symmetric parallel manipulator for Scho¨nflies-motion generation is taken. In previous work, analytically found objective functions for the optimal design were used. As a consequence, some limitations were detected and new functions are required. First, a manipulator description is made, and kinematic and dynamic problems are solved. Next, an operational and dexterous workspace along with its volume is found making use of a discretization. Further, the variation of this volume with dimensional parameters is shown for purpose of optimal design. Similarly, the manipulator’s dexterity based on the Frobenius norm is found and weighted with the measure of dispersion. Then, upon a type of testing trajectory over this workspace, kinematic and dynamic results in the actuators are proposed as objective functions in multiobjective optimization.

Optimal Dimensioning for Parallel Manipulators: Workspace, Dexterity, and Energy

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Oscar Altuzarra ◽  
C. Pinto ◽  
B. Sandru ◽  
A. Hernandez
Keyword(s):  
Parallel Manipulator ◽  
Optimization Problems ◽  
Parallel Manipulators ◽  
Design Parameters ◽  
Frobenius Norm ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Motion Generation ◽  
Schönflies Motion

In mechanism design and in the particular case of the parallel manipulator, most optimization problems involve simultaneously optimizing more than one objective function. In this paper, a method to identify Pareto-optimal solutions for the design of low-mobility parallel manipulators is presented. A 4-degree-of-freedom symmetric parallel manipulator for Schönflies-motion generation is taken as a case study. The design goals used are workspace volume and manipulator dexterity based on a dispersion weighted Frobenius norm. In addition, an expression for energy per cycle has been defined for different types of trajectory to evaluate the power drive. Finally, the set of Pareto-optimal solutions of the design parameters are represented in the design parameter space.

scholarly journals Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

2020 ◽  
Vol 2020 ◽  
pp. 1-23 ◽  
Author(s):  
Jiuyuan Huo ◽  
Liqun Liu
Keyword(s):  
Objective Function ◽  
Parameter Optimization ◽  
Optimization Problem ◽  
Hydrological Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Hydrological Forecasting ◽  
Model Parameter Optimization

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

Analysis and Optimization of Staggered Partial Diffuser Vanes in a Centrifugal Pump

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Hyeon-Seok Shim ◽  
Sang-Hoon Kim ◽  
Kwang-Yong Kim
Keyword(s):  
Centrifugal Pump ◽  
Stokes Equations ◽  
Maximum Pressure ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Baseline Design ◽  
Operating Range ◽  
Full Height

Abstract A performance analysis and three-objective design optimization were performed for the staggered partial diffuser vanes in a centrifugal pump using three-dimensional Reynolds-averaged Navier–Stokes equations. First, the performance of the diffuser vanes was evaluated for four different arrangements: full-height diffuser vanes, vaneless diffuser, half vanes attached to the hub, half vanes attached to the shroud, and staggered vanes attached alternately to the hub and the shroud. The staggered partial diffuser vanes were optimized using the following design variables: the installation angle of the vanes, the heights of the vanes attached to the hub and shroud, and the angle of rotation of the straight part on the pressure surface of the vanes. The objective functions were the hydraulic efficiency, the flowrate of the maximum pressure recovery, and the operating range of the diffuser. The Kriging model was used to construct surrogate models of the objective functions based on the results at the design points obtained by Latin hypercube sampling. The Pareto-optimal solutions were obtained by a multi-objective genetic algorithm (MOGA). The representative Pareto-optimal solutions for the staggered diffuser vanes obtained by the K-means clustering showed the improved performances in terms of both the hydraulic performance and operating range compared with the full-height diffuser vanes and the baseline design.

Aerodynamic Performances and Flow Fields of Pareto Optimal Solutions in an Aerodynamic Design of a Wind-Lens Turbine

2015 ◽  
Author(s):  
Nobuhito Oka ◽  
Masato Furukawa ◽  
Kazutoyo Yamada ◽  
Akihiro Oka ◽  
Yasushi Kurokawa
Keyword(s):  
Optimal Design ◽  
Wind Tunnel ◽  
Design Method ◽  
Flow Fields ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Aerodynamic Design ◽  
Aerodynamic Performances ◽  
Optimal Design Method

The new type of shrouded wind turbine called “wind-lens turbine” has been developed. The wind-lens turbine has a brimmed diffuser called “wind-lens”, by which the wind concentration on the turbine blade and the significant enhancement of the turbine output can be achieved. A simultaneous optimization method for the aerodynamic design of rotor blade and wind-lens has been developed. The present optimal design method is based on a genetic algorithm (GA) which enables multi objective aerodynamic optimization. In the present study, aerodynamic performances and flow fields of the Pareto optimal solutions of wind-lens turbines designed by the present optimal design method have been investigated by wind-tunnel tests and three-dimensional Reynolds averaged Navier-Stokes (RANS) analyses. Output power coefficients obtained from the wind-tunnel tests in the optimal wind-lens turbine exceeded the Betz limit, which is the performance limitation for bare wind turbines. The numerical results and the experimental results show that the suppression of flow separations in the diffuser is important to achieve significant improvement in aerodynamic performances. As a result, it is found that the aerodynamic performance of wind-lens turbine is significantly affected by the interrelationship between the internal and external flow fields around the wind-lens.

scholarly journals Sensitivity analysis for parametric vector optimization problems using differential equations approach

2001 ◽  
Vol 25 (9) ◽  
pp. 621-628
Author(s):  
Fatma M. Ali
Keyword(s):  
Differential Equations ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Parametric Vector Optimization ◽  
Local Solutions

A new method for obtaining sensitivity information for parametric vector optimization problems(VOP)vis presented, where the parameters in the objective functions and anywhere in the constraints. This method depends on using differential equations technique for solving multiobjective nonlinear programing problems which is very effective in finding many local Pareto optimal solutions. The behavior of the local solutions for slight perturbation of the parameters in the neighborhood of their chosen initial values is presented by using the technique of trajectory continuation. Finally some examples are given to show the efficiency of the proposed method.

A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems

2019 ◽  
Vol 53 (3) ◽  
pp. 867-886
Author(s):  
Mehrdad Ghaznavi ◽  
Narges Hoseinpoor ◽  
Fatemeh Soleimani
Keyword(s):  
Multiobjective Optimization ◽  
Newton Method ◽  
Optimization Problems ◽  
Order Relation ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Generalized Hukuhara Differentiability

In this study, a Newton method is developed to obtain (weak) Pareto optimal solutions of an unconstrained multiobjective optimization problem (MOP) with fuzzy objective functions. For this purpose, the generalized Hukuhara differentiability of fuzzy vector functions and fuzzy max-order relation on the set of fuzzy vectors are employed. It is assumed that the objective functions of the fuzzy MOP are twice continuously generalized Hukuhara differentiable. Under this assumption, the relationship between weakly Pareto optimal solutions of a fuzzy MOP and critical points of the related crisp problem is discussed. Numerical examples are provided to demonstrate the efficiency of the proposed methodology. Finally, the convergence analysis of the method under investigation is discussed.

Multiobjective Hybrid Optimization–Antioptimization for Force Design of Tensegrity Structures

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Makoto Ohsaki ◽  
Jingyao Zhang ◽  
Isaac Elishakoff
Keyword(s):  
Optimization Problem ◽  
Hybrid Approach ◽  
Programming Approach ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Tensegrity Structures ◽  
Tangent Stiffness Matrix ◽  
Lowest Eigenvalue

Properties of Pareto optimal solutions considering bounded uncertainty are first investigated using an illustrative example of a simple truss. It is shown that the nominal values of the Pareto optimal solutions considering uncertainty are slightly different from those without considering uncertainty. Next a hybrid approach of multiobjective optimization and antioptimization is presented for force design of tensegrity structures. We maximize the lowest eigenvalue of the tangent stiffness matrix and minimize the deviation of forces from the specified target distribution. These objective functions are defined as the worst values due to the possible errors in the fabrication and construction processes. The Pareto optimal solutions are found by solving the two-level optimization–antioptimization problems using a nonlinear programming approach for the upper optimization problem and enumeration of the vertices of the uncertain region for the lower antioptimization problem.

scholarly journals Optimization Of Multi-Module CrN/CrCN Coatings

2015 ◽  
Vol 60 (2) ◽  
pp. 1037-1043
Author(s):  
Ł. Szparaga ◽  
P. Bartosik ◽  
A. Gilewicz ◽  
J. Ratajski
Keyword(s):  
Optimization Procedure ◽  
Stress And Strain ◽  
Pareto Optimal ◽  
Mutual Distance ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Decision Criteria ◽  
Decision Variables ◽  
42Crmo4 Steel ◽  
The Stability

Abstract In the paper was proposed optimization procedure supporting the prototyping of the geometry of multi-module CrN/CrCN coatings, deposited on substrates from 42CrMo4 steel, in respect of mechanical properties. Adopted decision criteria were the functions of the state of internal stress and strain in the coating and substrate, caused by external mechanical loads. Using developed optimization procedure the set of optimal solutions (Pareto-optimal solutions) of coatings geometry parameters, due to the adopted decision criteria was obtained. For the purposes of analysis of obtained Pareto-optimal solutions, their mutual distance in the space of criteria and decision variables were calculated, which allowed to group solutions in the classes. Also analyzed the number of direct neighbors of Pareto-optimal solutions for the purposes of assessing the stability of solutions.

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