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.

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.

scholarly journals A Quantum Adiabatic Algorithm for Multiobjective Combinatorial Optimization

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 32 ◽  
Author(s):  
Benjamín Barán ◽  
Marcos Villagra
Keyword(s):  
Combinatorial Optimization ◽  
Multiobjective Optimization ◽  
Theorem Proving ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Quantum Annealing ◽  
Multiobjective Optimization Problems ◽  
First Time

In this work we show how to use a quantum adiabatic algorithm to solve multiobjective optimization problems. For the first time, we demonstrate a theorem proving that the quantum adiabatic algorithm can find Pareto-optimal solutions in finite-time, provided some restrictions to the problem are met. A numerical example illustrates an application of the theorem to a well-known problem in multiobjective optimization. This result opens the door to solve multiobjective optimization problems using current technology based on quantum annealing.

Presorting as a method of acceleration of algorithms in multi-objective optimization problems

2016 ◽  
Vol 0 (0) ◽  
pp. 5-11
Author(s):  
Andrzej Ameljańczyk
Keyword(s):  
Distance Function ◽  
Pareto Front ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Minkowski Distance ◽  
Finite Set ◽  
Feasible Solutions

The paper presents a method of algorithms acceleration for determining Pareto-optimal solutions (Pareto Front) multi-criteria optimization tasks, consisting of pre-ordering (presorting) set of feasible solutions. It is proposed to use the generalized Minkowski distance function as a presorting tool that allows build a very simple and fast algorithm Pareto Front for the task with a finite set of feasible solutions.

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 Risk-Based Multiobjective Optimal Seismic Design for RC Piers Using the Response Surface Method and NSGA-II

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Sicong Hu ◽  
Yixuan Zou ◽  
Yufeng Gai ◽  
Zheng Huang ◽  
Guquan Song
Keyword(s):  
Response Surface ◽  
Seismic Design ◽  
Seismic Risk ◽  
Design Method ◽  
Design Parameters ◽  
Surface Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Seismic Design Method

In this paper, a risk-based multiobjective optimal seismic design method for reinforced concrete (RC) piers is proposed. This method is used to determine the size and reinforcement ratios of piers to minimize the seismic risk of bridge systems and the construction cost of piers. The Pacific Earthquake Engineering Research- (PEER-) based probabilistic seismic risk assessment approach and the response surface method (RSM) are adopted to develop the seismic risk response surface model, which represents the relationship between the design parameters of piers and the seismic risk of bridge systems. The Pareto optimal solutions of piers are determined by applying an improved version of the nondominated sorting genetic algorithm (NSGA-II). As a case study, the proposed optimal seismic design method is applied to a continuous concrete box girder bridge. The optimal design schemes of piers according to two strategies are determined from the Pareto optimal solutions. The results show that the seismic risk response surface model can be used to accurately describe the relationship between the design parameters of piers and the seismic risk of bridge systems. The case study demonstrates the effectiveness of the proposed optimal seismic design method. The analysis of the Pareto optimal solutions allows designers to more rationally conduct the seismic design of piers.

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.

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