scholarly journals Generalized Augmented Lagrangian Problem and Approximate Optimal Solutions in Nonlinear Programming

2007 ◽  
Vol 2007 (1) ◽  
pp. 019323 ◽  
Author(s):  
Zhe Chen ◽  
Kequan Zhao ◽  
Yuke Chen
Keyword(s):  
Nonlinear Programming ◽  
Augmented Lagrangian ◽  
Optimal Solutions ◽  
Approximate Optimal Solutions

Iterative Fixture Layout and Clamping Force Optimization Using the Genetic Algorithm

2001 ◽  
Vol 124 (1) ◽  
pp. 119-125 ◽  
Author(s):  
Krishnakumar Kulankara ◽  
Srinath Satyanarayana ◽  
Shreyes N. Melkote
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Programming ◽  
Primary Objective ◽  
Fixture Design ◽  
Clamping Force ◽  
Optimal Solutions ◽  
Fixture Layout ◽  
Force Optimization ◽  
Nonlinear Programming Methods ◽  
Objective Being

Fixture design is a critical step in machining. An important aspect of fixture design is the optimization of the fixture, the primary objective being the minimization of workpiece deflection by suitably varying the layout of fixture elements and the clamping forces. Previous methods for fixture design optimization have treated fixture layout and clamping force optimization independently and/or used nonlinear programming methods that yield sub-optimal solutions. This paper deals with application of the genetic algorithm (GA) for fixture layout and clamping force optimization for a compliant workpiece. An iterative algorithm that minimizes the workpiece elastic deformation for the entire cutting process by alternatively varying the fixture layout and clamping force is proposed. It is shown via an example of milling fixture design that this algorithm yields a design that is superior to the result obtained from either fixture layout or clamping force optimization alone.

An improved formulation for optimizing rocker-bogie suspension rover for climbing steps

2019 ◽  
Vol 233 (18) ◽  
pp. 6538-6558 ◽  
Author(s):  
Sam Noble ◽  
K Kurien Issac
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Local Minimum ◽  
Single Step ◽  
Optimal Solutions ◽  
Performance Parameters ◽  
Smooth Functions ◽  
Gradient Based ◽  
Wheel Radius ◽  
Better Than

We address the problem of improving mobility of rovers with rocker-bogie suspension. Friction and torque requirements for climbing a single step were considered as performance parameters. The main contribution of the paper is an improved formulation for rover optimization using smooth functions, which enables use of powerful gradient based nonlinear programming (NLP) solvers for finding solutions. Our formulation does not have certain shortcomings present in some earlier formulations. We first formulate the problem of determining optimal torques to be applied to the wheels to minimize (a) friction requirement, and (b) torque requirement, and obtain demonstrably optimal solutions. We then formulate the problem of optimal design of the rover itself. Our solution for climbing a step of height two times the wheel radius is 13% better than that of the nominal rover. This solution is verified to be a local minimum by checking Karush–Kuhn–Tucker conditions. Optimal solutions were obtained for both forward and backward climbing. We show that some earlier formulations cannot obtain optimal solutions in certain situations. We also obtained optimal design for climbing steps of three different heights, with a friction requirement which is 15% lower than that of the nominal rover.

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