A Dynamical Trajectory-Based Methodology for Systematically Computing Multiple Optimal Solutions of General Nonlinear Programming Problems

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

Download Full-text

Iterative Fixture Layout and Clamping Force Optimization Using the Genetic Algorithm

Journal of Manufacturing Science and Engineering ◽

10.1115/1.1414127 ◽

2001 ◽

Vol 124 (1) ◽

pp. 119-125 ◽

Cited By ~ 55

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.

Download Full-text

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

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406219863086 ◽

2019 ◽

Vol 233 (18) ◽

pp. 6538-6558 ◽

Cited By ~ 1

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.

Download Full-text