Canonical Duality-Triality Theory: Bridge Between Nonconvex Analysis/Mechanics and Global Optimization in Complex System

2017 ◽  
pp. 1-47 ◽  
Author(s):  
David Yang Gao ◽  
Ning Ruan ◽  
Vittorio Latorre
Keyword(s):  
Complex System ◽  
Global Optimization ◽  
Canonical Duality ◽  
Triality Theory ◽  
Nonconvex Analysis

Evolutionary design of modular robotic arms

Robotica ◽  
2008 ◽  
Vol 26 (3) ◽  
pp. 323-330 ◽  
Author(s):  
O. Chocron
Keyword(s):  
Complex System ◽  
Global Optimization ◽  
Design Knowledge ◽  
Evolutionary Design ◽  
Artificial Evolution ◽  
3D Kinematics ◽  
Robotic Arms ◽  
Prismatic Joints ◽  
Evolution Dynamics ◽  
Complex System Design

SUMMARYThis paper proposes a method for task based design of modular serial robotic arms using evolutionary algorithms (EA). We introduce a 3D kinematics and a global optimization for both topology and configuration from task specifications. The search features revolute as well as prismatic joints and any number of DOF to build up a solution without using any design knowledge. A study of the evolution dynamics gives some keys to set evolution parameters that enable artificial evolution. An adapted algorithm dealing with the topology/configuration search tradeoff is proposed, descibed, and discussed. Illustrations of the algorithms results are given and conclusions are drawn from their analysis. Perspectives of this work are given, extending its reach to control and complex system design.

Fuzzy global optimization of complex system reliability

2000 ◽  
Vol 8 (3) ◽  
pp. 241-248 ◽  
Author(s):  
V. Ravi ◽  
P.J. Reddy ◽  
H.-J. Zimmermann
Keyword(s):  
Complex System ◽  
Global Optimization ◽  
System Reliability

scholarly journals Complete Solutions to General Box-Constrained Global Optimization Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Dan Wu ◽  
Youlin Shang
Keyword(s):  
Optimal Control ◽  
Global Optimization ◽  
Optimization Problems ◽  
Analytical Form ◽  
Optimization Method ◽  
Global Optimality ◽  
Constrained Optimal Control ◽  
Canonical Duality ◽  
General Nonlinear Programming ◽  
Complete Solutions

This paper presents a global optimization method for solving general nonlinear programming problems subjected to box constraints. Regardless of convexity or nonconvexity, by introducing a differential flow on the dual feasible space, a set of complete solutions to the original problem is obtained, and criteria for global optimality and existence of solutions are given. Our theorems improve and generalize recent known results in the canonical duality theory. Applications to a class of constrained optimal control problems are discussed. Particularly, an analytical form of the optimal control is expressed. Some examples are included to illustrate this new approach.

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