The Optimal Column

1974 ◽  
Vol 96 (1) ◽  
pp. 71-76 ◽  
Author(s):  
W. J. Carter ◽  
K. M. Ragsdell
Keyword(s):  
Search Algorithm ◽  
Elastic Behavior ◽  
Gradient Search ◽  
Optimal Column ◽  
Problem Of Lagrange

A new numerical search algorithm is presented which is employed to determine optimum shapes for pin-ended columns having elastic behavior. The search algorithm utilizes a gradient search scheme to seek out the optimum solutions. A Lagrange-like solution is given for the Strongest Column Problem of Lagrange.

Optimum Synthesis of Rigid Mechanisms Using Real Coded Quantum-Inspired Evolution Algorithm (RQIEA) With Neighborhood Search

2007 ◽  
Author(s):  
Ahmad Smaili ◽  
Mazen Hassanieh ◽  
Bachir Chaaya ◽  
Fawzan Al Fares
Keyword(s):  
Quantum Computing ◽  
Search Algorithm ◽  
Random Search ◽  
Quantum Gates ◽  
Neighborhood Search ◽  
Gradient Search ◽  
Quantum Bits ◽  
Optimum Synthesis ◽  
Evolution Algorithm ◽  
Optimization Schemes

A modified real coded quantum-inspired evolution algorithm (MRQIEA) is herein presented for optimum synthesis of planar rigid body mechanisms (RBMs). The MRQIEA employs elements of quantum computing such as quantum bits, registers, and quantum gates, neighborhood search engine, and gradient search to form a random search algorithm for solution optimization of a wide class of problems. A brief overview of the quantum computing elements and their adaptation to the optimization algorithm is first presented. The algorithm is then adapted to the synthesis problem of RBMs. Finally, the algorithm is demonstrated and compared to other search methods by way of three examples, including two benchmark examples that have been used in the literature to assess the performance of other optimization schemes.

A Tabu-Gradient Search-Based Optimization Technique for Synthesis of Mechanisms

2004 ◽  
Author(s):  
Ahmad Smaili ◽  
Naji Atallah
Keyword(s):  
Tabu Search ◽  
Global Minimum ◽  
Short Term Memory ◽  
Search Algorithm ◽  
Random Search ◽  
Optimization Technique ◽  
Optimization Methods ◽  
Gradient Search ◽  
Optimum Synthesis ◽  
Timing Task

Mechanism synthesis requires the use of optimization methods to obtain approximate solution whenever the desired number of positions the mechanism is required to traverse exceeds a few (five in a 4R linkage). Deterministic gradient-based methods are usually impractical when used alone because they move in the direction of local minima. Random search methods on the other hand have a better chance of converging to a global minimum. This paper presents a tabu-gradient search based method for optimum synthesis of planar mechanisms. Using recency-based short-term memory strategy, tabu-search is initially used to find a solution near global minimum, followed by a gradient search to move the solution ever closer to the global minimum. A brief review of tabu search method is presented. Then, tabu-gradient search algorithm is applied to synthesize a four-bar mechanism for a 10-point path generation with prescribed timing task. As expected, Tabu-gradient base search resulted in a better solution with less number of iterations and shorter run-time.

TU-D-ValA-06: Incorporation of Modulation Range Constraints Into a Gradient Search Algorithm for IMRT Optimization

2006 ◽  
Vol 33 (6Part17) ◽  
pp. 2202-2202 ◽  
Author(s):  
R Popple ◽  
I Brezovich ◽  
J Fiveash ◽  
J Duan ◽  
S Shen ◽  
...  
Keyword(s):  
Search Algorithm ◽  
Gradient Search

Optimal Rejection of Stochastic and Deterministic Disturbances

1997 ◽  
Vol 119 (1) ◽  
pp. 140-143 ◽  
Author(s):  
A. G. Sparks ◽  
D. S. Bernstein
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
Necessary Conditions ◽  
Search Algorithm ◽  
Gradient Search ◽  
Feedback Controllers ◽  
Internal Model Principle ◽  
Rejection Cost ◽  
The Cost ◽  
Quasi Newton

The problem of optimal H2 rejection of noisy disturbances while asymptotically rejecting constant or sinusoidal disturbances is considered. The internal model principle is used to ensure that the expected value of the output approaches zero asymptotically in the presence of persistent deterministic disturbances. Necessary conditions are given for dynamic output feedback controllers that minimize an H2 disturbance rejection cost plus an upper bound on the integral square output cost for transient performance. The necessary conditions provide expressions for the gradients of the cost with respect to each of the control gains. These expressions are then used in a quasi-Newton gradient search algorithm to find the optimal feedback gains.

scholarly journals THE PATH TOWARDS A LONGER LIFE: ON INVARIANT SETS AND THE ESCAPE TIME LANDSCAPE

2005 ◽  
Vol 15 (05) ◽  
pp. 1615-1624 ◽  
Author(s):  
ERIK M. BOLLT
Keyword(s):  
Simplex Method ◽  
Search Algorithm ◽  
Invariant Set ◽  
Invariant Sets ◽  
Escape Time ◽  
Two Dimensional ◽  
Gradient Search ◽  
Dimensional Flow ◽  
Chaotic Transients ◽  
Dimensional Instability

Unstable invariant sets are important to understand mechanisms behind many dynamically important phenomenon such as chaotic transients which can be physically relevant in experiments. However, unstable invariant sets are nontrivial to find computationally. Previous techniques such as the PIM triple method [Nusse & Yorke, 1989] and simplex method variant [Moresco & Dawson, 1999], and even the step-and-stagger method [Sweet et al., 2001] have computationally inherent dimension limitations. In the current study, we explicitly investigate the landscape of an invariant set, which leads us to a simple gradient search algorithm to construct points close to the invariant set. While the calculation of the necessary derivatives can be computationally very expensive, the methods of our algorithm are not as dimension dependant as the previous techniques, as we show by examples such as the two-dimensional instability example from [Sweet et al., 2001] followed by a four-dimensional instability example, and then a nine-dimensional flow from the Yoshida equations, with a two-dimensional instability.

Discrete-Continuous Configuration Optimization Methods for Structures Using the Harmony Search Algorithm

2006 ◽  
Vol 324-325 ◽  
pp. 1293-1296 ◽  
Author(s):  
K.S. Lee ◽  
Chang Sik Choi
Keyword(s):  
Search Algorithm ◽  
Random Search ◽  
Optimization Technique ◽  
Harmony Search ◽  
Optimization Methods ◽  
Harmony Search Algorithm ◽  
Perfect State ◽  
Gradient Search ◽  
Geometric Variables ◽  
Derivative Information

This paper proposes an efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat integrated discrete sizing and continuous geometric variables. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so derivative information is unnecessary. A benchmark truss example is presented to demonstrate the effectiveness and robustness of the new method, as compared to current optimization methods. The numerical results reveal that the proposed method is a powerful search and design optimization technique for structures with discrete member sizes, and may yield better solutions than those obtained using current methods.

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