A Convex Cutting Plane Algorithm for Global Solution of Generalized Polynomial Optimal Design Models

1996 ◽  
Vol 118 (1) ◽  
pp. 82-88 ◽  
Author(s):  
Chihsiung Lo ◽  
P. Y. Papalambros
Keyword(s):  
Global Optimization ◽  
Cutting Plane ◽  
Test Problems ◽  
Cutting Plane Algorithm ◽  
Computational Results ◽  
Design Models ◽  
Generalized Polynomial ◽  
Speed Reducer ◽  
Improved Performance ◽  
Search Approach

Global optimization algorithms for generalized polynomial design models using a global feasible search approach was discussed in a previous article. A new convex cutting plane algorithm (CONCUT) based on global feasible search and with improved performance is presented in this sequel article. Computational results of the CONCUT algorithm compared to one using linear cuts (LINCUT) are given for various test problems. A speed reducer design example illustrates the application of the algorithms.

A Convex Cutting Plane Algorithm for Global Solution of Generalized Polynomial Optimal Design Models

1992 ◽  
Author(s):  
Chihsiung Lo ◽  
Panos Y. Papalambros
Keyword(s):  
Global Optimization ◽  
Cutting Plane ◽  
Test Problems ◽  
Cutting Plane Algorithm ◽  
Computational Results ◽  
Design Models ◽  
Generalized Polynomial ◽  
Speed Reducer ◽  
Improved Performance ◽  
Search Approach

Abstract Global optimization algorithms for generalized polynomial design models using a global feasible search approach was discussed in a previous article. A new convex cutting plane algorithm (CONCUT) based on global feasible search and with improved performance is presented in this sequel article. Computational results of the CONCUT algorithm compared to one using linear cuts (LINCUT) are given for various test problems. Two design examples, a speed reducer and a corrugated bulkhead design, illustrate the application of the algorithms.

scholarly journals A Strong Class of Lifted Valid Inequalities for the Shortest Path Problem in Digraphs with Negative Cost Cycles

2015 ◽  
Vol 7 (4) ◽  
pp. 162 ◽  
Author(s):  
Mamane Souleye Ibrahim
Keyword(s):  
Shortest Path ◽  
Valid Inequalities ◽  
Cutting Plane ◽  
Shortest Path Problem ◽  
Integer Solution ◽  
Linear Relaxation ◽  
Cutting Plane Algorithm ◽  
Computational Results

In this paper, we address a strong class of lifted valid inequalities for the shortest path problem in digraphs with possibly negative cost cycles. We call these lifted inequalities the $incident \ lifted \ valid \ inequalities$ ($ILI$) as they are based on the incident arcs of a given vertex.  The $ILI$ inequalities are close in spirit of the so-called \textit{simple lifted valid inequalities} ($SLI$) and $cocycle \ lifted \ valid \ inequalities$ ($CLI$) introduced in Ibrahim et al. (2015). However, as we will see the $ILI$ inequalities are stronger than the first ones in term of linear relaxation strengthening. Indeed, contrary to  $SLI$ and $CLI$ inequalities, consider the same instances, in a cutting plane algorithm, the computational results prove that the $ILI$ inequalities provide the optimal integer solution for all the considered instances within no more than three iterations except one case for which after the first strengthening iteration, there exists no generated inequality.

Packing Steiner trees: a cutting plane algorithm and computational results

1996 ◽  
Vol 72 (2) ◽  
pp. 125-145 ◽  
Author(s):  
M. Grötschel ◽  
A. Martin ◽  
R. Weismantel
Keyword(s):  
Cutting Plane ◽  
Steiner Trees ◽  
Cutting Plane Algorithm ◽  
Computational Results

scholarly journals Finding Global Minima with a Filled Function Approach for Non-Smooth Global Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Weixiang Wang ◽  
Youlin Shang ◽  
Ying Zhang
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Numerical Test ◽  
Function Approach ◽  
Global Optimization Problem ◽  
Computational Results ◽  
Filled Function ◽  
Global Minima ◽  
Smooth Case ◽  
Definition Of

A filled function approach is proposed for solving a non-smooth unconstrained global optimization problem. First, the definition of filled function in Zhang (2009) for smooth global optimization is extended to non-smooth case and a new one is put forwarded. Then, a novel filled function is proposed for non-smooth the global optimization and a corresponding non-smooth algorithm based on the filled function is designed. At last, a numerical test is made. The computational results demonstrate that the proposed approach is effcient and reliable.

On Global Feasible Search for Global Design Optimization With Application to Generalized Polynomial Models

1992 ◽  
Author(s):  
Chihsiung Lo ◽  
Panos Y. Papalambros
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Model Transformation ◽  
Special Problem ◽  
Search Algorithms ◽  
Deterministic Global Optimization ◽  
Generalized Polynomial ◽  
Polynomial Models ◽  
Feasible Solutions ◽  
Global Design Optimization

Abstract A powerful idea for deterministic global optimization is the use of global feasible search, namely, algorithms that guarantee finding feasible solutions of nonconvex problems or prove that none exists. In this article, a set of conditions for global feasible search algorithms is established. The utility of these conditions is demonstrated on two algorithms that solve special problem classes globally. Also, a new model transformation is shown to convert a generalized polynomial problem into one of the special classes above. A flywheel design example illustrates the approach. A sequel article provides further computational details and design examples.

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

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