scholarly journals Design Optimization of a Speed Reducer Using Deterministic Techniques

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ming-Hua Lin ◽  
Jung-Fa Tsai ◽  
Nian-Ze Hu ◽  
Shu-Chuan Chang
Keyword(s):  
Programming Problem ◽  
Design Problem ◽  
Geometric Programming ◽  
Global Optimum ◽  
Mixed Integer ◽  
Piecewise Linearization ◽  
Design Problems ◽  
Acceptable Error ◽  
Generalized Geometric Programming ◽  
Speed Reducer

The optimal design problem of minimizing the total weight of a speed reducer under constraints is a generalized geometric programming problem. Since the metaheuristic approaches cannot guarantee to find the global optimum of a generalized geometric programming problem, this paper applies an efficient deterministic approach to globally solve speed reducer design problems. The original problem is converted by variable transformations and piecewise linearization techniques. The reformulated problem is a convex mixed-integer nonlinear programming problem solvable to reach an approximate global solution within an acceptable error. Experiment results from solving a practical speed reducer design problem indicate that this study obtains a better solution comparing with the other existing methods.

Optimal Design of a Speed Reducer

2013 ◽  
Vol 376 ◽  
pp. 327-330 ◽  
Author(s):  
Ming Hua Lin ◽  
Jung Fa Tsai
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Design Problem ◽  
Geometric Programming ◽  
Deterministic Approach ◽  
Piecewise Linearization ◽  
Design Problems ◽  
Speed Reducer ◽  
The Mathematical Model ◽  
Linearization Techniques

The mathematical model for optimal design of a speed reducer is a generalized geometric programming problem that is non-convex and not easy be globally solved. This paper applies a deterministic approach including convexification strategies and piecewise linearization techniques to globally solve speed reducer design problems. A practical speed reducer design problem is solved to demonstrate that this study obtains a better solution than other methods.

scholarly journals A Review of Piecewise Linearization Methods

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ming-Hua Lin ◽  
John Gunnar Carlsson ◽  
Dongdong Ge ◽  
Jianming Shi ◽  
Jung-Fa Tsai
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Convex Programming Problem ◽  
Nonlinear Programming Problem ◽  
Global Optimal Solution ◽  
Piecewise Linearization ◽  
Linearization Methods ◽  
Global Optimal

Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.

scholarly journals An Optimal Classification Method for Biological and Medical Data

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Yao-Huei Huang ◽  
Yu-Chien Ko ◽  
Hao-Chun Lu
Keyword(s):  
Global Optimum ◽  
Medical Data ◽  
Classification Method ◽  
Mixed Integer ◽  
Nonlinear Program ◽  
Piecewise Linearization ◽  
Linearization Technique ◽  
Numerical Examples ◽  
Optimal Classification

This paper proposes a union of hyperspheres by the mixed-integer nonlinear program to classify biological and medical datasets. A classifying program with nonlinear terms uses piecewise linearization technique to obtain a global optimum. The numerical examples illustrate that the proposed method can obtain the global optimum more effectively than current methods.

scholarly journals Dynamic Plan Control: An Effective Tool to Manage Demand Considering Mobile Internet Network Congestion

2020 ◽  
Vol 11 (1) ◽  
pp. 91
Author(s):  
Xiaoyu Ma ◽  
Jihong Zhang ◽  
Yuan Cao ◽  
Zhou He ◽  
Jonas Nebel
Keyword(s):  
Programming Problem ◽  
Service Provider ◽  
Service Providers ◽  
Control Method ◽  
Network Capacity ◽  
Mobile Internet ◽  
Mixed Integer ◽  
Mobile Service ◽  
Data Traffic ◽  
Potential Customers

Rapidly increasing mobile data traffic have placed a significant burden on mobile Internet networks. Due to limited network capacity, a mobile network is congested when it handles too much data traffic simultaneously. In turn, some customers leave the network, which induces a revenue loss for the mobile service provider. To manage demand and maximize revenue, we propose a dynamic plan control method for the mobile service providers under connection-speed-restriction pricing. This method allows the mobile service provider to dynamically set the data plans’ availability for potential customers’ new subscriptions. With dynamic plan control, the service provider can adjust data network utilization and achieve high customer satisfaction and a low churn rate, which reflect high service supply chain performance. To find the optimal control policy, we transform the high-dimensional dynamic programming problem into an equivalent mixed integer linear programming problem. We find that dynamic plan control is an effective tool for managing demand and increasing revenue in the long term. Numerical evaluation with a large European mobile service provider further supports our conclusion. Furthermore, when network capacity or potential customers’ willingness to join the network changes, the dynamic plan control method generates robust revenue for the service provider.

Design Option Decision Tree: A Method for Schematic Analysis of a Design Problem and Integration of Human Factors Data

1974 ◽  
Vol 18 (3) ◽  
pp. 368-375
Author(s):  
William B. Askren ◽  
Kenneth D. Korkan
Keyword(s):  
Decision Tree ◽  
Human Factors ◽  
Design Problem ◽  
Aircraft Design ◽  
Decision Point ◽  
Specific Design ◽  
Design Problems ◽  
Design Option ◽  
Design Options ◽  
Evaluation Parameters

A Design Option Decision Tree (DODT) is a graphic means of showing the design options available at each decision point in the design process. Several examples of DODTs for aircraft design problems are shown. The procedures for developing a DODT are described. A proposed method for use of the DODT to resolve a design problem is presented. This method includes evaluating the design options in the Tree for impact on the system, and tracing paths through the Tree as dictated by specific design goals. The use of human factors data as one of the evaluation parameters is illustrated. The paper concludes with a discussion of other uses of a DODT.

Sign in / Sign up

Export Citation Format

Share Document