Nonlinear Integer and Discrete Programming in Mechanical Design

1988 ◽  
Author(s):  
E. Sandgren
Keyword(s):  
Mechanical Design ◽  
General Purpose ◽  
Conceptual Level ◽  
Design Problems ◽  
Design Decisions ◽  
Design Variables ◽  
Nonlinear Mathematical Programming ◽  
Discrete Programming ◽  
Mathematical Programming Problems ◽  
Quadratic Programming Method

Abstract A general purpose algorithm for the solution of nonlinear mathematical programming problems containing integer, discrete, zero-one and continuous design variables is described. The algorithm implements a branch and bound procedure in conjunction with both an exterior penalty function and a quadratic programming method. Variable bounds are handled independently from the design constraints which removes the necessity to reformulate the problem at each branching node. Examples are presented to demonstrate the utility of the algorithm for solving design problems. The use of zero-one variables to represent design decisions in order to allow conceptual level design to be performed is demonstrated.

Nonlinear Integer and Discrete Programming in Mechanical Design Optimization

1990 ◽  
Vol 112 (2) ◽  
pp. 223-229 ◽  
Author(s):  
E. Sandgren
Keyword(s):  
Mathematical Programming ◽  
Mechanical Design ◽  
General Purpose ◽  
Design Problems ◽  
Design Constraints ◽  
Design Variables ◽  
Nonlinear Mathematical Programming ◽  
Discrete Programming ◽  
Mathematical Programming Problems ◽  
Quadratic Programming Method

A general purpose algorithm for the solution of nonlinear mathematical programming problems containing integer, discrete, zero-one, and continuous design variables is described. The algorithm implements a branch and bound procedure in conjunction with either an exterior penalty function or a quadratic programming method. Variable bounds are handled independently from the design constraints which removes the necessity to reformulate the problem at each branching node. Examples are presented to demonstrate the utility of the algorithm for solving design problems.

Nonlinear Integer and Discrete Programming for Topological Decision Making in Engineering Design

1990 ◽  
Vol 112 (1) ◽  
pp. 118-122 ◽  
Author(s):  
E. Sandgren
Keyword(s):  
Decision Making ◽  
Material Selection ◽  
Nonlinear Problems ◽  
Problem Formulation ◽  
General Purpose ◽  
Design Decisions ◽  
Topological Design ◽  
Design Variables ◽  
Discrete Programming ◽  
Quadratic Programming Method

The use of integer, discrete, and zero-one design variables to represent topological design decisions is presented. A general purpose algorithm for solving nonlinear problems involving material assembly and other topological decisions is described. The algorithm couples a branch and bound approach with an exterior penalty function and a quadratic programming method. Examples concerning the design of a support beam and a structural truss are presented with decisions involving material selection, assembly, and crossectional geometry included in the problem formulation.

Improving Mechanical Design Decisions With Alternate Formulations of Constraints

1990 ◽  
Author(s):  
John D. Watton ◽  
James R. Rinderle
Keyword(s):  
Mechanical Design ◽  
Simple Design ◽  
Active Constraint ◽  
Design Decisions ◽  
Design Synthesis ◽  
Design Variables ◽  
Design Activities ◽  
Physical Insight ◽  
Important Design ◽  
Quantitative Evaluations

Abstract Mechanical design equations which relate performance and functionality to design variables are often highly coupled, nonlinear parametric equations. The structure of these interacting equations can be simplified by a reformulation based on alternative design variables. For many design configurations the reformulation results in highly beneficial improvement in equation monotonicity and complexity. The benefits include convenience and expediency in quantitative evaluations in addition to enhanced physical insight. They facilitate such important design activities as computing satisfactory solutions, active constraint recognition for optimizations, and the decomposition of design decisions. The reformulations can be thought of as alternative views of the design configuration that provide abstractions that can promote design synthesis. In this paper we discuss and illustrate the nature of these benefits with a number of simple design examples.

A Network Reliability Approach to Optimal Decomposition of Design Problems

1994 ◽  
Author(s):  
Nestor F. Michelena ◽  
Panos Y. Papalambros
Keyword(s):  
Design Problem ◽  
Network Reliability ◽  
Network Connectivity ◽  
Master Problem ◽  
Design Problems ◽  
Decomposition Problem ◽  
Design Variables ◽  
Communication Links ◽  
Two Measures ◽  
Mathematical Programming Problems

Abstract This article addresses the problem of identifying the optimal decomposition of a design problem. Methods for solving decomposed mathematical programming problems require that an appropriate structure suitable for decomposition be identified. This first step consists of identifying linking (or coordinating) variables or functions that effect independent subproblems coordinated by a master problem. We present a network reliability-based solution of the optimal decomposition problem that avoids heuristics and subjective criteria for the identification of linking variables and evaluation of partitions. The relationships among design variables, i.e., the constraint functions, are modeled as the processing units of a network. The design variables themselves are modeled as the communication links between these units. The optimal decomposition problem is then reduced to one of finding the links that have the most effect on the overall network connectivity. Two measures of network reliability, all-terminal and pair-connected reliability, are used as measures of network (and design problem) connectivity. The optimal decomposition is attained by minimizing the network reliability while maximizing the number of operating links.

A Distributed Pool Architecture for Highly Constrained Optimization Problems in Complex Systems Design

2013 ◽  
Vol 13 (3) ◽  
Author(s):  
Vijitashwa Pandey ◽  
Zissimos P. Mourelatos
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Solution Process ◽  
Systems Design ◽  
Mixed Integer ◽  
Engineering Systems ◽  
Design Problems ◽  
Design Variables ◽  
Complex Engineering

Optimal design of complex engineering systems is challenging because numerous design variables and constraints are present. Dynamic changes in design requirements and lack of complete knowledge of subsystem requirements add to the complexity. We propose an enhanced distributed pool architecture to aid distributed solving of design optimization problems. The approach not only saves solution time but is also resilient against failures of some processors. It is best suited to handle highly constrained design problems, with dynamically changing constraints, where finding even a feasible solution (FS) is challenging. In our work, this task is distributed among many processors. Constraints can be easily added or removed without having to restart the solution process. We demonstrate the efficacy of our method in terms of computational savings and resistance to partial failures of some processors, using two mixed integer nonlinear programming (MINLP)-class mechanical design optimization problems.

A State Space Technique for Optimal Design of Mechanisms

1982 ◽  
Vol 104 (4) ◽  
pp. 792-798 ◽  
Author(s):  
V. N. Sohoni ◽  
E. J. Haug
Keyword(s):  
Optimal Design ◽  
State Space ◽  
Optimization Algorithm ◽  
System Optimization ◽  
Design Sensitivity ◽  
General Purpose ◽  
Design Problems ◽  
Design Variables ◽  
Space Technique ◽  
Element Technique

Problems of optimal design of mechanisms are formulated in a state space setting that allows treatment of general design objectives and constraints. A constrained multi-element technique is employed for velocity, acceleration, and kineto-static analysis of mechanisms. An adjoint variable technique is employed to compute derivatives with respect to design of general cost and constraint functions involving kinematic, force, and design variables. A generalized steepest descent optimization algorithm is employed, using the design sensitivity analysis methods developed, as the basis for a general purpose kinematic system optimization algorithm. Two optimal design problems are solved to demonstrate effectiveness of the method.

A Network Reliability Approach to Optimal Decomposition of Design Problems

1995 ◽  
Vol 117 (3) ◽  
pp. 433-440 ◽  
Author(s):  
N. F. Michelena ◽  
P. Y. Papalambros
Keyword(s):  
Mathematical Programming ◽  
Network Reliability ◽  
Master Problem ◽  
Design Problems ◽  
Decomposition Problem ◽  
Design Variables ◽  
Communication Links ◽  
Mathematical Programming Problems

Methods for solving partitioned mathematical programming problems require that an appropriate structure suitable for decomposition be identified. This first step consists of identifying linking variables that effect independent subproblems coordinated by a master problem. This article presents a network reliability-based solution of the optimal decomposition problem that avoids subjective criteria to identify linking variables and partitions. The relationships among design variables are modeled as the processing units of a network. The design variables themselves are modeled as the communication links between these units. The optimal decomposition is attained by minimizing the network reliability while maximizing the number of operating links.

A Distributed Pool Architecture for Highly Constrained Optimization Problems in Complex Systems Design

2011 ◽  
Author(s):  
Vijitashwa Pandey ◽  
Zissimos P. Mourelatos
Keyword(s):  
Complex Systems ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Systems Design ◽  
Optimization Approach ◽  
Dynamic Changes ◽  
Design Problems ◽  
Complete Knowledge ◽  
Design Variables ◽  
Design Requirements

The design of complex systems design is challenging because of the presence of numerous design variables and constraints. Dynamic changes in design requirements and lack of complete knowledge of subsystem requirements add to the complexity. A recently proposed pool architecture has been shown to aide distributed solving of optimization problems. The approach not only saves solution time but also has other benefits like resiliency against failures of some processors. We apply this approach in this paper, to highly constrained design problems, with dynamically changing constraints, where finding a feasible solution is challenging. This task is distributed between the processors in the methodology we propose. We demonstrate the efficacy of our method using an MINLP-class of mechanical design optimization problem. We demonstrate the computational savings and the resistance to partial failures in the processors. In addition, we show how the optimization approach can adapt to dynamic changes in design constraints.

Entropic Method for Sequencing Discrete Design Decisions

2009 ◽  
Author(s):  
Chiradeep Sen ◽  
Farhad Ameri ◽  
Joshua D. Summers
Keyword(s):  
Engineering Design ◽  
Design Process ◽  
Design Solution ◽  
Design Problems ◽  
Design Decisions ◽  
Additional Information ◽  
Task Sequencing ◽  
Design Variables ◽  
Engineering Design Problems ◽  
Measure Of Uncertainty

Early stages of engineering design processes are characterized by high levels of uncertainty due to incomplete knowledge. As the design progresses, additional information is externally added or internally generated within the design process. As a result, the design solution becomes increasingly well-defined and the uncertainty of the problem reduces, diminishing to zero at the end of the process when the design is fully defined. In this research a measure of uncertainty is proposed for a class of engineering design problems called discrete design problems. Previously, three components of complexity in engineering design, namely, size, coupling and solvability, were identified. In this research uncertainty is measured in terms of the number of design variables (size) and the dependency between the variables (coupling). The solvability of each variable is assumed to be uniform for the sake of simplicity. The dependency between two variables is measured as the effect of a decision made on one variable on the solution options available to the other variable. A measure of uncertainty is developed based on this premise, and applied to an example problem to monitor uncertainty reduction through the design process. Results are used to identify and compare three task-sequencing strategies in engineering design.

Multi-Objective Design Problem of Tire Wear and Visualization of Its Pareto Solutions2

2006 ◽  
Vol 34 (3) ◽  
pp. 170-194 ◽  
Author(s):  
M. Koishi ◽  
Z. Shida
Keyword(s):  
Inverse Problems ◽  
Conceptual Design ◽  
Dimensional Space ◽  
Design Stage ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Design Problems ◽  
Multi Objective ◽  
Design Engineers ◽  
Design Variables

Abstract Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

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