Combining Mathematical Programming and SysML for Automated Component Sizing of Hydraulic Systems

2010 ◽  
Author(s):  
Aditya A. Shah ◽  
Christiaan J. J. Paredis ◽  
Roger Burkhart ◽  
Dirk Schaefer
Keyword(s):  
Mathematical Programming ◽  
Problem Formulation ◽  
Automatic Generation ◽  
Modeling Language ◽  
Hydraulic Systems ◽  
Satisfactory Solution ◽  
Component Sizing ◽  
Declarative Modeling ◽  
State Of Practice ◽  
Architecture Component

In this paper, we present a framework that improves a designer’s capability to determine near-optimal sizes of components for a given system architecture. Component sizing is a hard problem to solve because of competing objectives, requirements from multiple disciplines, and the need for finding a solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, we introduce advances in the following two areas: a) Formulating a component sizing problem in a manner that is convenient to designers and b) Solving the problem efficiently so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal. An acausal, algebraic, equation-based, declarative modeling approach using mathematical programming (GAMS) is taken to solve these problems more efficiently. In addition the Systems Modeling Language (OMG SysML™) is used to formulate component sizing problems to facilitate problem formulation, model reuse and the automatic generation of low-level code that can be solved using GAMS and its solvers (BARON). This framework is demonstrated by applying it to an example of a hydraulic log splitter.

Combining Mathematical Programming and SysML for Automated Component Sizing of Hydraulic Systems

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Aditya A. Shah ◽  
Christiaan J. J. Paredis ◽  
Roger Burkhart ◽  
Dirk Schaefer
Keyword(s):  
Mathematical Programming ◽  
Graphical Representation ◽  
Problem Formulation ◽  
Automatic Generation ◽  
Hydraulic Systems ◽  
Component Sizing ◽  
Management Group ◽  
Declarative Modeling ◽  
Process Component ◽  
Multiple Scenarios

In this paper, we present a framework for automated component sizing to extend a designer's ability to evaluate a particular configuration during the architecture exploration phase of a design process. Component sizing is a hard problem to solve, both from a computational and modeling aspect. This is because of competing objectives, requirements from multiple disciplines, and the need to find a good solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, we introduce advances in the following two areas: (a) solving the problem efficiently so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal and (b) modeling a component sizing problem in a manner that is convenient to designers. An acausal, algebraic, equation-based, declarative modeling approach using mathematical programming (GAMS) is taken to solve these problems more efficiently. The object management group systems modeling language (OMG SysML™) is used to model component sizing problems in order to facilitate problem formulation, model reuse and automatic generation of low-level code that can be solved using GAMS and its solvers. This framework is demonstrated by applying it to an example of a hydraulic log splitter. Based on this initial example, we discuss two advantages of this framework—total time taken in solving multiple scenarios for a given configuration and the graphical representation of a problem in SysML.

A Mathematical Programming-Based Approach for Architecture Selection

2012 ◽  
Author(s):  
Aleksandr A. Kerzhner ◽  
Christiaan J. J. Paredis
Keyword(s):  
Mathematical Programming ◽  
Optimization Technique ◽  
Problem Formulation ◽  
Mixed Integer ◽  
Model Transformations ◽  
Continuous Variables ◽  
Solution Approach ◽  
Computational Support ◽  
Algebraic Constraints ◽  
Selection Of

Modern systems are difficult to design because there are a significant number of potential alternatives to consider. The specification of an alternative includes an architecture (which describes the components and connections of the system) and component sizings (the sizing parameter for each component). In current practice, designers rely mainly on their experience and intuition to select a desired architecture without much computational support and then spend most of their effort on optimizing component sizings. In this paper, an approach for representing an architecture selection as a mixed-integer linear programming optimization is presented; existing solvers are then used to identify promising candidate architectures at early stages of the design process. Mathematical programming is a common optimization technique, but it is rarely used for architecture selection because of the difficulty of manually formulating an architecture selection as a mathematical program. In this paper, the formulation is presented in a modular fashion so that model transformations can be applied to transform a problem formulation that is convenient for designers into the mathematical programming optimization. A modular superstructure representation is used to model the design space; in a superstructure a union of all potential architectures is represented as a set of discrete and continuous variables. Algebraic constraints are added to describe both acceptable variable combinations and system behavior to allow the solver to eliminate clearly poor alternatives and identify promising alternatives. The framework is demonstrated on the selection of an actuation subsystem for a hydraulic excavator, although the solution approach would be similar for most mechanical systems.

On the feasibility of constrained linear control problems with application to the ALSTOM gasifier

2005 ◽  
Vol 219 (3) ◽  
pp. 207-213 ◽  
Author(s):  
I K Kookos
Keyword(s):  
Problem Formulation ◽  
Control Law ◽  
Control Problems ◽  
Satisfactory Solution ◽  
Control Effort ◽  
Control Community ◽  
Academic Control ◽  
And Control ◽  
Process Constraints

In 1997 the ALSTOM Power Technology Centre issued an open challenge to the academic control community, which addressed the control of a gasifier plant at three different production levels. Despite the numerous attempts and control methodologies that have been applied to the ALSTOM benchmark case study no satisfactory solution has yet been presented. This work aims to study the feasibility of the gasifier control problem. It is shown that the problem formulation corresponds to an infeasible problem. More specifically, operation at nominal conditions (100 per cent load) is shown to be easy and minimum control effort is required to satisfy process specifications. Operation, on the other hand, at the 0 per cent load conditions is infeasible and as a result no control law can be found that satisfies all process constraints. In the light of the findings of this study it is recommended that the ALSTOM benchmark gasifier problem should be modified to alleviate the infeasibility problem.

scholarly journals On Linear and Quadratic Two-Stage Transportation Problem

2020 ◽  
pp. 5-14
Author(s):  
P. Stetsyuk ◽  
O. Lykhovyd ◽  
A. Suprun
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Transportation Problem ◽  
Quadratic Programming Problem ◽  
Modeling Language ◽  
Two Stage ◽  
Linear Programming Problems

Introduction. When formulating the classical two-stage transportation problem, it is assumed that the product is transported from suppliers to consumers through intermediate points. Intermediary firms and various kinds of storage facilities (warehouses) can act as intermediate points. The article discusses two mathematical models for two-stage transportation problem (linear programming problem and quadratic programming problem) and a fairly universal way to solve them using modern software. It uses the description of the problem in the modeling language AMPL (A Mathematical Programming Language) and depends on which of the known programs is chosen to solve the problem of linear or quadratic programming. The purpose of the article is to propose the use of AMPL code for solving a linear programming two-stage transportation problem using modern software for linear programming problems, to formulate a mathematical model of a quadratic programming two-stage transportation problem and to investigate its properties. Results. The properties of two variants of a two-stage transportation problem are described: a linear programming problem and a quadratic programming problem. An AMPL code for solving a linear programming two-stage transportation problem using modern software for linear programming problems is given. The results of the calculation using Gurobi program for a linear programming two-stage transportation problem, which has many solutions, are presented and analyzed. A quadratic programming two-stage transportation problem was formulated and conditions were found under which it has unique solution. Conclusions. The developed AMPL-code for a linear programming two-stage transportation problem and its modification for a quadratic programming two-stage transportation problem can be used to solve various logistics transportation problems using modern software for solving mathematical programming problems. The developed AMPL code can be easily adapted to take into account the lower and upper bounds for the quantity of products transported from suppliers to intermediate points and from intermediate points to consumers. Keywords: transportation problem, linear programming problem, AMPL modeling language, Gurobi program, quadratic programming problem.

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