### Abstract

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 SysMLTM) 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.

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 SysMLTM) 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.

Original language | English |
---|---|

Publication status | Published - 2010 |

Event | ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010, August 15, 2010 - August 18, 2010 - Montreal, QC, Canada Duration: 1 Jan 2010 → … |

### Conference

Conference | ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010, August 15, 2010 - August 18, 2010 |
---|---|

Country | Canada |

City | Montreal, QC |

Period | 1/01/10 → … |

### Keywords

- MINLP
- CSP
- mixed integer nonlinear programming
- constraint satisfaction problems
- SysML
- model transformations
- Component sizing
- GAMS

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## Cite this

Shah, A. A., Paredis, C., Burkhat, R., & Schaefer, D. (2010).

*Combining Mathematical Programming and SysML for Component Sizing of Hydraulic Systems*. Paper presented at ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010, August 15, 2010 - August 18, 2010, Montreal, QC, Canada.