Expressing Special Structures in an Algebraic Modeling Language for Mathematical Programming

1995 ◽  
Vol 7 (2) ◽  
pp. 166-190 ◽  
Author(s):  
Robert Fourer ◽  
David M. Gay
Keyword(s):  
Mathematical Programming ◽  
Modeling Language ◽  
Algebraic Modeling Language

scholarly journals An integrated platform for intuitive mathematical programming modeling using LaTeX

2018 ◽  
Vol 4 ◽  
pp. e161 ◽  
Author(s):  
Charalampos P. Triantafyllidis ◽  
Lazaros G. Papageorgiou
Keyword(s):  
Mathematical Programming ◽  
Error Detection ◽  
Development Process ◽  
Optimization Problems ◽  
Scientific Work ◽  
Input Language ◽  
Speed Up ◽  
Cross Platform ◽  
Algebraic Modeling Language ◽  
Friendly Graphical User Interface

This paper presents a novel prototype platform that uses the same LaTeX mark-up language, commonly used to typeset mathematical content, as an input language for modeling optimization problems of various classes. The platform converts the LaTeX model into a formal Algebraic Modeling Language (AML) representation based on Pyomo through a parsing engine written in Python and solves by either via NEOS server or locally installed solvers, using a friendly Graphical User Interface (GUI). The distinct advantages of our approach can be summarized in (i) simplification and speed-up of the model design and development process (ii) non-commercial character (iii) cross-platform support (iv) easier typo and logic error detection in the description of the models and (v) minimization of working knowledge of programming and AMLs to perform mathematical programming modeling. Overall, this is a presentation of a complete workable scheme on using LaTeX for mathematical programming modeling which assists in furthering our ability to reproduce and replicate scientific work.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document