This paper discusses a software system for solving large scale linear and mixed-integer optimization models. The system in its present form is the result of several years of research and development. The first functio...
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This paper discusses a software system for solving large scale linear and mixed-integer optimization models. The system in its present form is the result of several years of research and development. The first functional version of MOPS was completed 1987 for the IBM 6150 (a predecessor of the RS/6000) under AIX. A benchmark model from the Petroleum industry with 5563 rows and 6181 columns was solved with MOPS in 5 hours. The newest version solves this model in 6.51 minutes on a MS-DOS PC with i80486 processor (25 Mhz). This paper discusses only LP optimization. The MIP optimizer in MOPS is a prototype version which will undergo major changes in the future. We describe algorithmic aspects, implementation issues and numerical results on Netlib and other real-life LP models. Sophisticated LP optimizers - although simple from a mathematical point of view - are algorithmically very complex. The discussion is therefore limited to a few fundamental issues that we feel are important.
The issue of model validation is critical in the formulation and interpretation of mathematicalprogramming models, yet this problem is largely ignored by contemporary modeling languages and the systems they support. ...
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The issue of model validation is critical in the formulation and interpretation of mathematicalprogramming models, yet this problem is largely ignored by contemporary modeling languages and the systems they support. This research advances modeling languages for mathematicalprogramming by providing a formalism and defining a language for specifying a dimensional complement, called "typing," to the algebraic representation of models. Typing is a formal specification used to determine automatically whether the algebraic model is well-formed in the sense that its objective function and constraints are composed of homogeneous components and that operations performed using indices are meaningful. A provision is made for the definition of dimensional axioms that can be applied automatically to resolve dimensional differences. The addition of formal typing to mathematicalprogramming models also yields a powerful abstraction mechanism for integrated modeling.
This study investigates the progress made in LP and MILP solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average,...
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This study investigates the progress made in LP and MILP solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving LP/MILP, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for LP and around 50 for MILP, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time.(c) 2022 The Authors. Published by Elsevier Ltd on behalf of Association of European Operational Research Societies (EURO). This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).
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