GUSS: Solving Collections of Data Related Models Within GAMS
In many applications, optimization of a collection of problems is required where each problem is structurally the same, but in which some or all of the data defining the instance is updated. Such models are easily specified within modern modeling systems, but have often been slow to solve due to the time needed to regenerate the instance, and the inability to use advance solution information (such as basis factorizations) from previous solves as the collection is processed. We describe a new language extension, GUSS, that gathers data from different sources/symbols to define the collection of models (called scenarios), updates a base model instance with this scenario data and solves the updated model instance and scatters the scenario results to symbols in the GAMSdatabase. We demonstrate the utility of this approach in three applications, namely data envelopment analysis, cross validation and stochastic dual dynamic programming. The language extensions are available for general use in all versions of GAMSstarting with release 23.7.
KeywordsData Envelopment Analysis Data Envelopment Analysis Model Model Instance Solve Statement GAMS Model
This work is supported in part by Air Force Grant FA9550-10-1-0101, DOE grant DE-SC0002319, and National Science Foundation Grant CMMI-0928023.
- 5.Birge, J.R., Louveaux, F.: Introduction to stochastic programming. Springer, London (1997)Google Scholar
- 7.Bussieck, M.R., Meeraus, A.: General algebraic modeling system (GAMS). In: Kallrath, J. (eds.) Modeling Languages in Mathematical Optimization, pp. 137–157. Kluwer Academic Publishers, Norwell, MA (2003)Google Scholar
- 11.Cooper, W.W., Seiford, L.M., Tone, K.: Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver Software. Kluwer Academic Publishers, Boston, MA (2000)Google Scholar
- 13.Efron, B., Tibshirani, R.: Improvements on cross-validation: The.632 + bootstrap method. J. Amer. Stat. Assoc. 92, 548–560 (1997)Google Scholar
- 14.Farrell, M.J.: The measurement of productive efficiency. J. Roy. Stat. Soc. A (General) 120(3), 253–290 (1957)Google Scholar
- 17.Geisser, S.: Predictive Inference. Chapman and Hall, New York (1993)Google Scholar
- 18.Kallrath, J. (ed.): Modeling languages in mathematical optimization. Kluwer Academic Publishers, Norwell, MA (2003)Google Scholar
- 19.Kohavi, R.: A study of cross-validation and bootstrap for accuracy estimation and model selection. In: Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence 2, pp. 1137–1143. Morgan Kaufmann, San Mateo (1995)Google Scholar
- 24.Seiford, L.M., Zhu, J.: Sensitivity analysis of DEA models for simultaneous changes in all the data. J. Oper. Res. Soc. 49, 1060–1071 (1998)Google Scholar
- 27.Velaśquez, J., Restrepo, P., Campo, R.: Dual dynamic programming: A note on implementation. Water Resour. Res. 35(7) (1999)Google Scholar