SAMPL
Paradigm | multi-paradigm: declarative, imperative |
---|---|
Designed by | Gautam Mitra, Enza Messina, Valente Patrick |
First appeared | 2001 |
Stable release | 20120523
/ May 23, 2013 |
OS | Cross-platform (multi-platform) |
License | Proprietary |
Filename extensions | .mod .dat .run .sampl |
Website | www |
Influenced by | |
AMPL |
SAMPL, which stands for "Stochastic AMPL", is an algebraic modeling language resulting by expanding the well-known language AMPL with extended syntax and keywords. It is designed specifically for representing stochastic programming problems[1] and, through recent extensions, problems with chance constraints, integrated chance constraints and robust optimization problems. It can generate the deterministic equivalent version of the instances, using all the solvers AMPL connects to,[2] or generate an SMPS representation and use specialized decomposition based solvers, like FortSP.
Language Features
SAMPL shares all language features with AMPL, and adds some constructs specifically designed for expressing scenario based stochastic programming and robust optimization.
Stochastic programming features and constructs
To express scenario-based SP problems, additional constructs describe the tree structure and group the decision variable into stages. Moreover, it is possible to specify which parameter stores the probabilities for each branch of the tree and which set represents the scenario set. Other constructs to easily define chance constraints and integrated chance constraint in an SP problem are available as well. Using these language constructs allows to retain the structure of the problem, hence making it available to the solvers, which might exploit it using specialized decomposition methods like Benders' decomposition to speed-up the solution.
Robust optimization constructs
SAMPL supports constructs to describe three types of robust optimization formulations:
Availability
SAMPL is currently available as a part of the software AMPLDev (distributed by www.optirisk-systems.com). It supports many popular 32- and 64-bit platforms including Windows, Linux and Mac OS X. A free evaluation version with limited functionality is available.[6]
A stochastic programming sample model
The following is the SAMPL version of a simple problem (Dakota[7]), to show the SP related constructs. It does not include the data file, which follows the normal AMPL syntax (see the example provided in the AMPL Wikipedia page for further reference).
set Prod; set Resource; # Scenarios (future possible realizations) scenarioset Scen; # Definition of the problem as a two-stage problem tree Tree := twostage; # Demand for each product in each scenario random param Demand{Prod, Scen}; # Probability of each scenario probability P{Scen}; # Cost of each unit of resource param Cost{Resource}; # Requirement in terms of resources units to produce one unit of each product param ProdReq{Resource,Prod}; # Selling price of each product param Price{Prod}; # Initial budget param Budget; # Amount of resources to buy var buy{r in Resource} >= 0, suffix stage 1; # Amount of each product to produce var amountprod{p in Prod, s in Scen} >= 0, suffix stage 2; # Amount of each product to sell var amountsell{p in Prod, s in Scen} >= 0, suffix stage 2; # Total final wealth, as expected total income from sales minus costs for the resources maximize wealth: sum{s in Scen} P[s] * (sum{p in Prod} Price[p] * amountsell[p,s] - sum{r in Resource} Cost[r] * buy[r]); subject to # Make sure you have enough resources to produce what we intend to balance{r in Resource, s in Scen}: buy[r] >= sum{p in Prod} ProdReq[r,p] * amountprod[p, s]; # Make sure we do not sell what we did not produce production{p in Prod, s in Scen}: amountsell[p,s] <= amountprod[p,s]; # Make sure we do not sell more than the market demand sales{p in Prod, s in Scen}: amountsell[p,s] <= Demand[p,s]; # Respect initial budget budgetres: sum{r in Resource} Cost[r] * buy[r] <= Budget;
Solvers connectivity
SAMPL instance level format for SP problems is SMPS, and therefore the problem can be solved by any solver which supports that standard. One of such solvers (FortSP) is included in the standard SAMPL distribution. Regarding robust optimization problems, the needed solver depend on the specific formulation used, as Ben-Tal and Nemirovski formulation need a second-order cone capable solver.
See also
- Algebraic modeling language
- AIMMS
- AMPL
- FortSP
- GAMS – General Algebraic Modeling System
- GLPK – free open source system based on a subset of AMPL
- MPS (format)
- Robust optimization
- Stochastic programming
References
- ^
Christian Valente, Gautam Mitra, Mustapha Sadki and Robert Fourer (2009). "Extending algebraic modelling languages for stochastic programming". INFORMS Journal on Computing. 21 (1): 107–122. doi:10.1287/ijoc.1080.0282.
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: CS1 maint: multiple names: authors list (link) - ^ http://www.ampl.com/solvers.html
- ^ Allen L Soyster (1974). "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming". Operations Research. 21 (5): 1154–1157. doi:10.1287/opre.21.5.1154.
- ^ Bertsimas, Dimitris; Sim, Melvyn (2004). "The Price of Robustness". Operations Research. 52 (1): 35–53. doi:10.1287/opre.1030.0065.
- ^ Aharon Ben-Tal; Arkadi Nemirovski (1998). "Robust convex optimization". Mathematics of Operations Research. 23 (4): 769–805. doi:10.1287/moor.23.4.769.
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suggested) (help) - ^ http://optirisk-systems.com/products_ampldevSP.asp
- ^ Higle, Julia L, Wallace, Stein W (2003). "Sensitivity analysis and uncertainty in linear programming". Interfaces. 33 (4). INFORMS: 53–60. doi:10.1287/inte.33.4.53.16370.
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