Designed by Gautam Mitra, Enza Messina, Valente Patrick First appeared 2001; 16 years ago (2001) Stable release 20120523 / May 23, 2013; 3 years ago (2013-05-23) OS Cross-platform (multi-platform) | ||
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 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, or generate an SMPS representation and use specialized decomposition based solvers, like FortSP.
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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.
A stochastic programming sample model
The following is the SAMPL version of a simple problem (Dakota), 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 problemtree Tree := twostage;# Demand for each product in each scenariorandom param Demand{Prod, Scen};# Probability of each scenarioprobability P{Scen}; # Cost of each unit of resourceparam Cost{Resource};# Requirement in terms of resources units to produce one unit of each productparam ProdReq{Resource,Prod};# Selling price of each productparam Price{Prod};# Initial budgetparam Budget;# Amount of resources to buyvar buy{r in Resource} >= 0, suffix stage 1;# Amount of each product to producevar amountprod{p in Prod, s in Scen} >= 0, suffix stage 2;# Amount of each product to sellvar amountsell{p in Prod, s in Scen} >= 0, suffix stage 2;# Total final wealth, as expected total income from sales minus costs for the resourcesmaximize 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 tobalance{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 produceproduction{p in Prod, s in Scen}: amountsell[p,s] <= amountprod[p,s];# Make sure we do not sell more than the market demandsales{p in Prod, s in Scen}: amountsell[p,s] <= Demand[p,s];# Respect initial budgetbudgetres: 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.