SAMPL

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.

SAMPL shares all language features with AMPL, and adds some constructs specifically designed for expressing scenario based stochastic programming and robust optimization.

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]

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).

setProd;setResource;# Scenarios (future possible realizations)scenarioset Scen; # Definition of the problem as a two-stage problemárbol Árbol := dos etapas ; # Demand for each product in each scenarioParámetro aleatorio Demanda{Prod, Scen}; # Probability of each scenarioprobabilidad P{Escena}; # Cost of each unit of resourceparamCost{Resource};# Requirement in terms of resources units to produce one unit of each productparamProdReq{Resource,Prod};# Selling price of each productparamPrice{Prod};# Initial budgetparamBudget;# Amount of resources to buyvarbuy{rinResource}>=0,sufijo etapa 1; # Amount of each product to producevaramountprod{pinProd,sinScen}>=0,sufijo etapa 2; # Amount of each product to sellvaramountsell{pinProd,sinScen}>=0,sufijo etapa 2; # Total final wealth, as expected total income from sales minus costs for the resourcesmaximizewealth:sum{sinScen}P[s]*(sum{pinProd}Price[p]*amountsell[p,s]-sum{rinResource}Cost[r]*buy[r]);subjectto# Make sure you have enough resources to produce what we intend tobalance{rinResource,sinScen}:buy[r]>=sum{pinProd}ProdReq[r,p]*amountprod[p,s];# Make sure we do not sell what we did not produceproduction{pinProd,sinScen}:amountsell[p,s]<=amountprod[p,s];# Make sure we do not sell more than the market demandsales{pinProd,sinScen}:amountsell[p,s]<=Demand[p,s];# Respect initial budgetbudgetres:sum{rinResource}Cost[r]*buy[r]<=Budget;

El formato de instancia SAMPL para problemas SP es SMPS, por lo que el problema puede resolverse con cualquier solucionador que admita dicho estándar. Uno de estos solucionadores (FortSP) está incluido en la distribución estándar de SAMPL. En cuanto a los problemas de optimización robusta, el solucionador necesario depende de la formulación específica utilizada; por ejemplo, las formulaciones de Ben-Tal y Nemirovski requieren un solucionador con capacidad para conos de segundo orden .

• Lenguaje de modelado algebraico
• AIMMS
• AMPL
• FuerteSP
• GAMS – Sistema General de Modelado Algebraico
• GLPK : sistema de código abierto gratuito basado en un subconjunto de AMPL.
• HiGHS - HiGHS es un software de alto rendimiento, tanto serial como paralelo, para resolver modelos de programación lineal dispersa (LP), programación entera mixta (MIP) y programación cuadrática (QP) a gran escala.
• MPS (formato)
• Optimización robusta
• Programación estocástica

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• Página principal de OptiRisk Systems
• Página principal del solucionador HiGHS