A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
A Symbolic Model Specificationfor Energy EfficiencyOptimization Models
Emilio L. Cano1 Javier M. Moguerza1
1Department of Statistics and Operations ResearchUniversity Rey Juan Carlos, Spain
Annual Meeting 2012, Phoenix, AZ
October 14-17
INFORMS Annual Meeting 2012 1/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Outline
1 IntroductionEnRiMa ProjectDSS Description
2 Optimization ModelsDSS ModulesStrategic ModelOperational Model
3 Symbolic Model SpecificationRepresentationSolver Manager
4 Reproducible Research
INFORMS Annual Meeting 2012 2/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Outline
1 IntroductionEnRiMa ProjectDSS Description
2 Optimization ModelsDSS ModulesStrategic ModelOperational Model
3 Symbolic Model SpecificationRepresentationSolver Manager
4 Reproducible Research
INFORMS Annual Meeting 2012 3/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Introduction
The overall objective of EnRiMa is todevelop a decision-support system (DSS)for operators of energy-efficient buildingsand spaces of public use.
INFORMS Annual Meeting 2012 4/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Consortium
INFORMS Annual Meeting 2012 5/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
EnRiMa DSS
INFORMS Annual Meeting 2012 6/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Outline
1 IntroductionEnRiMa ProjectDSS Description
2 Optimization ModelsDSS ModulesStrategic ModelOperational Model
3 Symbolic Model SpecificationRepresentationSolver Manager
4 Reproducible Research
INFORMS Annual Meeting 2012 7/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Decision Scope
EnRiMaDSSStrategicModule
OperationalModule
StrategicDVs
StrategicConstraints
Upper-LevelOperational DVs
Upper-LevelEnergy-BalanceConstraints
Lower-LevelEnergy-BalanceConstraints
Lower-LevelOperational DVs
INFORMS Annual Meeting 2012 8/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Strategic Constraints
spi = Gi ·∑
a′≤p,a′≥0
AGp−a′
i ·
(sia
′
i −∑
a′′≤p,a′′>a′
sda′,a′′
i
)
∀ i ∈ I, p ∈ P
z p,m,ti ,k ≤
∑k∈K
DT · AF p,m,ti · spi
∀ i ∈ I, p ∈ P , m ∈M, t ∈ T ∀ k ∈ KPF (i)
INFORMS Annual Meeting 2012 9/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Upper-level Energy BalanceConstraints
∑i∈I
z p,m,ti ,k +
∑n∈NB(k,n,p,m,t),m
′∈M′B(k,n,p,m,t)
up,m,t ,m′
k ,n
−∑i∈I
yp,m,ti ,k −
∑n∈NS(k,n,p,m,t),m
′∈M′S(k,n,p,m,t)
wp,m,t ,m′
k ,n
−∑
j∈JSto
rip,m,tj ,k ≥ Dp,m,t
k −∑
j∈JSto
rop,m,tj ,k
−∑
j∈JPU
OD j ,k · xpj
∀ k ∈ K, p ∈ P , m ∈M, t ∈ T
INFORMS Annual Meeting 2012 10/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Lower-level Energy BalanceConstraints
Ψt =δ
η· ξ ·
(ζ − Γt)
ln(ζ−Λt
Γt−Λt
) · 1
%
ϕ
,∀ t ∈ TO
INFORMS Annual Meeting 2012 11/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Outline
1 IntroductionEnRiMa ProjectDSS Description
2 Optimization ModelsDSS ModulesStrategic ModelOperational Model
3 Symbolic Model SpecificationRepresentationSolver Manager
4 Reproducible Research
INFORMS Annual Meeting 2012 12/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Symbolic Model Specification
The SMS contains the mathematicalrepresentation of optimization models forall relevant energy subsystems and theirinteractions.
This mathematical representation iscomposed of variables, parameters, andrelations between them. Individualentities (variables and parameters) areidentified through the indices representingthe elements in different set.
INFORMS Annual Meeting 2012 13/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Data-driven Modelling
INFORMS Annual Meeting 2012 14/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Sets and Indices
> head(SMSsets(model1SMS)[,c(1,3,4,6,7,8,9)])
id tag sDes loc inSet aux subSet
1 1 NA Energy-creating technology sub NA NA FALSE
2 2 NA Energy-storing technology sub NA NA FALSE
3 3 NA Type of energy sub NA NA FALSE
4 4 NA Type of pollutant sub NA NA FALSE
5 5 NA Energy market sub NA NA FALSE
6 6 NA Long-term period sup NA NA FALSE
> cat(getSets(model1SMS, format = "tex", compact = FALSE))
\begin{description}
\item[$i$] Energy-creating technology.
\item[$j$] Energy-storing technology.
\item[$k$] Type of energy.
\item[$l$] Type of pollutant.
\item[$n$] Energy market.
\item[$p$] Long-term period.
\item[$m$] Mid-term period.
\item[$t$] Short-term period.
\item[$a$] Technology age. a = 0,...,P-1
\end{description}
INFORMS Annual Meeting 2012 15/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Decision Variables
> head(SMSvars(model1SMS)[,c(1,2,4, 7,9)])
id symbol sDes units ind
1 1 si Generators to be installed Devices 1, 6
2 2 sd Generators to be decommissioned Devices 1, 6, 9
3 3 s Available generation capacity kW 1, 6
4 4 xi Storing devices to be installed Devices 2, 6
5 5 xd Storing devices to be decommissioned Devices 2, 6, 9
6 6 x Available storing capacity kWh 2, 6
> cat(getVars(model1SMS, format = "tex"))
\begin{description}
... ...
\item[$ \mathit{s}_{i}^{p}$] Available generation capacity (kW).
... ...
\item[$ \mathit{r}_{j,k}^{p,m,t}$] Energy stored (kWh).
\item[$ \mathit{c}_{}^{}$] TotalCost (EUR).
\item[$ \mathit{e}_{}^{p,m,t}$] Primary energy consumed (kWh).
\end{description}
INFORMS Annual Meeting 2012 16/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Parameters
> head(SMSpars(model1SMS)[, c(1,2,4,7, 10)])
id symbol sDes units ind
1 1 D Energy demand kWh 3, 6, 7, 8
2 2 G Generation capacity kW/Device 1
3 3 GS Storage capacity kW/Device 2
4 4 AG Generation aging factor kW/kWh 1, 11
5 5 AS Storage aging factor kW/kW 2, 11
6 6 AV Technology availability factor kW/kW 1, 6, 7, 8
> cat(getPars(model1SMS, format = "tex"))
\begin{description}
\item[$ \mathit{D}_{k}^{p,m,t}$] Energy demand (kWh).
\item[$ \mathit{G}_{i}^{}$] Generation capacity (kW/Device).
\item[$ \mathit{GS}_{j}^{}$] Storage capacity (kW/Device).
... ...
\item[$ \mathit{IL}_{}^{}$] Investment limit (EUR).
... ...
\end{description}
INFORMS Annual Meeting 2012 17/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Equations
> head(SMSeqs(model1SMS)[,c(1,2,6,7,8)])
id symbol nature relation domain
1 1 eqAvailg constraint eq 1, 6
2 2 eqAvails constraint eq 2, 6
3 3 eqDecomLimg constraint lte 1, 6
4 4 eqDecomLims constraint lte 2, 6
5 5 eqEnergyBal constraint gte 3, 6, 7, 8
6 6 eqOutputCalc constraint eq 1, 6, 7, 8, 20
> head(model1SMS@terms[,c(1,6,7,8,9,10,11)])
id eq side parent nature item setSums
1 1 1 l NA vars 3 NA
2 2 1 r NA pars 2 NA
3 3 1 r 2 pars 4 NA
4 4 1 r 3 vars 1 NA
5 5 1 r 3 vars 2 NA
6 1 2 l NA vars 6 NA
> cat(getEq(model1SMS, 1, format = "tex"))
INFORMS Annual Meeting 2012 18/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Equations (cont.)
\mathit{s}_{i}^{p} = \mathit{G}_{i}^{} \cdot
\sum _{ \mathit{a'} \leq \mathit{p} , \mathit{a'}\geq \mathit{0} } \mathit{AG}_{i}^{\mathit{p}-\mathit{a'}}\cdot \left ( \mathit{si}_{i}^{\mathit{a'}}-\sum _{ \mathit{a''} \leq \mathit{p} ,
\mathit{a''} > \mathit{a'} }
\mathit{sd}_{i}^{\mathit{a'},\mathit{a''}} \right)
\qquad \forall \;i \in \mathcal{I},\; p \in \mathcal{P}
INFORMS Annual Meeting 2012 19/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Instance
INFORMS Annual Meeting 2012 20/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Instance (cont.)
> instancePars(model1Instance, "CI")[sort(sample(1:975,
10, FALSE )),]
i p a value
251 CHP 22 19 1021.45984
313 CHP 25 12 830.54032
450 PV 16 4 18.57636
476 PV 17 14 24.96507
517 PV 20 1 17.00000
578 PV 22 21 30.70389
581 PV 23 2 17.51000
586 PV 23 7 20.29889
669 Wind 6 3 212.18000
758 Wind 15 2 206.00000
> instanceSets(model1Instance, c("i"))
[1] "CHP" "PV" "Wind"
INFORMS Annual Meeting 2012 21/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Problem
> wProblem(example1Instance, "basicExample.gms", "gams", "lp")
*GAMS file created with R
$if NOT set outfile $set outfile outSol
Sets
i Technology / RTE, PV, CHP/
j Period / winter, spring, summer, autumn/
t Year / 2013, 2014, 2015, 2016, 2017/
;
...
parameter
D(j,t) Demand Level
/ winter .2013 = 5.25
spring .2013 = 5.83333333333333
...
autumn .2017 = 7.75833333333333
/ ;
Variables
x(i, t)
y(i, j, t)
s(i, t)
z
;
Positive variable x ;
INFORMS Annual Meeting 2012 22/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Problem (cont.)Positive variable y ;
Positive variable s ;
;
Equations
eqAvail (i,t) Available technologies capacity calculation
eqDemand (j,t) Production plan for demand
eqCapacity (i,j,t) Technologies capacity
Cost Total Cost
;
eqAvail(i,t) .. s(i,t) =e= s(i,t-1)+x(i,t)-x(i,t-LT(i)) ;
eqDemand(j,t) .. Sum((i), y(i,j,t)) =e= D(j,t) ;
eqCapacity(i,j,t) .. y(i,j,t) =l= G(i,j,t)*s(i,t) ;
Cost .. z =e= Sum((t), (Sum((i), CI(i,t)*x(i,t))+Sum((i,j), CO(i,j,t)*DT(j,t)*y(i,j,t)))) ;
Model Deterministic1 /all/;
solve Deterministic1 using lp minimizing z ;
scalars modelstat, solvestat, obj;
modelstat = Deterministic1.modelstat;
solvestat = Deterministic1.solvestat;
obj = Deterministic1.objVal;
execute_unload '%outfile%', modelstat, solvestat, obj, x, y, s, z ;
INFORMS Annual Meeting 2012 23/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Architecture
INFORMS Annual Meeting 2012 24/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Architecture (cont.)
> # .... Data preparation
> load("./data/exampleCMS.RData")
> wProblem(mod1Instance, "example.gms", "gams", "lp")
> #
> # solve
> gams("example.gms --outfile=exampleSol.gdx")
> #
> ## import solution
> oldOpt <- options(stringsAsFactors= FALSE)
> importGams(model1Instance)<- "exampleSol.gdx"
> options(oldOpt)
> #
> getsolution(model1Instance)
INFORMS Annual Meeting 2012 25/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
DSS Integration
INFORMS Annual Meeting 2012 26/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Outline
1 IntroductionEnRiMa ProjectDSS Description
2 Optimization ModelsDSS ModulesStrategic ModelOperational Model
3 Symbolic Model SpecificationRepresentationSolver Manager
4 Reproducible Research
INFORMS Annual Meeting 2012 27/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Reproducible OResearch
The goal of reproducible research is to tiespecific instructions to data analysis andexperimental data so that results can berecreated, better understood and verified
INFORMS Annual Meeting 2012 28/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Summary
In this presentation the method used torepresent and solve the optimizationmodels developed within the EnRiMaDSS have been described
An integrated framework allows torepresent the models in several formatsboth human and machine readable.
OutlookIntegration of dual-level scenario treesExtend representation formats: HTML,ODF, . . .Further formats: AMPL, XML, . . .user-friendly input
INFORMS Annual Meeting 2012 29/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Summary
In this presentation the method used torepresent and solve the optimizationmodels developed within the EnRiMaDSS have been described
An integrated framework allows torepresent the models in several formatsboth human and machine readable.
OutlookIntegration of dual-level scenario treesExtend representation formats: HTML,ODF, . . .Further formats: AMPL, XML, . . .user-friendly input
INFORMS Annual Meeting 2012 29/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Acknowledgements
R-project
GAMS Software
EnRiMa project partners
This work has been partially funded by the projects:
Energy Efficiency and Risk Management in Public Buildings (EnRiMa) EC’sFP7 project (number 260041)Project RIESGOS-CM: code S2009/ESP-1685AGORANET project (IPT-430000-2010-32)HAUS: IPT-2011-1049-430000EDUCALAB: IPT-2011-1071-430000DEMOCRACY4ALL: IPT-2011-0869-430000
CORPORATE COMMUNITY: IPT-2011-0871-430000
INFORMS Annual Meeting 2012 30/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
References
COIN-OR Foundation. Internet, 2012. URL http://www.coin-or.org/.retrieved 2012-06-12.
EnRiMa. Energy efficiency and risk management in public buildings.www.enrima-project.eu, 2012.
GAMS. gdxrrw: interfacing gams and R. Internet, 2012. URLhttp://support.gams-software.com/doku.php?id=gdxrrw:
interfacing_gams_and_r. retrieved 2012-03-06.
R Development Core Team. R: A Language and Environment for StatisticalComputing. R Foundation for Statistical Computing, Vienna, Austria,2012. URL http://www.R-project.org/. ISBN 3-900051-07-0.
Stefan Theussl. CRAN task view: Optimization and mathematicalprogramming, 2012. URL http://cran.r-project.org/.
INFORMS Annual Meeting 2012 31/32
A Symbolic ModelSpecification forEnergy Efficiency
Optimization Models
INFORMS 2012
Emilio L. Cano andJavier M. Moguerza
Introduction
EnRiMa Project
DSS Description
Optimization Models
DSS Modules
Strategic Model
Operational Model
Symbolic ModelSpecification
Representation
Solver Manager
ReproducibleResearch
References
Discussion
Thanks for your attention !
@emilopezcano
INFORMS Annual Meeting 2012 32/32