| Title: | Optimisation with Continuous Convex Piecewise (Linear and Quadratic) Functions |
|---|---|
| Description: | Continuous convex piecewise linear (ccpl) resp. quadratic (ccpq) functions can be implemented with sorted breakpoints and slopes. This includes functions that are ccpl (resp. ccpq) on a convex set (i.e. an interval or a point) and infinite out of the domain. These functions can be very useful for a large class of optimisation problems. Efficient manipulation (such as log(N) insertion) of such data structure is obtained with map standard template library of C++ (that hides balanced trees). This package is a wrapper on such a class based on Rcpp modules. |
| Authors: | Robin Girard |
| Maintainer: | Robin Girard <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 0.4.6.1 |
| Built: | 2025-01-28 10:07:35 UTC |
| Source: | https://github.com/cran/ConConPiWiFun |
Continuous convex piecewise linear (ccpl) resp. quadratic (ccpq) functions can be implemented with sorted breakpoints and slopes. This includes functions that are ccpl (resp. ccpq) on a convex set (i.e. an interval or a point) and infinite out of the domain. These functions can be very usefull for a large class of optimisation problems. Efficient manipulation (such as log(N) insertion) of such data structure is obtained with map standard template library of C++ (that hides balanced trees). This package is a wrapper on such a class based on Rcpp modules.
| Package: | ConConPiWiFun |
| Type: | Package |
| Version: | 0.3.0 |
| Date: | 2013-02-08 |
| License: | GPL |
Robin Girard
Maintainer: <[email protected]>
Related Papers are
library(ConConPiWiFun) #### See #? cplfunction for continuous convex piecewise functions #? cplfunctionvec for (optimized) list of continnuous convex piecewise functionslibrary(ConConPiWiFun) #### See #? cplfunction for continuous convex piecewise functions #? cplfunctionvec for (optimized) list of continnuous convex piecewise functions
This includes functions that are ccpl (resp. ccpq) on a convex set (i.e. an interval or a point) and infinite out of the domain. These functions can be very usefull for a large class of optimisation problems. Efficient manipulation (such as log(N) insertion) of such data structure is obtained with map standard template library of C++ (that hides balanced trees). This package is a wrapper on such a class based on Rcpp modules.
Robin Girard
to See Also as cplfunction,
## #Construction of a piecewise linear function ## Slopes=c(-1,2,Inf) # increasing ! convexity is required Breakpoints=c(-Inf,2,4) # increasing. length is number of slopes +1 FirstNonInfBreakpointVal=3 CCPWLfunc1=new(cplfunction,Slopes,Breakpoints,FirstNonInfBreakpointVal) plot(CCPWLfunc1) #visualisation method ###Etoile transformation (legendre transform of f) # Changes f no return value CCPWLfunc1$Etoile() plot(CCPWLfunc1) #if f = CCPWLfunc1 CCPWLfunc1 becomes is f^*(y) =inf_x {xy-f(x)} CCPWLfunc1$Etoile() plot(CCPWLfunc1) ## (f^*)^* is f ! ###Squeeze function # Changes f, no return value left=-Inf; right=3 CCPWLfunc1$Squeeze(left,right) # CCPWLfunc1 is now infinite (or not definite) out of [left,right] # i.e. all breakpoints out of [left,right] removed ###Swap function # Changes f no return value ! y=2; CCPWLfunc1$Swap(y) plot(CCPWLfunc1); #now f = CCPWLfunc1 is replaced by x -> f(y-x) ### Sum function (uses fast insertion) do not affect operands CCPWLfunc1=new(cplfunction,c(-1,2,Inf) ,c(-Inf,2,4),0) CCPWLfunc2=new(cplfunction,c(-1,2,Inf),c(-Inf,1,3),0) CCPWLfunc1plus2=Suml(CCPWLfunc1,CCPWLfunc2) CCPWLfunc1plus2 par(mfrow=c(1,3)) plot(CCPWLfunc2,col='red'); plot(CCPWLfunc1,col='blue'); plot(CCPWLfunc1plus2); rm(list=ls()) gc()## #Construction of a piecewise linear function ## Slopes=c(-1,2,Inf) # increasing ! convexity is required Breakpoints=c(-Inf,2,4) # increasing. length is number of slopes +1 FirstNonInfBreakpointVal=3 CCPWLfunc1=new(cplfunction,Slopes,Breakpoints,FirstNonInfBreakpointVal) plot(CCPWLfunc1) #visualisation method ###Etoile transformation (legendre transform of f) # Changes f no return value CCPWLfunc1$Etoile() plot(CCPWLfunc1) #if f = CCPWLfunc1 CCPWLfunc1 becomes is f^*(y) =inf_x {xy-f(x)} CCPWLfunc1$Etoile() plot(CCPWLfunc1) ## (f^*)^* is f ! ###Squeeze function # Changes f, no return value left=-Inf; right=3 CCPWLfunc1$Squeeze(left,right) # CCPWLfunc1 is now infinite (or not definite) out of [left,right] # i.e. all breakpoints out of [left,right] removed ###Swap function # Changes f no return value ! y=2; CCPWLfunc1$Swap(y) plot(CCPWLfunc1); #now f = CCPWLfunc1 is replaced by x -> f(y-x) ### Sum function (uses fast insertion) do not affect operands CCPWLfunc1=new(cplfunction,c(-1,2,Inf) ,c(-Inf,2,4),0) CCPWLfunc2=new(cplfunction,c(-1,2,Inf),c(-Inf,1,3),0) CCPWLfunc1plus2=Suml(CCPWLfunc1,CCPWLfunc2) CCPWLfunc1plus2 par(mfrow=c(1,3)) plot(CCPWLfunc2,col='red'); plot(CCPWLfunc1,col='blue'); plot(CCPWLfunc1plus2); rm(list=ls()) gc()
This is a wrapper to stl vector of convex piecewise linear functions. Allows to loop efficiently on such list.
Robin Girard
to See Also as cplfunction, cpqfunctionvec
#### # construction of a vector of # continuous convex piecewise linear functions CCPWLfuncList=new(cplfunctionvec) CCPWLfuncList$push_back(new(cplfunction,c(-1,1) ,c(-Inf,0),0)) CCPWLfuncList$push_back(new(cplfunction,c(-1,1) ,c(-Inf,0),0)) CCPWLfuncList=new(cplfunctionvec) n=1000; Y=rnorm(n); S1=array(-1,n);S2=array(1,n); B0=array(-Inf,n); B1=rnorm(n); for (i in 1:n){ CCPWLfuncList$push_back(new(cplfunction,c(S1[i],S2[i]) ,c(B0[i],B1[i]),0)) } CCPWLfuncList$size() ## gives the size ## The same but faster CCPWLfuncList=new(cplfunctionvec) CCPWLfuncList$SerialPush_2Breaks_Functions(S1,S2,B0,B1); #### method OptimMargInt solves # min_x sum_i=1^n C_i(x_i) # Pmoins_i<= x_i <=Pplus_i i=1,...,n # Cmoins_i<= sum_j=1^i x_j <=Cplus_i i=1,...,n Pmoins=array(-1,n);Pplus=array(1,n);Cmoins=array(0,n);Cplus=array(5,n); res=CCPWLfuncList$OptimMargInt(Pmoins,Pplus,Cmoins,Cplus) par(mfrow=c(1,2)) plot(Y,type='l',ylim=range(res$xEtoile)) lines(y=Pmoins,x=1:n,col='blue'); lines(y=Pplus,x=1:n,col='blue'); lines(y=res$xEtoile,x=1:n,col='red') text(x=800,y=3,paste("Optimum=",signif(sum(abs(res$xEtoile-Y)),digits=6))) plot(Y,type='l',ylim=c(min(Y),max(diffinv(res$xEtoile)[1:n+1]))) lines(y=Cmoins,x=1:n,col='blue'); lines(y=Cplus,x=1:n,col='blue'); lines(y=diffinv(res$xEtoile)[1:n+1],x=1:n,col='red') rm(list=ls()) gc()#### # construction of a vector of # continuous convex piecewise linear functions CCPWLfuncList=new(cplfunctionvec) CCPWLfuncList$push_back(new(cplfunction,c(-1,1) ,c(-Inf,0),0)) CCPWLfuncList$push_back(new(cplfunction,c(-1,1) ,c(-Inf,0),0)) CCPWLfuncList=new(cplfunctionvec) n=1000; Y=rnorm(n); S1=array(-1,n);S2=array(1,n); B0=array(-Inf,n); B1=rnorm(n); for (i in 1:n){ CCPWLfuncList$push_back(new(cplfunction,c(S1[i],S2[i]) ,c(B0[i],B1[i]),0)) } CCPWLfuncList$size() ## gives the size ## The same but faster CCPWLfuncList=new(cplfunctionvec) CCPWLfuncList$SerialPush_2Breaks_Functions(S1,S2,B0,B1); #### method OptimMargInt solves # min_x sum_i=1^n C_i(x_i) # Pmoins_i<= x_i <=Pplus_i i=1,...,n # Cmoins_i<= sum_j=1^i x_j <=Cplus_i i=1,...,n Pmoins=array(-1,n);Pplus=array(1,n);Cmoins=array(0,n);Cplus=array(5,n); res=CCPWLfuncList$OptimMargInt(Pmoins,Pplus,Cmoins,Cplus) par(mfrow=c(1,2)) plot(Y,type='l',ylim=range(res$xEtoile)) lines(y=Pmoins,x=1:n,col='blue'); lines(y=Pplus,x=1:n,col='blue'); lines(y=res$xEtoile,x=1:n,col='red') text(x=800,y=3,paste("Optimum=",signif(sum(abs(res$xEtoile-Y)),digits=6))) plot(Y,type='l',ylim=c(min(Y),max(diffinv(res$xEtoile)[1:n+1]))) lines(y=Cmoins,x=1:n,col='blue'); lines(y=Cplus,x=1:n,col='blue'); lines(y=diffinv(res$xEtoile)[1:n+1],x=1:n,col='red') rm(list=ls()) gc()
This includes functions that are ccpq on a convex set (i.e. an interval or a point) and infinite out of the domain. These functions can be very usefull for a large class of optimisation problems. Efficient manipulation (such as log(N) insertion) of such data structure is obtained with map standard template library of C++ (that hides balanced trees). This package is a wrapper on such a class based on Rcpp modules.
Robin Girard
to See Also as cplfunction,
## #Construction of a piecewise quadratic function ## Slopes1=c(-1,2) Slopes0=c(-2,0)# increasing ! convexity is required Breakpoints=c(-Inf,2,4) # increasing. length is number of slopes +1 FirstNonInfBreakpointVal=3 CCPWLfunc1=new(cpqfunction,Slopes0,Slopes1,Breakpoints,FirstNonInfBreakpointVal) CCPWLfunc1$get_BreakPoints_() ## return Breaks AND Slopes plot(CCPWLfunc1) ###Etoile transformation (legendre transform of f) # Changes f no return value CCPWLfunc1$Etoile() CCPWLfunc1$get_BreakPoints_() CCPWLfunc1$Etoile() CCPWLfunc1$get_BreakPoints_() ## (f^*)^* is f ! ###Squeeze function # Changes f, no return value left=-1; right=4 CCPWLfunc1$Squeeze(left,right) # CCPWLfunc1 is now infinite (or not definite) out of [left,right] # i.e. all breakpoints out of [left,right] removed CCPWLfunc1$get_BreakPoints_() ###Swap function # Changes f no return value ! y=2; CCPWLfunc1$Swap(y) CCPWLfunc1$get_BreakPoints_() #now f = CCPWLfunc1 is replaced by x -> f(y-x) ### Sum function (uses fast insertion) do not affect operands CCPWLfunc1=new(cpqfunction,Slopes0,Slopes1,Breakpoints,FirstNonInfBreakpointVal) CCPWLfunc2=new(cpqfunction,Slopes0,Slopes1+1,Breakpoints,FirstNonInfBreakpointVal) CCPWLfunc1plus2=Sumq(CCPWLfunc1,CCPWLfunc2) CCPWLfunc1plus2$get_BreakPoints_() rm(list=ls()) gc()## #Construction of a piecewise quadratic function ## Slopes1=c(-1,2) Slopes0=c(-2,0)# increasing ! convexity is required Breakpoints=c(-Inf,2,4) # increasing. length is number of slopes +1 FirstNonInfBreakpointVal=3 CCPWLfunc1=new(cpqfunction,Slopes0,Slopes1,Breakpoints,FirstNonInfBreakpointVal) CCPWLfunc1$get_BreakPoints_() ## return Breaks AND Slopes plot(CCPWLfunc1) ###Etoile transformation (legendre transform of f) # Changes f no return value CCPWLfunc1$Etoile() CCPWLfunc1$get_BreakPoints_() CCPWLfunc1$Etoile() CCPWLfunc1$get_BreakPoints_() ## (f^*)^* is f ! ###Squeeze function # Changes f, no return value left=-1; right=4 CCPWLfunc1$Squeeze(left,right) # CCPWLfunc1 is now infinite (or not definite) out of [left,right] # i.e. all breakpoints out of [left,right] removed CCPWLfunc1$get_BreakPoints_() ###Swap function # Changes f no return value ! y=2; CCPWLfunc1$Swap(y) CCPWLfunc1$get_BreakPoints_() #now f = CCPWLfunc1 is replaced by x -> f(y-x) ### Sum function (uses fast insertion) do not affect operands CCPWLfunc1=new(cpqfunction,Slopes0,Slopes1,Breakpoints,FirstNonInfBreakpointVal) CCPWLfunc2=new(cpqfunction,Slopes0,Slopes1+1,Breakpoints,FirstNonInfBreakpointVal) CCPWLfunc1plus2=Sumq(CCPWLfunc1,CCPWLfunc2) CCPWLfunc1plus2$get_BreakPoints_() rm(list=ls()) gc()
This is a wrapper to stl vector of convex piecewise quadratic functions. Allows to loop efficiently on such list.
Robin Girard
to See Also as cpqfunction, cplfunctionvec
CCPWLfuncList=new(cpqfunctionvec) CCPWLfuncList$push_back(new(cpqfunction,c(0),c(1),c(-2, 2),0)) CCPWLfuncList$push_back(new(cpqfunction,c(0),c(1),c(-2, 2),0)) CCPWLfuncList=new(cpqfunctionvec) n=1000; Y=rnorm(n); S0=array(0,n)+Y;S1=array(1,n)+Y; B0=array(-Inf,n); B1=array(Inf,n); for (i in 1:n){ CCPWLfuncList$push_back(new(cpqfunction,S0[i],S1[i] ,c(B0[i],B1[i]),0)) } CCPWLfuncList$size() ## gives the size ## The same but faster CCPWLfuncList=new(cpqfunctionvec) CCPWLfuncList$SerialPush_0Breaks_Functions(S0,S1); #### method OptimMargInt solves # min_x sum_i=1^n C_i(x_i) # Pmoins_i<= x_i <=Pplus_i i=1,...,n # Cmoins_i<= sum_j=1^i x_j <=Cplus_i i=1,...,n Pmoins=array(-1,n);Pplus=array(1,n);Cmoins=array(0,n);Cplus=array(5,n); res=CCPWLfuncList$OptimMargInt(Pmoins,Pplus,Cmoins,Cplus) par(mfrow=c(1,2)) plot(Y,type='l') lines(y=Pmoins,x=1:n,col='blue'); lines(y=Pplus,x=1:n,col='blue'); lines(y=res$xEtoile,x=1:n,col='red') text(x=800,y=3,paste("Optimum=",signif(sum(abs(res$xEtoile-Y)),digits=6))) plot(Y,type='l',ylim=c(min(Y),max(diffinv(res$xEtoile)[1:n+1]))) lines(y=Cmoins,x=1:n,col='blue'); lines(y=Cplus,x=1:n,col='blue'); lines(y=diffinv(res$xEtoile)[1:n+1],x=1:n,col='red') rm(list=ls()) gc()CCPWLfuncList=new(cpqfunctionvec) CCPWLfuncList$push_back(new(cpqfunction,c(0),c(1),c(-2, 2),0)) CCPWLfuncList$push_back(new(cpqfunction,c(0),c(1),c(-2, 2),0)) CCPWLfuncList=new(cpqfunctionvec) n=1000; Y=rnorm(n); S0=array(0,n)+Y;S1=array(1,n)+Y; B0=array(-Inf,n); B1=array(Inf,n); for (i in 1:n){ CCPWLfuncList$push_back(new(cpqfunction,S0[i],S1[i] ,c(B0[i],B1[i]),0)) } CCPWLfuncList$size() ## gives the size ## The same but faster CCPWLfuncList=new(cpqfunctionvec) CCPWLfuncList$SerialPush_0Breaks_Functions(S0,S1); #### method OptimMargInt solves # min_x sum_i=1^n C_i(x_i) # Pmoins_i<= x_i <=Pplus_i i=1,...,n # Cmoins_i<= sum_j=1^i x_j <=Cplus_i i=1,...,n Pmoins=array(-1,n);Pplus=array(1,n);Cmoins=array(0,n);Cplus=array(5,n); res=CCPWLfuncList$OptimMargInt(Pmoins,Pplus,Cmoins,Cplus) par(mfrow=c(1,2)) plot(Y,type='l') lines(y=Pmoins,x=1:n,col='blue'); lines(y=Pplus,x=1:n,col='blue'); lines(y=res$xEtoile,x=1:n,col='red') text(x=800,y=3,paste("Optimum=",signif(sum(abs(res$xEtoile-Y)),digits=6))) plot(Y,type='l',ylim=c(min(Y),max(diffinv(res$xEtoile)[1:n+1]))) lines(y=Cmoins,x=1:n,col='blue'); lines(y=Cplus,x=1:n,col='blue'); lines(y=diffinv(res$xEtoile)[1:n+1],x=1:n,col='red') rm(list=ls()) gc()
Optimisation of storage operation with market prices taking into acount storage efficiency and network taxes.
OptimPriceStorage(Prices,Pplus,Pmoins,Cplus,Cmoins=0, efficiencyS=0,efficiencyP=efficiencyS,networkTax=0)OptimPriceStorage(Prices,Pplus,Pmoins,Cplus,Cmoins=0, efficiencyS=0,efficiencyP=efficiencyS,networkTax=0)
Prices |
A vector of prices |
Pplus |
A value for the upper power constraint or a vector of values with the same size as Prices |
Pmoins |
A value for the lower power constraint or a vector of values with the same size as Prices |
Cplus |
A value for the upper capacity constraint or a vector of values with the same size as Prices |
Cmoins |
A value for the lower capacity constraint or a vector of values with the same size as Prices |
efficiencyS |
storage efficiency when storing electricity |
efficiencyP |
storage efficiency when producing electricity |
networkTax |
networkTax |
function OptimPriceStorage solves # min_x sum_i=1^n Y_i*efficiencyP x_i*(x_i<0)+(Y_i*efficiencyS +networkTax)*x_i*(x_i>0) # Pmoins_i<= x_i <=Pplus_i i=1,...,n # Cmoins_i<= sum_j=1^i x_j <=Cplus_i i=1,...,n
when efficiency=1 and networkTax=0 this gives # min_x sum_i=1^n Y_i x_i # Pmoins_i<= x_i <=Pplus_i i=1,...,n # Cmoins_i<= sum_j=1^i x_j <=Cplus_i i=1,...,n
A list with
Operation |
the optimal operation for each time step |
Revenue |
the revenue for each time step |
TODO
Robin Girard
TODO
to See Also cplfunction (method OptimMargInt that is more general)
n=8760 Prices=runif(n,1,100) ##uniform random prices in [1;100] in Euro/MWh Pmax=1; Pmin=-1; Cmax=5; ## 1MW maximum during 5 hours. res=OptimPriceStorage(Prices,Pmax,Pmin,Cmax) # solving the optimization problem sum(res$Revenue)## Revenue res=OptimPriceStorage(Prices,Pmax,Pmin,Cmax,efficiencyS=0.8) # solving the optimization problem sum(res$Revenue)## Revenuen=8760 Prices=runif(n,1,100) ##uniform random prices in [1;100] in Euro/MWh Pmax=1; Pmin=-1; Cmax=5; ## 1MW maximum during 5 hours. res=OptimPriceStorage(Prices,Pmax,Pmin,Cmax) # solving the optimization problem sum(res$Revenue)## Revenue res=OptimPriceStorage(Prices,Pmax,Pmin,Cmax,efficiencyS=0.8) # solving the optimization problem sum(res$Revenue)## Revenue