| polygon1.mos |
(!*********************************************************************
Mosel NL examples
=================
file polygon1.mos
`````````````````
Maximize the area of polygon of N vertices and diameter of 1.
The position of vertices is indicated as (rho,theta) coordinates
where rho denotes the distance to the base point (vertex with number N)
and theta the angle from the x-axis.
-- Formulation using direct algebraic expressions --
(c) 2008 Fair Issac Corporation
Creation: 2002, rev. Feb. 2013
*********************************************************************!)
model "Polygon 1"
uses "mmxnlp"
parameters
N=5 ! Number of vertices
SOLVER=0 ! 0: SLP, 1: Knitro
end-parameters
declarations
RN = 1..N
Area: nlctr
rho : array(RN) of mpvar ! Distance of vertex from the base point
theta : array(RN) of mpvar ! Angle from x-axis
D: array(RN,RN) of nlctr ! Limit on side length
end-declarations
! Objective: sum of areas
Area:= (sum (i in 2..N-1) (rho(i)*rho(i-1)*sin(theta(i)-theta(i-1)))) * 0.5
! Bounds and start values for decision variables
forall(i in 1..N-1) do
rho(i) >= 0.1
rho(i) <= 1
setinitval(rho(i), 4*i*(N + 1 - i)/((N+1)^2))
setinitval(theta(i), M_PI*i/N)
end-do
! Third side of all triangles <= 1
forall(i in 1..N-2, j in i+1..N-1)
D(i,j):= rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1
! Vertices in increasing order
forall(i in 2..N-1) theta(i) >= theta(i-1) +.01
! Boundary conditions
theta(N-1) <= M_PI ! Last vertex above x-axis
! Optional parameter settings
setparam("xnlp_verbose", true) ! Enable XNLP output log
setparam("xnlp_solver", SOLVER) ! Select the solver
! Solve the problem
maximise(Area)
! Solution output
writeln("Area = ", getobjval)
forall (i in 1..N-1)
writeln("V", i, ": r=", getsol(rho(i)), " theta=", getsol(theta(i)))
end-model
|
|
| polygon1_graph.mos |
(!*********************************************************************
Mosel NL examples
=================
file polygon1_graph.mos
```````````````````````
Maximize the area of polygon of N vertices and diameter of 1.
The position of vertices is indicated as (rho,theta) coordinates
where rho denotes the distance to the base point (vertex with number N)
and theta the angle from the x-axis.
-- Formulation using direct algebraic expressions, solution graph --
(c) 2013 Fair Issac Corporation
Creation: Feb. 2013, rev. Sep. 2017
*********************************************************************!)
model "Polygon 1 (graph)"
uses "mmxnlp", "mmsvg"
parameters
N=5 ! Number of vertices
SOLVER=0 ! 0: SLP, 1: Knitro
end-parameters
declarations
RN = 1..N
Area: nlctr
rho : array(RN) of mpvar ! Distance of vertex from the base point
theta : array(RN) of mpvar ! Angle from x-axis
D: array(RN,RN) of nlctr ! Limit on side length
end-declarations
! Objective: sum of areas
Area:= (sum (i in 2..N-1) (rho(i)*rho(i-1)*sin(theta(i)-theta(i-1)))) * 0.5
! Bounds and start values for decision variables
forall(i in 1..N-1) do
rho(i) >= 0.1
rho(i) <= 1
setinitval(rho(i), 4*i*(N + 1 - i)/((N+1)^2))
setinitval(theta(i), M_PI*i/N)
end-do
! Third side of all triangles <= 1
forall(i in 1..N-2, j in i+1..N-1)
D(i,j):= rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1
! Vertices in increasing order
forall(i in 2..N-1) theta(i) >= theta(i-1) +.01
! Boundary conditions
theta(N-1) <= M_PI ! Last vertex above x-axis
! Optional parameter settings
setparam("xnlp_verbose", true) ! Enable XNLP output log
setparam("xnlp_solver", SOLVER) ! Select the solver
! Solve the problem
maximise(Area)
! Solution output
writeln("Area = ", getobjval)
forall (i in 1..N-1)
writeln("V", i, ": r=", getsol(rho(i)), " theta=", getsol(theta(i)))
!**************** Graphical representation of results ****************
declarations
X,Y: array(0..N) of real
end-declarations
X(N):=0; Y(N):=0 ! Position for base vertex N
X(0):=X(N); Y(0):=Y(N)
forall(i in 1..N-1) do ! Calculate vertex positions
X(i):=cos(theta(i).sol)*rho(i).sol+X(N)
Y(i):=sin(theta(i).sol)*rho(i).sol+Y(N)
end-do
svgaddgroup("P", "Polygon")
forall(i in 1..N) do ! Draw the resulting polygon
svgaddpoint(X(i),Y(i))
svgaddtext(X(i)+0.03,Y(i)+0.02, string(i))
end-do
svgaddpolygon(sum(i in 1..N) [X(i),Y(i)])
! Scale the size of the displayed graph
svgsetgraphscale(200)
svgsetgraphpointsize(2)
svgsave("polygon.svg")
svgrefresh
svgwaitclose("Close browser window to terminate model execution.", 1)
end-model
|
|
| polygon2.mos |
(!*********************************************************************
Mosel NL examples
=================
file polygon2.mos
`````````````````
Maximize the area of polygon of N vertices and diameter of 1.
The position of vertices is indicated as (rho,theta) coordinates
where rho denotes the distance to the base point (vertex with number N)
and theta the angle from the x-axis.
-- Formulation using a simple Mosel user function --
(c) 2008 Fair Issac Corporation
Creation: 2002, rev. Feb. 2013
*********************************************************************!)
model "Polygon 2"
uses "mmxnlp"
parameters
N=5 ! Number of vertices
SOLVER=0 ! 0: SLP, 1: Knitro
end-parameters
declarations
RN = 1..N
Area: nlctr
rho : array(RN) of mpvar ! Distance of vertex from the base point
theta : array(RN) of mpvar ! Angle from x-axis
D: array(RN,RN) of nlctr ! Limit on side length
FunctionArg: array(RN,{"rho","theta"}) of nlctr ! User function arguments
AreaFunction : userfunc ! User function definition
end-declarations
! Objective: sum of areas. Definition of a user function
AreaFunction := userfuncMosel("MoselArea")
! Create function arguments
forall (i in 1..N) do
FunctionArg(i, "rho") := rho(i)
FunctionArg(i, "theta") := theta(i)
end-do
! Use the Mosel user function in a formula for the objective
Area := F(AreaFunction,FunctionArg)
! Bounds and start values for decision variables
forall (i in 1..N-1) do
rho(i) >= 0.1
rho(i) <= 1
setinitval(rho(i),4*i*(N + 1 - i)/((N+1)^2))
setinitval(theta(i),M_PI*i/N)
end-do
! Third side of all triangles <= 1
forall(i in 1..N-2, j in i+1..N-1)
D(i,j) := rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1
! Vertices in increasing order
forall (i in 2..N-1) theta(i) >= theta(i-1) +.01
! Boundary conditions (last vertex above x-axis)
theta(N-1) <= M_PI
! Uncomment to display user function info
! userfuncinfo(AreaFunction)
! Optional parameter settings
setparam("xnlp_verbose", true) ! Enable XNLP output log
setparam("xnlp_solver", SOLVER) ! Select the solver
! Solve the problem
maximise(Area)
! Solution output
writeln("Area = ", getobjval)
forall (i in 1..N-1)
writeln("V",i,": r=",getsol(rho(i))," theta=",getsol(theta(i)))
! **** Definition of the Mosel user function ****
public function MoselArea(I: array(Indices: range, Types: set of string) of real): real
returned := (sum (i in 2..N-1) (I(i,"rho")*I(i-1,"rho")*sin(I(i,"theta")-I(i-1,"theta")))) * 0.5
end-function
end-model
|
|
| polygon3.mos |
(!*********************************************************************
Mosel NL examples
=================
file polygon3.mos
`````````````````
Maximize the area of polygon of N vertices and diameter of 1.
The position of vertices is indicated as (rho,theta) coordinates
where rho denotes the distance to the base point (vertex with number N)
and theta the angle from the x-axis.
-- Formulation using a multi-valued Mosel user function --
(c) 2008 Fair Issac Corporation
Creation: 2002, rev. Feb. 2013
*********************************************************************!)
model "Polygon 3"
uses "mmxnlp"
parameters
N=5 ! Number of vertices
SOLVER=0 ! 0: SLP, 1: Knitro
end-parameters
declarations
RN = 1..N
Area: nlctr
rho : array(RN) of mpvar ! Distance of vertex from the base point
theta : array(RN) of mpvar ! Angle from x-axis
D: array(RN,RN) of nlctr ! Limit on side length
FunctionArg: array(RN,{"rho","theta"}) of nlctr ! User function arguments
AreaFunction : userfunc ! User function definition
k: integer
end-declarations
! Objective: sum of areas. Definition of a user function
AreaFunction := userfuncMosel("MoselArea")
! Create function arguments
forall (i in 1..N) do
FunctionArg(i, "rho") := rho(i)
FunctionArg(i, "theta") := theta(i)
end-do
! Use the Mosel user function in a formula for the objective
Area := F(AreaFunction, FunctionArg, 1)
! Bounds and start values for decision variables
forall (i in 1..N-1) do
rho(i) >= 0.1
rho(i) <= 1
setinitval(rho(i),4*i*(N + 1 - i)/((N+1)^2))
setinitval(theta(i),M_PI*i/N)
end-do
! Third side of all triangles <= 1
k := 2;
forall(i in 1..N-2, j in i+1..N-1, k as counter)
D(i,j) := F(AreaFunction, FunctionArg, k) <= 1
! Vertices in increasing order
forall (i in 2..N-1) theta(i) >= theta(i-1) +.01
! Boundary conditions (last vertex above x-axis)
theta(N-1) <= M_PI
! Uncomment to display user function info
! userfuncinfo(AreaFunction)
! Optional parameter settings
setparam("xnlp_verbose", true) ! Enable XNLP output log
setparam("xnlp_solver", SOLVER) ! Select the solver
! Solve the problem
maximise(Area)
! Solution output
writeln("Area = ", getobjval)
forall (i in 1..N-1)
writeln("V",i,": r=",getsol(rho(i))," theta=",getsol(theta(i)))
! **** Definition of the Mosel user function ****
public procedure MoselArea(I: array(Indices: range, Types: set of string) of real,
CalcValues: array(RetIndices: set of integer) of real)
! Area
CalcValues(1) := (sum (i in 2..N-1) (I(i,"rho")*I(i-1,"rho")*sin(I(i,"theta")-I(i-1,"theta")))) * 0.5
! Distances
k := 2
forall (i in 1..N-2,j in i+1..N-1, k as counter)
CalcValues(k) := I(i,"rho")^2 + I(j,"rho")^2 - I(i,"rho")*I(j,"rho")*2*cos(I(j,"theta")-I(i,"theta"))
end-procedure
end-model
|
|
| polygon4.mos |
(!*********************************************************************
Mosel NL examples
=================
file polygon4.mos
`````````````````
Maximize the area of polygon of N vertices and diameter of 1.
The position of vertices is indicated as (rho,theta) coordinates
where rho denotes the distance to the base point (vertex with number N)
and theta the angle from the x-axis.
-- Formulation using a single-valued function of type
Excel spreadsheet (XLS) --
(c) 2008 Fair Issac Corporation
Creation: 2002, rev. Feb. 2013
*********************************************************************!)
model "Polygon 4"
uses "mmxnlp"
parameters
N=5 ! Number of vertices
SOLVER=0 ! 0: SLP, 1: Knitro
end-parameters
declarations
RN = 1..N
Area: nlctr
rho : array(RN) of mpvar ! Distance of vertex from the base point
theta : array(RN) of mpvar ! Angle from x-axis
D: array(RN,RN) of nlctr ! Limit on side length
FunctionArg: list of nlctr ! User function arguments
AreaFunction: userfunc ! User function definition
end-declarations
! Objective: sum of areas. Definition of a user function
AreaFunction := userfuncExcel("polygonsheet.xls", "Sheet1")
! Create function arguments
! Excel functions use their first columns as input: use a list to ensure correct order
forall (i in 1..N-1) do
FunctionArg += [nlctr(rho(i))]
FunctionArg += [nlctr(theta(i))]
end-do
! Use the Excel user function in a formula for the objective
Area := F(AreaFunction,FunctionArg)
! Bounds and start values for decision variables
forall (i in 1..N-1) do
rho(i) >= 0.1
rho(i) <= 1
setinitval(rho(i),4*i*(N + 1 - i)/((N+1)^2))
setinitval(theta(i),M_PI*i/N)
end-do
! Third side of all triangles <= 1
forall (i in 1..N-2, j in i+1..N-1)
D(i,j) := rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1
! Vertices in increasing order
forall (i in 2..N-1) theta(i) >= theta(i-1) +.01
! Boundary conditions (last vertex above x-axis)
theta(N-1) <= M_PI
! Uncomment to display user function info
! userfuncinfo(AreaFunction)
! Optional parameter settings
setparam("xnlp_verbose", true) ! Enable XNLP output log
setparam("xnlp_solver", SOLVER) ! Select the solver
! Solve the problem
maximise(Area)
! Solution output
writeln("Area = ", getobjval)
forall (i in 1..N-1)
writeln("V",i,": r=",getsol(rho(i))," theta=",getsol(theta(i)))
end-model
|
|
| polygon5.mos |
(!*********************************************************************
Mosel NL examples
=================
file polygon5.mos
`````````````````
Maximize the area of polygon of N vertices and diameter of 1.
The position of vertices is indicated as (rho,theta) coordinates
where rho denotes the distance to the base point (vertex with number N)
and theta the angle from the x-axis.
-- Formulation using a single-valued function of type
Excel Macro (XLF) --
(c) 2008 Fair Issac Corporation
Creation: 2002, rev. Feb. 2013
*********************************************************************!)
model "Polygon 5"
uses "mmxnlp"
parameters
N=5 ! Number of vertices
SOLVER=0 ! 0: SLP, 1: Knitro
end-parameters
declarations
RN = 1..N
Area: nlctr
rho : array(RN) of mpvar ! Distance of vertex from the base point
theta : array(RN) of mpvar ! Angle from x-axis
D: array(RN,RN) of nlctr ! Limit on side length
FunctionArg: list of nlctr ! User function arguments
AreaFunction: userfunc ! User function definition
end-declarations
! Objective: sum of areas. Definition of a user function
AreaFunction := userfuncExcelMacro("polygonmacro.xls", "Sheet1", "Area")
! Create function arguments
! Excel functions use their first columns as input: use a list to ensure correct order
forall (i in 1..N-1) do
FunctionArg += [nlctr(rho(i))]
FunctionArg += [nlctr(theta(i))]
end-do
! Use the Excel user function in a formula for the objective
Area := F(AreaFunction,FunctionArg)
! Bounds and start values for decision variables
forall (i in 1..N-1) do
rho(i) >= 0.1
rho(i) <= 1
setinitval(rho(i),4*i*(N + 1 - i)/((N+1)^2))
setinitval(theta(i),M_PI*i/N)
end-do
! Third side of all triangles <= 1
forall (i in 1..N-2, j in i+1..N-1)
D(i,j) := rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1
! Vertices in increasing order
forall (i in 2..N-1) theta(i) >= theta(i-1) +.01
! Boundary conditions (last vertex above x-axis)
theta(N-1) <= M_PI
! Uncomment to display user function info
! userfuncinfo(AreaFunction)
! Optional parameter settings
setparam("xnlp_verbose", true) ! Enable XNLP output log
setparam("xnlp_solver", SOLVER) ! Select the solver
! Solve the problem
maximise(Area)
! Solution output
writeln("Area = ", getobjval)
forall (i in 1..N-1)
writeln("V",i,": r=",getsol(rho(i))," theta=",getsol(theta(i)))
end-model
|
|
| polygon6.mos |
(!*********************************************************************
Mosel NL examples
=================
file polygon6.mos
`````````````````
Maximize the area of polygon of N vertices and diameter of 1.
The position of vertices is indicated as (rho,theta) coordinates
where rho denotes the distance to the base point (vertex with number N)
and theta the angle from the x-axis.
-- Formulation using a multi-valued function of type
Excel Macro (XLF) --
(c) 2008 Fair Issac Corporation
Creation: 2002, rev. Feb. 2013
*********************************************************************!)
model "Polygon 6"
uses "mmxnlp"
parameters
N=5 ! Number of vertices
SOLVER=0 ! 0: SLP, 1: Knitro
end-parameters
declarations
RN = 1..N
Area: nlctr
rho : array(RN) of mpvar ! Distance of vertex from the base point
theta : array(RN) of mpvar ! Angle from x-axis
D: array(RN,RN) of nlctr ! Limit on side length
FunctionArg: list of nlctr ! User function arguments
AreaFunction: userfunc ! User function definition
k: integer
end-declarations
! Objective: sum of areas. Definition of a user function
AreaFunction := userfuncExcelMacro("polygonmacro.xls", "Sheet1", "ArrayArea")
! Create function arguments
! Excel functions use their first columns as input: use a list to ensure correct order
forall (i in 1..N) do
FunctionArg += [nlctr(rho(i))]
FunctionArg += [nlctr(theta(i))]
end-do
! Use the Excel user function in a formula for the objective
Area := F(AreaFunction, FunctionArg, 1)
! Bounds and start values for decision variables
forall (i in 1..N-1) do
rho(i) >= 0.1
rho(i) <= 1
setinitval(rho(i),4*i*(N + 1 - i)/((N+1)^2))
setinitval(theta(i),M_PI*i/N)
end-do
! Third side of all triangles <= 1
k := 2
forall (i in 1..N-2, j in i+1..N-1, k as counter)
D(i,j) := F(AreaFunction, FunctionArg, k) <= 1
! Vertices in increasing order
forall (i in 2..N-1) theta(i) >= theta(i-1) +.01
! Boundary conditions (last vertex above x-axis)
theta(N-1) <= M_PI
! Uncomment to display user function info
! userfuncinfo(AreaFunction)
! Optional parameter settings
! setparam("xnlp_verbose", true) ! Enable XNLP output log
setparam("xnlp_solver", SOLVER) ! Select the solver
! Solve the problem
maximise(Area)
! Solution output
writeln("Area = ", getobjval)
forall (i in 1..N-1)
writeln("V",i,": r=",getsol(rho(i))," theta=",getsol(theta(i)))
end-model
|
|
| polygon7.mos |
(!*********************************************************************
Mosel NL examples
=================
file polygon7.mos
`````````````````
Maximize the area of polygon of N vertices and diameter of 1.
The position of vertices is indicated as (rho,theta) coordinates
where rho denotes the distance to the base point (vertex with number N)
and theta the angle from the x-axis.
-- Formulation using a single-valued dynamic library function --
!!! Before running this model, compile mydll.c into mydll.fct
!!! using the provided makefile
(c) 2008 Fair Issac Corporation
Creation: 2002, rev. Feb. 2013
*********************************************************************!)
model "Polygon 7"
uses "mmxnlp"
parameters
N=5 ! Number of vertices
SOLVER=0 ! 0: SLP, 1: Knitro
end-parameters
declarations
RN = 1..N
Area: nlctr
rho : array(RN) of mpvar ! Distance of vertex from the base point
theta : array(RN) of mpvar ! Angle from x-axis
D: array(RN,RN) of nlctr ! Limit on side length
FunctionArg: list of nlctr ! User function arguments
AreaFunction: userfunc ! User function definition
end-declarations
! Objective: sum of areas. Definition of a user function
AreaFunction := userfuncDLL("./mydll.fct", "AreaInC")
! Create function arguments
! C functions use their first columns as input: use a list to ensure correct order
forall (i in 1..N-1) do
FunctionArg += [nlctr(rho(i))]
FunctionArg += [nlctr(theta(i))]
end-do
! Use the library user function in a formula for the objective
Area := F(AreaFunction,FunctionArg)
! Bounds and start values for decision variables
forall (i in 1..N-1) do
rho(i) >= 0.1
rho(i) <= 1
setinitval(rho(i),4*i*(N + 1 - i)/((N+1)^2))
setinitval(theta(i),M_PI*i/N)
end-do
! Third side of all triangles <= 1
forall (i in 1..N-2, j in i+1..N-1)
D(i,j) := rho(i)^2 + rho(j)^2 - rho(i)*rho(j)*2*cos(theta(j)-theta(i)) <= 1
! Vertices in increasing order
forall (i in 2..N-1) theta(i) >= theta(i-1) +.01
! Boundary conditions (last vertex above x-axis)
theta(N-1) <= M_PI
! Uncomment to display user function info
! userfuncinfo(AreaFunction)
! Optional parameter settings
setparam("xnlp_verbose", true) ! Enable XNLP output log
setparam("xnlp_solver", SOLVER) ! Select the solver
! Solve the problem
maximise(Area)
! Solution output
writeln("Area = ", getobjval)
forall (i in 1..N-1)
writeln("V",i,": r=",getsol(rho(i))," theta=",getsol(theta(i)))
end-model
|
|
