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personal:blog:2017:0203_jump_for_gams_users [2017/02/03 14:45] antonello |
personal:blog:2017:0203_jump_for_gams_users [2017/02/07 10:26] antonello [Declaration of the model] |
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Pkg.add(" | Pkg.add(" | ||
Pkg.add(" | Pkg.add(" | ||
- | Pkg.add(" | + | Pkg.add(" |
</ | </ | ||
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You will need to import as a minima the '' | You will need to import as a minima the '' | ||
- | <code julia> | + | < |
- | # Import of the JuMP and DataFrames modules (the latter one just to import the data from a header-based table, as in the original trasnport example in GAMS | + | # Import of the JuMP and DataFrames modules (the latter one just to import the data from a header based table, as in the original trasnport example in GAMS |
using JuMP, DataFrames | using JuMP, DataFrames | ||
</ | </ | ||
Line 56: | Line 56: | ||
<code julia> | <code julia> | ||
- | # Sets | + | # Define sets # |
+ | # | ||
+ | # | ||
+ | # | ||
plants | plants | ||
markets = [" | markets = [" | ||
Line 64: | Line 67: | ||
==== Definition of the " | ==== Definition of the " | ||
- | Capacity of plants and demand of markets are directly defined as dictionaries, | + | Capacity of plants and demand of markets are directly defined as dictionaries, |
<code julia> | <code julia> | ||
- | # Parameters | + | # Define parameters # |
+ | # Parameters | ||
+ | # | ||
+ | # / | ||
+ | # san-diego | ||
a = Dict( # capacity of plant i in cases | a = Dict( # capacity of plant i in cases | ||
" | " | ||
" | " | ||
) | ) | ||
+ | |||
+ | # | ||
+ | # / | ||
+ | # chicago | ||
+ | # topeka | ||
b = Dict( # demand at market j in cases | b = Dict( # demand at market j in cases | ||
" | " | ||
Line 78: | Line 90: | ||
) | ) | ||
- | # distance in thousands of miles | + | # Table d(i, |
+ | # new-york | ||
+ | # seattle | ||
+ | # san-diego | ||
d_table = wsv""" | d_table = wsv""" | ||
plants | plants | ||
Line 85: | Line 100: | ||
""" | """ | ||
d = Dict( (r[: | d = Dict( (r[: | ||
+ | # Here we are converting the table in a " | ||
# r[: | # r[: | ||
# m: the second key | # m: the second key | ||
# r[Symbol(m)]: | # r[Symbol(m)]: | ||
+ | # Scalar f freight in dollars per case per thousand miles /90/ ; | ||
f = 90 # freight in dollars per case per thousand miles | f = 90 # freight in dollars per case per thousand miles | ||
+ | # Parameter c(i, | ||
+ | # c(i,j) = f * d(i,j) / 1000 ; | ||
# We first declare an empty dictionary and then we fill it with the values | # We first declare an empty dictionary and then we fill it with the values | ||
c = Dict() # transport cost in thousands of dollars per case ; | c = Dict() # transport cost in thousands of dollars per case ; | ||
[ c[p,m] = f * d[p,m] / 1000 for p in plants, m in markets] | [ c[p,m] = f * d[p,m] / 1000 for p in plants, m in markets] | ||
</ | </ | ||
+ | The above code take advantage of [[http:// | ||
+ | If we take the creation of the d dictionary as example, without List Comprehensions we would have had to write a nested for loop like: | ||
+ | <code julia> | ||
+ | d = Dict() | ||
+ | for r in eachrow(d_table) | ||
+ | for m in markets | ||
+ | d = (r[: | ||
+ | end | ||
+ | end | ||
+ | </ | ||
+ | Using List Comprehension is however quicker to code and more readable. | ||
Line 105: | Line 135: | ||
<code julia> | <code julia> | ||
- | # Model declaration | + | # Model declaration |
- | trmodel = Model() | + | trmodel = Model() |
</ | </ | ||
==== Declaration of the model variables ==== | ==== Declaration of the model variables ==== | ||
- | Variables can have multiple-dimensions - that is, being indexed under several indexes -, and bounds are given at the same time as their declaration. | + | Variables can have multiple-dimensions - that is, being indexed under several indexes -, and bounds are given at the same time as their declaration.\\ |
+ | Differently from GAMS, we don't need to define the variable that is on the left hand side of the objective function. | ||
<code julia> | <code julia> | ||
- | # Variables | + | ## Define variables ## |
+ | # | ||
+ | # | ||
+ | # | ||
+ | # Positive Variable x ; | ||
@variables trmodel begin | @variables trmodel begin | ||
x[p in plants, m in markets] >= 0 # shipment quantities in cases | x[p in plants, m in markets] >= 0 # shipment quantities in cases | ||
Line 125: | Line 161: | ||
<code julia> | <code julia> | ||
- | # Constraints | + | ## Define contrains ## |
+ | # supply(i) | ||
+ | # supply(i) .. sum (j, x(i,j)) =l= a(i) | ||
+ | # demand(j) | ||
+ | # demand(j) .. sum(i, x(i,j)) =g= b(j); | ||
@constraints trmodel begin | @constraints trmodel begin | ||
supply[p in plants], | supply[p in plants], | ||
Line 151: | Line 191: | ||
<code julia> | <code julia> | ||
print(trmodel) | print(trmodel) | ||
- | </code | + | </code> |
==== Resolution of the model ==== | ==== Resolution of the model ==== | ||
Line 159: | Line 199: | ||
<code julia> | <code julia> | ||
status = solve(trmodel) | status = solve(trmodel) | ||
- | </julia> | + | </code> |
==== Visualisation of the results ==== | ==== Visualisation of the results ==== | ||
+ | While you can do any fancy output you may wish after you retrieve the optimal value of the variables with '' | ||
+ | Notice that you can also easily retrieve the dual value associated to the constraint with '' | ||
<code julia> | <code julia> | ||
Line 167: | Line 209: | ||
println(" | println(" | ||
println(getvalue(x)) | println(getvalue(x)) | ||
+ | println(" | ||
+ | [println(" | ||
+ | println(" | ||
+ | [println(" | ||
else | else | ||
println(" | println(" | ||
Line 173: | Line 219: | ||
</ | </ | ||
- | ==== Set definition ==== | ||
- | Sets are created as attributes object of the main model objects and all the information is given as parameter in the constructor function. Specifically, | ||
- | <code python> | ||
- | ## Define sets ## | ||
- | # Sets | ||
- | # | ||
- | # | ||
- | model.i = Set(initialize=[' | ||
- | model.j = Set(initialize=[' | ||
- | </ | ||
- | ==== Parameters | + | ==== Editing and running the script |
- | Parameter objects are created specifying the sets over which they are defined and are initialised with either a python dictionary or a scalar: | + | Differently from GAMS you can use whatever editor environment you wish to code a JuMP script. If you don't need debugging features, |
- | <code python> | + | If you want advanced features and debugging capabilities you can use a dedicated Julia IDE, like e.g. [[http://junolab.org/|Juno]]. |
- | ## Define parameters ## | + | |
- | # | + | |
- | # a(i) capacity of plant i in cases | + | |
- | # / | + | |
- | # san-diego | + | |
- | # | + | |
- | # / | + | |
- | # chicago | + | |
- | # topeka | + | |
- | model.a = Param(model.i, initialize={' | + | |
- | model.b = Param(model.j, initialize={' | + | |
- | # Table d(i,j) distance | + | |
- | # new-york | + | |
- | # seattle | + | |
- | # san-diego | + | |
- | dtab = { | + | |
- | (' | + | |
- | (' | + | |
- | | + | |
- | (' | + | |
- | (' | + | |
- | (' | + | |
- | } | + | |
- | model.d = Param(model.i, | + | |
- | # Scalar f freight in dollars per case per thousand miles | + | |
- | model.f = Param(initialize=90, | + | |
- | </code> | + | |
- | A third, powerful way to initialize a parameter is using a user-defined function.\\ | + | |
- | This function will be automatically called by pyomo with any possible (i,j) set. In this case pyomo will actually call c_init() six times in order to initialize the model.c parameter. | + | |
- | <code python> | + | |
- | # Parameter c(i, | + | |
- | # c(i,j) = f * d(i,j) / 1000 ; | + | |
- | def c_init(model, | + | |
- | return model.f * model.d[i,j] / 1000 | + | |
- | model.c = Param(model.i, | + | |
- | </ | + | |
- | ==== Variables ==== | + | If you are using instead the Julia console, |
- | Similar to parameters, variables are created specifying their domain(s). For variables we can also specify | + | |
- | Differently from GAMS, we don't need to define the variable that is on the left hand side of the objective function. | + | |
- | <code python> | + | |
- | ## Define variables ## | + | |
- | # Variables | + | |
- | # | + | |
- | # | + | |
- | # Positive Variable x ; | + | |
- | model.x = Var(model.i, | + | |
- | </ | + | |
- | ==== Constrains | + | ===== Further help ===== |
- | At this point, it should not be a surprise that constrains are again defined as model objects with the required information passed as parameter in the constructor function. | + | Documentation |
- | <code python> | + | |
- | ## Define contrains ## | + | |
- | # supply(i) | + | |
- | # supply(i) .. sum (j, x(i, | + | |
- | def supply_rule(model, | + | |
- | return sum(model.x[i, | + | |
- | model.supply = Constraint(model.i, | + | |
- | # demand(j) | + | |
- | # demand(j) .. sum(i, x(i,j)) =g= b(j); | + | |
- | def demand_rule(model, | + | |
- | return sum(model.x[i, | + | |
- | model.demand = Constraint(model.j, | + | |
- | </ | + | |
- | The above code take advantage | + | |
- | If we take the supply_rule as example, this is actually called two times by pyomo (once for each of the elements of i). Without List Comprehensions we would have had to write our function using a for loop, like: | + | |
- | <code python> | + | |
- | def supply_rule(model, | + | |
- | supply = 0.0 | + | |
- | for j in model.j: | + | |
- | supply += model.x[i,j] | + | |
- | return supply <= model.a[i] | + | |
- | </ | + | |
- | Using List Comprehension is however quicker to code and more readable. | + | |
- | ==== Objective & solving ==== | + | Happy modelling with JuMP ;-) |
- | The definition of the objective is similar to those of the constrains, except that most solvers require a scalar objective function, hence a unique function, and we can specify the sense (direction) of the optimisation. | + | |
- | <code python> | + | |
- | ## Define Objective and solve ## | + | |
- | # cost define objective function | + | |
- | # cost .. z =e= sum((i,j), c(i, | + | |
- | # Model transport /all/ ; | + | |
- | # Solve transport using lp minimizing z ; | + | |
- | def objective_rule(model): | + | |
- | return sum(model.c[i, | + | |
- | model.objective = Objective(rule=objective_rule, | + | |
- | </ | + | |
- | As we are here looping over two distinct sets, we can see how List Comprehension really simplifies the code. The objective function could have being written without List Comprehension as: | + | |
- | <code python> | + | |
- | def objective_rule(model): | + | |
- | obj = 0.0 | + | |
- | for ki in model.i: | + | |
- | for kj in model.j: | + | |
- | obj += model.c[ki, | + | |
- | return obj | + | |
- | </ | + | |
- | ==== Retrieving the output | + | ===== Complete script |
- | To retrieve the output and do something with it (either to just display it -like we do here-, to plot a graph with [[http:// | + | |
- | This function is called by pyomo after the solver has finished. | + | |
- | <code python> | + | |
- | ## Display of the output ## | + | |
- | # Display x.l, x.m ; | + | |
- | def pyomo_postprocess(options=None, instance=None, results=None): | + | |
- | model.x.display() | + | |
- | </ | + | |
- | We can print model structure information with '' | + | |
- | Results are also by default saved in a results.json file or, if PyYAML is installed in the system, in results.yml. | + | |
- | ==== Editing and running | + | Here is the complete |
- | Differently from GAMS you can use whatever editor environment you wish to code a pyomo script. If you don't need debugging features, a simple text editor like Notepad++ (in windows), gedit or kate (in Linux) will suffice. They already have syntax highlight for python.\\ | + | |
- | If you want advanced features and debugging capabilities you can use a dedicated Python IDE, like e.g. [[https:// | + | |
- | You will normally run the script as '' | + | <code Julia> |
- | If you want to run the script as '' | + | # Transposition in JuMP of the basic transport |
- | <code python> | + | # |
- | # This is an optional code path that allows the script to be run outside of | + | # This problem finds a least cost shipping schedule |
- | # pyomo command-line. For example: | + | # requirements at markets and supplies at factories. |
- | if __name__ == ' | + | # |
- | #This replicates what the pyomo command-line tools does | + | # - Original formulation: |
- | from pyomo.opt import SolverFactory | + | # Princeton University Press, Princeton, New Jersey, 1963. |
- | import pyomo.environ | + | # - Gams implementation: |
- | opt = SolverFactory(" | + | # Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide. |
- | instance = model.create() | + | # The Scientific Press, Redwood City, California, 1988. |
- | | + | # - JuMP implementation: |
- | #sends results to stdout | + | |
- | | + | |
- | | + | |
- | </ | + | |
- | Finally, if you are very lazy and want to run the script with just ./ | + | using JuMP, DataFrames |
- | <code python> | + | |
- | # | + | |
- | # -*- coding: utf-8 -*- | + | |
- | </ | + | |
- | ===== Further help ===== | + | # Sets |
- | Documentation of pyomo is available from [[https:// | + | plants |
+ | markets | ||
- | Happy modelling with pyomo ;-) | + | # Parameters |
- | ===== Complete script ===== | + | a = Dict( # capacity of plant i in cases |
+ | " | ||
+ | " | ||
+ | ) | ||
+ | b = Dict( # demand at market j in cases | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | ) | ||
- | Here is the complete script: | + | # distance in thousands of miles |
- | + | d_table = wsv""" | |
- | <code python> | + | plants |
- | # | + | seattle |
- | # -*- coding: utf-8 -*- | + | san_diego |
- | + | ||
""" | """ | ||
- | Basic example of transport model from GAMS model library translated to Pyomo | + | d = Dict( (r[:plants],m) => r[Symbol(m)] for r in eachrow(d_table), m in markets) |
- | + | ||
- | To run this you need pyomo and a linear solver installed. | + | |
- | When these dependencies are installed you can solve this example in one of | + | |
- | this ways (glpk is the default solver): | + | |
- | + | ||
- | ./ | + | |
- | python transport.py | + | |
- | pyomo solve transport.py | + | |
- | pyomo solve --solver=glpk transport.py | + | |
- | + | ||
- | To display the results: | + | |
- | + | ||
- | cat results.json | + | |
- | cat results.yml (if PyYAML is installed on your system) | + | |
- | + | ||
- | GAMS equivalent code is inserted as single-dash comments. The original GAMS code | + | |
- | needs slighly different ordering of the commands and it's available at | + | |
- | http:// | + | |
- | + | ||
- | Original problem formulation: | + | |
- | Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. | + | |
- | Princeton University Press, Princeton, New Jersey, 1963. | + | |
- | GAMS implementation: | + | |
- | Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide. | + | |
- | The Scientific Press, Redwood City, California, 1988. | + | |
- | Pyomo translation: | + | |
- | Antonello Lobianco | + | |
- | + | ||
- | This file is in the Public Domain | + | |
- | """ | + | |
- | + | ||
- | # Import | + | |
- | from pyomo.environ import * | + | |
- | + | ||
- | # Creation of a Concrete Model | + | |
- | model = ConcreteModel() | + | |
- | + | ||
- | ## Define sets ## | + | |
- | # Sets | + | |
- | # | + | |
- | # | + | |
- | model.i = Set(initialize=[' | + | |
- | model.j = Set(initialize=[' | + | |
- | + | ||
- | ## Define parameters ## | + | |
- | # | + | |
- | # a(i) | + | |
- | # / | + | |
- | # san-diego | + | |
- | # | + | |
- | # / | + | |
- | # chicago | + | |
- | # topeka | + | |
- | model.a = Param(model.i, | + | |
- | model.b = Param(model.j, | + | |
- | # Table d(i, | + | |
- | # new-york | + | |
- | # seattle | + | |
- | # san-diego | + | |
- | dtab = { | + | |
- | (' | + | |
- | (' | + | |
- | (' | + | |
- | (' | + | |
- | (' | + | |
- | (' | + | |
- | } | + | |
- | model.d = Param(model.i, | + | |
- | # Scalar f freight in dollars per case per thousand miles /90/ ; | + | |
- | model.f = Param(initialize=90, | + | |
- | # Parameter c(i, | + | |
- | # c(i,j) = f * d(i,j) / 1000 ; | + | |
- | def c_init(model, | + | |
- | return model.f * model.d[i, | + | |
- | model.c = Param(model.i, | + | |
- | + | ||
- | ## Define variables ## | + | |
- | # Variables | + | |
- | # | + | |
- | # | + | |
- | # Positive Variable x ; | + | |
- | model.x = Var(model.i, | + | |
- | + | ||
- | ## Define contrains ## | + | |
- | # supply(i) | + | |
- | # supply(i) .. sum (j, x(i,j)) =l= a(i) | + | |
- | def supply_rule(model, | + | |
- | return sum(model.x[i, | + | |
- | model.supply = Constraint(model.i, rule=supply_rule, | + | |
- | # demand(j) | + | |
- | # demand(j) .. sum(i, x(i,j)) =g= b(j); | + | |
- | def demand_rule(model, | + | |
- | return sum(model.x[i, | + | |
- | model.demand = Constraint(model.j, | + | |
- | ## Define Objective and solve ## | + | f = 90 # freight in dollars per case per thousand miles |
- | # cost define objective function | + | |
- | # cost .. z =e= sum((i,j), c(i, | + | c = Dict() # transport |
- | # | + | [ c[p,m] = f * d[p,m] / 1000 for p in plants, m in markets] |
- | # Solve transport using lp minimizing z ; | + | |
- | def objective_rule(model): | + | |
- | return sum(model.c[i,j]*model.x[i,j] for i in model.i for j in model.j) | + | |
- | model.objective = Objective(rule=objective_rule, | + | |
- | + | # Model declaration | |
- | ## Display of the output | + | trmodel = Model() |
- | # Display | + | |
- | def pyomo_postprocess(options=None, instance=None, results=None): | + | # Variables |
- | | + | @variables trmodel begin |
- | + | x[p in plants, m in markets] >= 0 # shipment quantities in cases | |
- | # This is an optional code path that allows the script to be run outside of | + | end |
- | # pyomo command-line. | + | |
- | if __name__ | + | # Constraints |
- | + | @constraints trmodel begin | |
- | | + | supply[p in plants], |
- | | + | sum(x[p,m] for m in markets) |
- | | + | |
- | | + | sum(x[p,m] for p in plants) |
- | | + | end |
- | | + | |
- | | + | # Objective |
- | | + | @objective trmodel Min begin |
- | | + | sum(c[p,m]*x[p,m] for p in plants, m in markets) |
+ | end | ||
+ | |||
+ | print(trmodel) | ||
+ | |||
+ | status = solve(trmodel) | ||
+ | |||
+ | if status | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | | ||
+ | |||
+ | else | ||
+ | | ||
+ | | ||
+ | end | ||
# Expected result: | # Expected result: | ||
Line 470: | Line 326: | ||
# | # | ||
</ | </ | ||
- | |||
- | |||
- | |||
- | ~~DISCUSSION~~ | ||
- | |||
- | |||
- | |||
~~DISCUSSION~~ | ~~DISCUSSION~~ | ||