Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
personal:blog:2017:0203_jump_for_gams_users [2017/02/03 14:09] antonello |
personal:blog:2017:0203_jump_for_gams_users [2023/12/22 11:39] (current) antonello [Further help] |
||
---|---|---|---|
Line 15: | Line 15: | ||
You have plenty of development environment to choose from (e.g. Jupiter, Juno), a clear modern language, the possibility to interface your model with third party libraries.. all of this basically for free.\\ | You have plenty of development environment to choose from (e.g. Jupiter, Juno), a clear modern language, the possibility to interface your model with third party libraries.. all of this basically for free.\\ | ||
It is also, at least for my user case, much faster than GAMS. Aside the preparation of the model to pass to the solver, where it is roughly equivalent, in the solver execution I can benefit of having on my system a version of IPOPT compiled with the much more performing ma27 linear solver, while for GAMS I would have to rely on the embedded version that is compiled with the MUMPS linear solver. That's part of the flexibility you gain in using JuMP in place of GAMS. | It is also, at least for my user case, much faster than GAMS. Aside the preparation of the model to pass to the solver, where it is roughly equivalent, in the solver execution I can benefit of having on my system a version of IPOPT compiled with the much more performing ma27 linear solver, while for GAMS I would have to rely on the embedded version that is compiled with the MUMPS linear solver. That's part of the flexibility you gain in using JuMP in place of GAMS. | ||
- | That's said, for people that don't need such flexibility, | + | That's said, for people that don't need such flexibility, |
Line 23: | Line 23: | ||
===== Installation ===== | ===== Installation ===== | ||
- | Step 1: | + | **Step 1:** |
- | Option a: Get an account on [[https:// | + | |
- | Option b: Install Julia for your platform ([[http:// | + | |
- | Step 2: | + | |
- | Run, only once, the following code to install JuMP language and a couple of open source solvers: | + | |
- | Pkg.update() | + | |
- | Pkg.add(" | + | |
- | Pkg.add(" | + | |
- | Pkg.add(" | + | |
- | Pkg.add(" | + | |
- | ==== Ubuntu ==== | + | **Step 2:** |
- | //(tested in Ubuntu 14.04 LTS)// | + | |
- | * **Install | + | Run, only once, the following code to install JuMP language and a couple of open source solvers: |
- | * '' | + | <code julia> |
- | * **Install pyomo:** | + | using Pkg # Load the package manager |
- | * '' | + | Pkg.update() |
- | * '' | + | Pkg.add(" |
- | * **Install solvers:** | + | Pkg.add(" |
- | * //linear and MIP solver (glpk)//: '' | + | Pkg.add(" |
- | * //non-linaer | + | Pkg.add(" |
- | + | Pkg.add(" | |
- | ==== Windows and Mac ==== | + | </code> |
- | Please refer to the [[https:// | + | |
===== Model components ===== | ===== Model components ===== | ||
- | ==== Creation of the Model ==== | + | ==== Importing |
- | In pyomo everything is an object. The various components of the model (sets, parameters, variables, constrains, objective..) are all attributes of the main model object while being objects themselves.\\ | + | |
- | There are two type of models in pyomo: A '' | + | You will need to import as a minima |
- | The first thing to do in the script is hence to load the pyomo library and to create a new ConcreteModel (we have little imagination here, and we call our model " | + | |
- | < | + | < |
- | # Import of the pyomo module | + | # Import of the JuMP, GLPK, CSV and DataFrames modules (the latter twos just to import the data from a header based table, as in the original trasnport example in GAMS |
- | from pyomo.environ import * | + | using CSV, DataFrames, GLPK, JuMP |
- | + | ||
- | # Creation of a Concrete Model | + | |
- | model = ConcreteModel() | + | |
</ | </ | ||
- | ==== Set definition | + | ==== Defining the " |
- | Sets are created as attributes object | + | |
- | < | + | JuMP doesn' |
- | ## Define sets ## | + | While many works with position-based lists, I find more readable using dictionaries instead. So the " |
+ | One note: it seems that Julia/JuMP don't like much the " | ||
+ | |||
+ | < | ||
+ | # Define sets # | ||
# Sets | # Sets | ||
# | # | ||
# | # | ||
- | model.i = Set(initialize=['seattle',' | + | plants |
- | model.j = Set(initialize=[' | + | markets |
</ | </ | ||
- | ==== Parameters | + | |
- | Parameter objects are created specifying the sets over which they are defined and are initialised with either | + | ==== Definition of the " |
- | < | + | |
- | ## Define parameters | + | Capacity of plants and demand of markets |
+ | |||
+ | < | ||
+ | # Define parameters # | ||
# | # | ||
# | # | ||
# / | # / | ||
# san-diego | # san-diego | ||
+ | a = Dict( # capacity of plant i in cases | ||
+ | " | ||
+ | " | ||
+ | ) | ||
+ | |||
# | # | ||
# / | # / | ||
# chicago | # chicago | ||
# topeka | # topeka | ||
- | model.a | + | b = Dict( # demand at market j in cases |
- | model.b | + | " |
- | # Table d(i, | + | "chicago" |
+ | "topeka" | ||
+ | ) | ||
+ | |||
+ | # Table d(i, | ||
# new-york | # new-york | ||
# seattle | # seattle | ||
# san-diego | # san-diego | ||
- | dtab = { | + | d_table |
- | | + | plants |
- | (' | + | seattle |
- | (' | + | san_diego |
- | | + | """ |
- | (' | + | d = Dict( (r[:plants],m) => r[Symbol(m)] for r in eachrow(d_table), m in markets) |
- | (' | + | # Here we are converting the table in a " |
- | } | + | # r[: |
- | model.d = Param(model.i, model.j, initialize=dtab, doc=' | + | # m: the second key |
- | # Scalar f freight in dollars per case per thousand miles /90/ ; | + | # r[Symbol(m)]: |
- | model.f = Param(initialize=90, doc=' | + | |
- | </ | + | # Scalar f freight in dollars per case per thousand miles /90/ ; |
- | A third, powerful way to initialize a parameter is using a user-defined function.\\ | + | f = 90 # freight |
- | 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, |
- | # Parameter c(i, | + | |
# c(i,j) = f * d(i,j) / 1000 ; | # c(i,j) = f * d(i,j) / 1000 ; | ||
- | def c_init(model, i, j): | + | # We first declare an empty dictionary and then we fill it with the values |
- | | + | c = Dict() # transport cost in thousands of dollars per case ; |
- | model.c = Param(model.i, | + | [ 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. | ||
+ | |||
+ | |||
+ | ==== Declaration of the model ==== | ||
+ | |||
+ | Here we declare a JuML optimisation model and we give it a name. This name will be then passed as first argument to all the subsequent operations, like creation of variables, constraints and objective function.\\ | ||
+ | The solver engine to use is given as argument of the '' | ||
+ | We could pass solver-specific options with the '' | ||
+ | '' | ||
- | ==== Variables | + | <code julia> |
- | Similar to parameters, variables | + | # Model declaration (transport model) |
+ | trmodel | ||
+ | </ | ||
+ | |||
+ | ==== Declaration of the model variables | ||
+ | |||
+ | Variables can have multiple-dimensions - that is, being indexed under several indexes -, and bounds | ||
Differently from GAMS, we don't need to define the variable that is on the left hand side of the objective function. | Differently from GAMS, we don't need to define the variable that is on the left hand side of the objective function. | ||
- | < | + | |
+ | < | ||
## Define variables ## | ## Define variables ## | ||
# Variables | # Variables | ||
Line 123: | Line 152: | ||
# | # | ||
# Positive Variable x ; | # Positive Variable x ; | ||
- | model.x = Var(model.i, model.j, bounds=(0.0,None), doc=' | + | @variables trmodel begin |
+ | | ||
+ | end | ||
</ | </ | ||
- | ==== Constrains | + | ==== Declaration of the model constraints |
- | 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. | + | |
- | < | + | As in GAMS, each constraint can actually |
+ | |||
+ | < | ||
## Define contrains ## | ## Define contrains ## | ||
# supply(i) | # supply(i) | ||
# supply(i) .. sum (j, x(i,j)) =l= a(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, | ||
# demand(j) | # demand(j) | ||
# demand(j) .. sum(i, x(i,j)) =g= b(j); | # demand(j) .. sum(i, x(i,j)) =g= b(j); | ||
- | def demand_rule(model, j): | + | @constraints trmodel begin |
- | | + | supply[p in plants], # observe supply limit at plant p |
- | model.demand | + | sum(x[p,m] for m in markets) <= a[p] |
+ | demand[m in markets], # satisfy | ||
+ | sum(x[p,m] for p in plants) > | ||
+ | end | ||
</ | </ | ||
- | 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: | + | ==== Declaration |
- | < | + | |
- | def supply_rule(model, | + | Contrary to constraints and variables, the objective is always |
- | | + | |
- | for j in model.j: | + | < |
- | | + | # Objective |
- | | + | @objective trmodel Min begin |
+ | | ||
+ | end | ||
</ | </ | ||
- | Using List Comprehension is however quicker to code and more readable. | ||
- | ==== Objective & solving ==== | + | ==== Human-readable visualisation |
- | The definition | + | |
- | <code python> | + | If we wish we can get the optimisation model printed in a human-readable fashion, so we can expect all is like it should be |
- | ## Define Objective and solve ## | + | |
- | # cost define objective function | + | < |
- | # cost .. z =e= sum((i,j), c(i, | + | print(trmodel) |
- | # Model transport /all/ ; | + | |
- | # Solve transport using lp minimizing z ; | + | |
- | def objective_rule(model): | + | |
- | return sum(model.c[i, | + | |
- | model.objective | + | |
- | </ | + | |
- | 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: | + | |
- | < | + | |
- | def objective_rule(model): | + | |
- | obj = 0.0 | + | |
- | for ki in model.i: | + | |
- | for kj in model.j: | + | |
- | obj += model.c[ki, | + | |
- | return obj | + | |
</ | </ | ||
- | ==== Retrieving | + | ==== Resolution of the model ==== |
- | To retrieve | + | |
- | This function is called by pyomo after the solver has finished. | + | It is at this point that the solver is called |
- | < | + | |
- | ## Display of the output ## | + | < |
- | # Display x.l, x.m ; | + | optimize!(trmodel) |
- | def pyomo_postprocess(options=None, | + | status = termination_status(trmodel) |
- | | + | |
</ | </ | ||
- | 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 | + | ==== Visualisation of the results |
- | Differently from GAMS you can use whatever editor environment | + | While you can do any fancy output |
- | If you want advanced features and debugging capabilities | + | Notice that you can also easily retrieve the dual value associated to the constraint with '' |
- | You will normally run the script as '' | + | < |
- | If you want to run the script as '' | + | if status |
- | < | + | |
- | # This is an optional code path that allows the script to be run outside of | + | |
- | # pyomo command-line. | + | |
- | if __name__ | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | else |
- | | + | |
- | | + | |
- | | + | end |
- | | + | |
</ | </ | ||
- | Finally, if you are very lazy and want to run the script | + | |
- | <code python> | + | ==== Editing |
- | #!/usr/bin/env python | + | Differently from GAMS you can use whatever editor environment you wish to code a JuMP script. If you don't need debugging features, a simple text editor like Notepad++ (in windows), gedit or kate (in Linux) |
- | # -*- coding: utf-8 -*- | + | If you want advanced features and debugging capabilities you can use a dedicated Julia IDE, like the [[https://www.julia-vscode.org/|Julia extension for VSCode]]. |
- | </ | + | |
+ | If you are using instead the Julia terminal, | ||
===== Further help ===== | ===== Further help ===== | ||
- | Documentation of pyomo is available from [[https://software.sandia.gov/ | + | Documentation of JuMP is available from [[https://jump.dev/|this page]], |
+ | |||
+ | Happy modelling with JuMP ;-) | ||
- | Happy modelling with pyomo ;-) | ||
===== Complete script ===== | ===== Complete script ===== | ||
Here is the complete script: | Here is the complete script: | ||
- | < | + | < |
- | #!/ | + | # Transport example |
- | # -*- coding: utf-8 -*- | + | |
+ | # Transposition in JuMP of the basic transport model used in the GAMS tutorial | ||
+ | # | ||
+ | # This problem finds a least cost shipping schedule that meets | ||
+ | # requirements at markets and supplies at factories. | ||
+ | # | ||
+ | # - Original formulation: | ||
+ | # Princeton University Press, Princeton, New Jersey, 1963. | ||
+ | # - Gams implementation: This formulation is described in detail in: | ||
+ | # Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide. | ||
+ | # The Scientific Press, Redwood City, California, 1988. | ||
+ | # - JuMP implementation: | ||
- | """ | + | using CSV, DataFrames, GLPK, JuMP |
- | Basic example of transport model from GAMS model library translated to Pyomo | + | |
- | To run this you need pyomo and a linear solver installed. | + | # Sets |
- | When these dependencies are installed you can solve this example in one of | + | plants |
- | this ways (glpk is the default solver): | + | markets = [" |
- | ./ | + | # Parameters |
- | | + | a = Dict( # capacity of plant i in cases |
- | pyomo solve transport.py | + | " |
- | | + | " |
+ | ) | ||
+ | b = Dict( # demand at market j in cases | ||
+ | " | ||
+ | " | ||
+ | " | ||
+ | ) | ||
- | To display the results: | + | # distance in thousands of miles |
+ | d_table = CSV.read(IOBuffer(""" | ||
+ | plants | ||
+ | seattle | ||
+ | san_diego | ||
+ | """ | ||
+ | d = Dict( (r[:plants],m) => r[Symbol(m)] for r in eachrow(d_table), | ||
- | cat results.json | + | f = 90 # freight in dollars per case per thousand miles |
- | cat results.yml (if PyYAML is installed on your system) | + | |
- | GAMS equivalent code is inserted as single-dash comments. The original GAMS code | + | c = Dict() # transport cost in thousands |
- | needs slighly different ordering | + | [ c[p,m] = f * d[p, |
- | http:// | + | |
- | Original problem formulation: | + | # Model declaration |
- | | + | trmodel = Model(GLPK.Optimizer) # transport model |
- | 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 | + | # Variables |
- | """ | + | @variables trmodel begin |
+ | x[p in plants, m in markets] >= 0 # shipment quantities | ||
+ | end | ||
- | # Import | + | # Constraints |
- | from pyomo.environ import * | + | @constraints trmodel begin |
+ | supply[p in plants], | ||
+ | sum(x[p,m] for m in markets) | ||
+ | demand[m in markets], | ||
+ | sum(x[p,m] for p in plants) | ||
+ | end | ||
- | # Creation of a Concrete Model | + | # Objective |
- | model = ConcreteModel() | + | @objective trmodel Min begin |
+ | sum(c[p, | ||
+ | end | ||
- | ## Define sets ## | + | print(trmodel) |
- | # Sets | + | |
- | # | + | |
- | # | + | |
- | model.i = Set(initialize=[' | + | |
- | model.j = Set(initialize=[' | + | |
- | ## Define parameters ## | + | optimize!(trmodel) |
- | # | + | status = termination_status(trmodel) |
- | # a(i) | + | |
- | # / | + | if status == MOI.OPTIMAL |
- | # san-diego | + | |
- | # b(j) | + | |
- | # / | + | |
- | # chicago | + | |
- | # topeka | + | |
- | model.a | + | |
- | model.b = Param(model.j, initialize={' | + | |
- | # Table d(i,j) | + | |
- | # new-york | + | |
- | # seattle | + | |
- | # san-diego | + | |
- | dtab = { | + | |
- | (' | + | |
- | (' | + | |
- | | + | |
- | (' | + | |
- | (' | + | |
- | (' | + | |
- | | + | |
- | model.d = Param(model.i, model.j, initialize=dtab, | + | |
- | # Scalar f freight in dollars per case per thousand miles /90/ ; | + | |
- | model.f = Param(initialize=90, doc=' | + | |
- | # Parameter c(i,j) transport cost in thousands of dollars per case ; | + | |
- | # 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, | + | |
- | ## Define variables ## | + | else |
- | # Variables | + | |
- | # x(i,j) shipment quantities in cases | + | |
- | # | + | end |
- | # Positive Variable x ; | + | |
- | model.x = Var(model.i, | + | |
- | + | ||
- | ## Define contrains ## | + | |
- | # supply(i) observe supply limit at plant 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, | + | |
- | # 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 ## | ||
- | # 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, | ||
- | |||
- | |||
- | ## Display of the output ## | ||
- | # Display x.l, x.m ; | ||
- | def pyomo_postprocess(options=None, | ||
- | model.x.display() | ||
- | |||
- | # This is an optional code path that allows the script to be run outside of | ||
- | # pyomo command-line. | ||
- | if __name__ == ' | ||
- | |||
- | #This replicates what the pyomo command-line tools does | ||
- | from pyomo.opt import SolverFactory | ||
- | import pyomo.environ | ||
- | opt = SolverFactory(" | ||
- | instance = model.create() | ||
- | results = opt.solve(instance) | ||
- | #sends results to stdout | ||
- | results.write() | ||
- | pyomo_postprocess(None, | ||
- | |||
# Expected result: | # Expected result: | ||
# obj= 153.675 | # obj= 153.675 | ||
Line 360: | Line 333: | ||
# | # | ||
</ | </ | ||
- | |||
- | |||
- | |||
- | ~~DISCUSSION~~ | ||
- | |||
- | |||
- | |||
~~DISCUSSION~~ | ~~DISCUSSION~~ | ||