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Add Hydro Thermal Scheduling example
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‎docs/src/tutorial.md‎

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## Hydro Thermal Scheduling
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In this tutorial, we show how to run the [FAST tutorial example](https://web.stanford.edu/~lcambier/fast/tuto.php) using this package.
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The big difference between this example and the example quickstart example is that in this example we will model serial independence.
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The big difference between this example and the quickstart example is that in this example we will model serial independence.
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There will be 5 stages and 2 scenarios per stages except for the first stage which has only one scenario.
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Each pair of scenario will have the same parent.
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An IJulia notebook of this example can be found [in the examples folder](https://github.com/JuliaStochOpt/StructDualDynProg.jl/blob/master/examples/Hydro_Thermal_Scheduling.ipynb).
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We start by setting the constants:
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```julia

‎examples/.gitignore‎

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.ipynb_checkpoints

‎examples/Hydro_Thermal_Scheduling.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"In this tutorial, we show how to run the [FAST tutorial example](https://web.stanford.edu/~lcambier/fast/tuto.php) using this package.\n",
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"The big difference between this example and the quickstart example is that in this example we will model serial independence.\n",
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"There will be 5 stages and 2 scenarios per stages except for the first stage which has only one scenario.\n",
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"Each pair of scenario will have the same parent.\n",
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"\n",
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"We start by setting the constants:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"const num_stages = 5\n",
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"const numScen = 2\n",
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"const C = 5\n",
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"const V = 8\n",
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"const d = 6\n",
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"const r = [2, 10];"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We now create a matrix to store all the variables of all the models.\n",
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"This allows us to use the variables of other models from a given model.\n",
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"We also create an array of the first model of each stage to give play the role of parent for the models of the next stage."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"using StructJuMP\n",
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"x = Matrix{JuMP.Variable}(num_stages, numScen)\n",
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"y = Matrix{JuMP.Variable}(num_stages, numScen)\n",
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"p = Matrix{JuMP.Variable}(num_stages, numScen)\n",
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"models = Vector{JuMP.Model}(num_stages);"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Now, we create all the models.\n",
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"Note that each model declares that its parent is the first model (i.e. the model `ξ == 1`) of the previous stage.\n",
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"Hence if it is not the first model, it also declares that it has the same children than the first model of its stage.\n",
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"This is how serial independence is modeled in [StructJuMP](https://github.com/StructJuMP/StructJuMP.jl)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"for s in 1:num_stages\n",
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" for ξ in 1:(s == 1 ? 1 : numScen) # for the first stage there is only 1 scenario\n",
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" if s == 1\n",
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" model = StructuredModel(num_scenarios=numScen)\n",
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" else\n",
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" model = StructuredModel(parent=models[s-1], prob=1/2, same_children_as=(ξ == 1 ? nothing : models[s]), id=ξ, num_scenarios=(s == num_stages ? 0 : numScen))\n",
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" end\n",
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" x[s, ξ] = @variable(model, lowerbound=0, upperbound=V)\n",
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" y[s, ξ] = @variable(model, lowerbound=0)\n",
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" p[s, ξ] = @variable(model, lowerbound=0)\n",
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" if s > 1\n",
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" @constraint(model, x[s, ξ] <= x[s-1, 1] + r[ξ] - y[s, ξ])\n",
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" else\n",
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" @constraint(model, x[s, ξ] <= mean(r) - y[s, ξ])\n",
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" end\n",
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" @constraint(model, p[s, ξ] + y[s, ξ] >= d)\n",
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" @objective(model, Min, C * p[s, ξ])\n",
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" # models[s] contains the first model only\n",
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" if ξ == 1\n",
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" models[s] = model\n",
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" end\n",
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" end\n",
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"end"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We first need to pick an LP solver, see [here](http://www.juliaopt.org/) for a list of the available choices."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"using GLPKMathProgInterface\n",
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"solver = GLPKMathProgInterface.GLPKSolverLP();"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We now create the lattice, note that the master problem is `models[1]`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {},
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"outputs": [],
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"source": [
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"using CutPruners\n",
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"const pruner = AvgCutPruningAlgo(-1)\n",
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"using StructDualDynProg\n",
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"sp = stochasticprogram(models[1], num_stages, solver, pruner);"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The SDDP algorithm can now be run on the lattice:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"StructDualDynProg.SDDPSolution(:Optimal, 23.75, [0.0, 6.0, 0.0], Dict{Any,Any}(Pair{Any,Any}(:stats, | Total time | Number | Average time\n",
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" Solving problem | 0min 1s 523ms 41μs | 66 | 0min 0s 23ms 76μs\n",
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" Merging paths | 0min 0s 143ms 9μs | 6 | 0min 0s 23ms 834μs\n",
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"Adding feasibility cuts | 0min 0s 0ms 0μs | 0 | min s ms μs\n",
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"Adding optimality cuts | 0min 0s 77ms 615μs | 11 | 0min 0s 7ms 55μs\n",
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"Setting parent solution | 0min 0s 35ms 22μs | 64 | 0min 0s 0ms 547μs\n",
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" | 0min 1s 635ms 680μs |),Pair{Any,Any}(:nfcuts, 0),Pair{Any,Any}(:nocuts, 11),Pair{Any,Any}(:niter, 2)))"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"sol = SDDP(sp, num_stages, K = 16, stopcrit = Pereira(2., 0.5) | IterLimit(10))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 0.6.3",
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"language": "julia",
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"name": "julia-0.6"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "0.6.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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