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| 1 | +# # Path-finding on image maps |
| 2 | + |
| 3 | +#= |
| 4 | +In this tutorial, we showcase InferOptBenchmarks.jl capabilities on one of its main benchmarks: the Warcraft benchmark. |
| 5 | +This benchmark problem is a simple path-finding problem where the goal is to find the shortest path between the top left and bottom right corners of a given image map. |
| 6 | +The map is represented as a 2D image representing a 12x12 grid, each cell having an unknown travel cost depending on the terrain type. |
| 7 | +=# |
| 8 | + |
| 9 | +# First, let's load the package and create a benchmark object as follows: |
| 10 | +using InferOptBenchmarks |
| 11 | +b = WarcraftBenchmark() |
| 12 | + |
| 13 | +# ## Dataset generation |
| 14 | + |
| 15 | +# These benchmark objects behave as generators that can generate various needed elements in order to build an algorithm to tackle the problem. |
| 16 | +# First of all, all benchmarks are capable of generating datasets as needed, using the [`generate_dataset`](@ref) method. |
| 17 | +# This method takes as input the benchmark object for which the dataset is to be generated, and a second argument specifying the number of samples to generate: |
| 18 | +dataset = generate_dataset(b, 50); |
| 19 | + |
| 20 | +# We obtain a vector of [`DataSample`](@ref) objects, containing all needed data for the problem. |
| 21 | +# Subdatasets can be created through regular slicing: |
| 22 | +train_dataset, test_dataset = dataset[1:45], dataset[46:50] |
| 23 | + |
| 24 | +# And getting an individual sample will return a [`DataSample`](@ref) with four fields: `x`, `instance`, `θ`, and `y`: |
| 25 | +sample = test_dataset[1] |
| 26 | +# `x` correspond to the input features, i.e. the input image (3D array) in the Warcraft benchmark case: |
| 27 | +x = sample.x |
| 28 | +# `θ` correspond to the true unknown terrain weights. We use the opposite of the true weights in order to formulate the optimization problem as a maximization problem: |
| 29 | +θ_true = sample.θ |
| 30 | +# `y` correspond to the optimal shortest path, encoded as a binary matrix: |
| 31 | +y_true = sample.y |
| 32 | +# `instance` is not used in this benchmark, therefore set to nothing: |
| 33 | +isnothing(sample.instance) |
| 34 | + |
| 35 | +# For some benchmarks, we provide the following plotting method [`plot_data`](@ref) to visualize the data: |
| 36 | +plot_data(b, sample) |
| 37 | +# We can see here the terrain image, the true terrain weights, and the true shortest path avoiding the high cost cells. |
| 38 | + |
| 39 | +# ## Building a pipeline |
| 40 | + |
| 41 | +# InferOptBenchmarks also provides methods to build an hybrid machine learning and combinatorial optimization pipeline for the benchmark. |
| 42 | +# First, the [`generate_statistical_model`](@ref) method generates a machine learning predictor to predict cell weights from the input image: |
| 43 | +model = generate_statistical_model(b) |
| 44 | +# In the case of the Warcraft benchmark, the model is a convolutional neural network built using the Flux.jl package. |
| 45 | +θ = model(x) |
| 46 | +# Note that the model is not trained yet, and its parameters are randomly initialized. |
| 47 | + |
| 48 | +# Finally, the [`generate_maximizer`](@ref) method can be used to generate a combinatorial optimization algorithm that takes the predicted cell weights as input and returns the corresponding shortest path: |
| 49 | +maximizer = generate_maximizer(b; dijkstra=true) |
| 50 | +# In the case o fthe Warcraft benchmark, the method has an additional keyword argument to chose the algorithm to use: Dijkstra's algorithm or Bellman-Ford algorithm. |
| 51 | +y = maximizer(θ) |
| 52 | +# As we can see, currently the pipeline predicts random noise as cell weights, and therefore the maximizer returns a straight line path. |
| 53 | +plot_data(b, DataSample(; x, θ, y)) |
| 54 | +# We can evaluate the current pipeline performance using the optimality gap metric: |
| 55 | +starting_gap = compute_gap(b, test_dataset, model, maximizer) |
| 56 | + |
| 57 | +# ## Using a learning algorithm |
| 58 | + |
| 59 | +# We can now train the model using the InferOpt.jl package: |
| 60 | +using InferOpt |
| 61 | +using Flux |
| 62 | +using Plots |
| 63 | + |
| 64 | +perturbed_maximizer = PerturbedMultiplicative(maximizer; ε=0.2, nb_samples=100) |
| 65 | +loss = FenchelYoungLoss(perturbed_maximizer) |
| 66 | + |
| 67 | +starting_gap = compute_gap(b, test_dataset, model, maximizer) |
| 68 | + |
| 69 | +opt_state = Flux.setup(Adam(1e-3), model) |
| 70 | +loss_history = Float64[] |
| 71 | +for epoch in 1:50 |
| 72 | + val, grads = Flux.withgradient(model) do m |
| 73 | + sum(loss(m(sample.x), sample.y) for sample in train_dataset) / length(train_dataset) |
| 74 | + end |
| 75 | + Flux.update!(opt_state, model, grads[1]) |
| 76 | + push!(loss_history, val) |
| 77 | +end |
| 78 | + |
| 79 | +plot(loss_history; xlabel="Epoch", ylabel="Loss", title="Training loss") |
| 80 | + |
| 81 | +# |
| 82 | + |
| 83 | +final_gap = compute_gap(b, test_dataset, model, maximizer) |
| 84 | + |
| 85 | +# |
| 86 | +θ = model(x) |
| 87 | +y = maximizer(θ) |
| 88 | +plot_data(b, DataSample(; x, θ, y)) |
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