L2OViz.jl

L2OViz.jl visualizes the solutions to multiple instances of an optimization problem. It supports visualizing the solutions of the same instances from multiple solvers for comparison. It also has a special feature for visualizing variables with a graph structure in a grid layout of subplots which correspond to the adjacency matrix.

Data Format Specifications

For each variable, the values should be stored in a Matrix where each row contains the values of the variable in each problem instance. For example,

y_dim = 5
n_instances = 3
y = randn(y_dim, n_instances)

contains the values of a 5-dimensional variable for 3 instances of an optimization problem.

plot_variable accepts a variable number of Matrix inputs, each corresponding to a solver.

Graph variables

Variables that correspond to the edges of a (multi-edge) undirected graph can be visualized in a grid layout of subplots which correspond to coordinates in the adjacency matrix.

The graph topology is specified by I and J, ordered vectors containing endpoints of the edges. It is assumed that at most one of (i,j) and (j,i) is present, since the graph is undirected. It is assumed that, across all the problem instances, the variable corresponds to the same graph topology. The values are still stored as a Matrix, where the number of rows is the number of edges of the graph (dimension of the variable), and the number of columns is n_instances. Each column contains the values of the variable in each problem instance. That is, all the variables are treated as vector variables in L2OViz.jl.

In some cases the underlying graph is multi-edge. If there are multiple edges between a vertex pair, only the highest-scoring one is kept (see Thresholding).

plot_graph_variable accepts a variable number of Matrix inputs, each corresponding to a solver.

Currently, directed graph variables are not supported.

Visualization

The values of each variable entry across all the problem instances are visualized in a scatter point subplot. plot_variable simply places the subplots side-by-side. plot_graph_variable arranges the subplots into a grid layout, where the subplot at coordinate (i, j) visualizes the (i, j) entry of the variable as specified in (I, J).

The data of Solver A and Solver B do not have to be for the same problem instances. In this case, different x should be provided.

Animation

animate_variable and animate_graph_variable are animated counterparts to plot_variable and plot_graph_variable. Each frame uses the same subplot layout as its non-animated counterpart. The animation can be exported as a GIF.

Thresholding

When the dimension of the variable to visualize is too high, vis_threshold limits the number of entries that are visualized. significance_fn is used to select the most interesting entries of the variable.

For graph variables, the vis_threshold vertices with the highest maximum scores over its edges are selected. Only the data on this induced subgraph are visualized.

If multiple edges between a vertex pair are selected, only the highest-scoring one is kept (with a warning).

By default, significance_fn chooses the solutions with the maximum absolute sum across all instances of all solvers. This can be used to, for example, visualize the variables where a solver produces highest error compared to a reference (by calling the plotting functions on the error instead of the solutions).

Example: Optimal Power Flow

exp/viz_opf.jl defines viz_opf and animate_opf, utility functions for visualizing OPF solution data using system topology from PGLib.jl and PowerModels.jl.

viz_opf supports two calling modes:

• Single variable (variables::String, var_data::Matrix...): each var_data argument is a (n_dim × n_instances) Matrix of the named variable of a solver.
• Multiple variables (variables::Vector{String}, var_data::Dict...): each var_data argument is a Dict mapping variable names to matrices, one per solver. Multiple images will be saved.

animate_opf supports two similar calling modes (single- and multiple-variable). Refer to animate_variable and animate_graph_variable for the corresponding data formats.

By default (flat=false), the plot type is inferred from each variable's dimension:

• Equal to the number of branches → plot_graph_variable/animate_graph_variable, with I/J being f_bus/t_bus in sorted branch key order obtained from make_basic_network(pglib(system_name)).
• Equal to the number of buses → plot_variable/animate_variable.

When flat=true, all variables use plot_variable/animate_variable.

Output images are named {system_name}_{variable}.png/{system_name}_{variable}.gif.

Example viz_opf outputs with synthetic data

Example animate_opf outputs with synthetic data