Examples

Example network instances

Five example network instances can be found in the data/example_networks/ folder of the GitHub repository. These were generated with the generate_data_instances_set.py script with the standard settings for the second method of generating random network instances (see the API for explanations).

These networks range in size from 6x6 to 9x9. The basic settings of the smspsa/main.py script automatically runs the SM-SPSA algorithm on all five network instances. Which output is provided can be specified by the variables PLOT_NETWORK, PLOT_MATRICES, PLOT_OBJECTIVE and SAVE_OUTPUT (also see output data).

Example_network_0

The following shows the results of running SM-SPSA on “example_network_0” to illustrate how the SM-SPSA algorithm works. The “normal” version of the algorithm is used with the standard settings as provided in smspsa/main.py. The objective is to maximise the stationary distribution of node 7. The centred mass heuristic is used and the resulting transition matrix is optimised with SM-SPSA.

Figure 1 shows the network plot of the transition matrix that will be optimised.

Figure 1: The network that will be optimised.

The final objective value is equal to 0.42, which represents an increase of 241% compared to the objective value of the initial transition matrix. Figure 2 shows the objective value at each iteration. Figure 3 shows the final network plot.

Figure 2: The objective value plot of the optimisation of “example_network_0”

Figure 3: The optimised network.