Fig 1.
Example of the genotype-phenotype mapping in MBEANN.
A genome consists of operons, each of which corresponds to a subnetwork within the neural network. In this example, the genome of the neural network consists of three operons, that is, operon0, operon1, and operon2. Note that operon0 includes only nodes from the input and output layers, along with the direct connections between them. When the add-node mutation is applied to operon0, a new operon is created using the added hidden node.
Fig 2.
Example of the add-node mutation.
In this figure, the connection of link0, which has the weight value of w0, is selected and replaced with node3, link2, and link3. If the selected connection to be replaced belongs to operon0, a new operon is generated with the new node and connections.
Fig 3.
Example of the add-connection mutation.
A new connection with the weight value of w5 is created from node1 to node3. The nodes to be connected are selected either from two nodes within the same operon or from one in operon0 and the other in the operon being mutated. The weight value of the new connection is set to zero.
Fig 4.
Screenshots of (A) HalfCheetah-v4 and (B) Ant-v4 provided in OpenAI Gym using the MuJoCo physics simulator.
Fig 5.
Transitions of the fitness value of the best individual in HalfCheetah-v4.
Each line represents the mean of the best fitness values over 15 trials, and the shaded regions around them indicate the standard deviations.
Fig 6.
Transitions of the fitness value of the best individual in Ant-v4.
Each line represents the mean of the best fitness values over 15 trials, and the shaded regions around them indicate the standard deviations.
Fig 7.
Transitions of the network structure of the best individual in HalfCheetah-v4.
(A) Transitions of the number of nodes in the individual, including 17 input and 6 output nodes. (B) Transitions of the number of connections. Each line represents the mean over 15 trials, and the shaded regions around them indicate the standard deviations.
Fig 8.
Transitions of the network structure of the best individual in Ant-v4.
(A) Transitions of the number of nodes in the individual, including 27 input and 8 output nodes. (B) Transitions of the number of connections. Each line represents the mean over 15 trials, and the shaded regions around them indicate the standard deviations.
Fig 9.
Results of the re-evaluation for 100 trials using the best-evolved individuals.
Fig 10.
Transitions of the step size of the best individual in HalfCheetah-v4.
Each line represents the mean over 15 trials, while the shaded regions around them show the standard deviations.
Fig 11.
Transitions of the step size of the best individual in Ant-v4.
Each line represents the mean over 15 trials, while the shaded regions around them show the standard deviations.