## Figures index

#### From

#### On Application of Neural Networks' Modeling for Analytical Comparative Study between Two Optimally Selected Made Decisions by Ant Colony Systems

*American Journal of Educational Research*.

**2018**, 6(4), 308-318 doi:10.12691/education-6-4-3

**Fig****ure****1.**A simplified schematic structure of a single biological neuron adapted from [12]

**Fig****ure****2.**A single neuron (k) model coupled with synaptic weights from other neurons (i,……,p)

**Fig****ure****3.**A simplified schematic diagram for a (FFANN) model (adapted from, [12])

**Figure 4.**Simplified view for interactive learning process

**Figure 5.**Generalized ANN block diagram simulating two diverse learning paradigms adapted from [11].

**Fig****ure****6****.**Schematic illustration of the ant algorithm. (*At the top*). Selection of a shorter path between a nest and a food source by natural ants. The ants travel between the nest and food through trail #1 and trail #2. Initially, ants are distributed equally on both trails. (*At the bottom*). Since trail #1 is shorter than trail #2, trail #1 becomes their favorite pathway with a higher pheromone concentration. (Adapted from [18])

**Fig****ure****7****.**Ant Behavior A. Ants in a pheromone trail between nest and food; B. An obstacle interrupts the trail; C. Ants find two paths to go around the obstacle; D. A new pheromone trail is formed along the shorter path.

**Fig****ure****8****.**(a) illustrates a diamond bridge composed of two identical branches. The ants pass through that bridge adopting bifurcation (distributed) Strategy (b) Percentage of the ant workers per three minutes period that are passing on the two(upper and lower) branches of the diamond bridge (Adapted from [19])

**Fig****ure****9****.**Percentage of the ant workers that are passing on the collectivity selected winning branch of the diamond bridge {shown at the above Figure 3)} resulting after 20 experiments measured every three minutes(dotes). Noting that horizontal axis represents the cumulative number of ant passages on both branches of the diamond bridge. The dashed curve represents the average values. The solid curve represents the average of 200 Monte-Carlo Simulations (Adapted from [19])

**Fig****ure****10****.**

**Fig****ure****11****.**

**Figure 12.**Communication among ant mates (agents), determines the synergistic effect considering various intercommunication levels leading to different average speed values to reach the optimal TSP solution {Adapted from [26]}

**Figure 13.**Learning performance to get accurate solution with different gain factors 0.05, 1, and 2, while #cycles = 300 and Learning Rate = 0.3

**Figure 14.**Graphical representation of learning performance of model with different gain factor values (λ)

**Fig****ure 15.**Adaptability performance concerned with Hebbian (self-organized) learning algorithm with learning rates (0.05, 0.1, 0.2). (Adapted from [24])

**Fig****ure 16.**

**Fig****ure 17.**Illustrated the simulated output results presented as percentage degree [%] of normalized achievement outcomes versus # Neurons for different learning rate values η (0.01,0.1,and 0.3). and constant gain factor = 1

**Figure 18.**Adaptability performance concerned with error correction (supervised) learning algorithm with learning rates (0.05, 0.1, 0.2) (Adapted from [24])

**Figure 19.**Error correction performance based on time response parameter with considering three different learning rates: 0.05, 0.1 and 0.3 for gain factor = 0.5, while #cycles = 300

**Fig****ure 20.**Illustrates relative error values [%], versus # Neurons, that measures learning performance for different learning rates values η (0.01, 0.1, and 0.3). when #cycles = 300 and gain factor = 1