Merging Thresholds

Ant encounters determine the features and colonies that are to be merged. The number of en- counters seen by each ant at each node is determined by the visibility range. Further controlling all this is the fact that all encounters are only temporarily available to the ant, according to a time-window.

3.8.6.1 Feature Merging Threshold Parameter

This parameter influences colony merging and pheromone deposition in the following ways. Lower feature merging thresholds cause ants to immediately combine features as per figure (3.8, a). This premature combination has another side effect, as feature combinations cause ants to rapidly become specific to a particular area of graph space. This increases the likelihood of ants merging into colonies. However, this restricted area causes a number of smaller colonies to form rather than the complete colonies required, as is shown in figure (3.8, b). Increasing the feature merging threshold to a mid-value (in this case 6), increases the quality of colony merging into the top N colonies. Consequently the feature merge delay encourages further exploration of the domain [figure (3.8, b)]. This colony belonging directly influences the termination of the algorithm, and this terminates faster when more ants belong to the top N colonies [figure (3.8, d)].

The influence of this parameter is driven by the various pheromone-feature combinations which are deposited upon merging. An interesting eventuality occurs when a higher feature merge threshold is chosen. High values inhibit ants from merging their features so readily, this causing

FIGURE3.8: Results of varying the feature merging parameter are given as follows; figure (a) shows the average feature combinations carried by ants, figure (b) shows the distribution of ants in top N colonies versus other smaller colonies, figure (c) shows the repetition in traversed nodes, and figure (d) shows the progressive decline in the number of colonies present and the

termination criteria.

ants to look solely for one feature. This turns the MPACA into a singular feature search, similar to the common ACO, which is known to optimise paths quite rapidly. Thus, as per figure (3.8, c), higher merge thresholds correspond to the highest repetition of nodes traversed. The contrary of this does not occur. Lower merge values as in this analysis, where value 6 is chosen, still allow feature merging to take place, implying that the search is not driven by a singular feature in such a case, with repetition being much lower than the case for value 9. When the feature merging threshold is lowered to value 3, in this case repetition increases slightly. This limited increase occurs as the lower feature merge causes the ants to stabilise quicker the features they are after, which in turn is reinforced more often than would occur if the ants keep exchanging the features they are carrying.

3.8.6.2 Colony Merging Threshold Parameter

FIGURE3.9: Results of varying the colony merging parameter are given as follows; figure (a) shows the average feature combinations carried by ants, figure (b) shows the distribution of ants in top N colonies versus other smaller colonies, figure (c) shows the repetition in traversed nodes, and figure (d) shows the progressive decline in the number of colonies present and the

termination criteria.

The colony merging threshold is the founding mechanism for cluster formation. Colony mem- bership is an isolated parameter as it does not influence any other parameter. It is only mean- ingful in the context of the colony formation. Thus, as figures (3.9, a) and (3.9, c) demonstrate, there is limited statistical significance difference (excluding that attributable to sampling and in- herent randomness within the model) when varying colony membership levels vis-a-vis feature merging or ant movement. Hence, whilst feature merging directly influences colony formation, the opposite is not so. This is due to the fact that a colony can have ants with multiple feature combinations, and search specialisation occurs at the ant level, not at the colony level. On the other hand the two benchmarks affected by this parameter change are colony membership into the top N colonies, and the termination criteria, respectively depicted in figures (3.9, b) and

(3.9, d). Low colony membership means more ants are engulfed into the top N colonies, and algorithm termination on the other hand is heavily dependent on the colony merging thresh- old. A low threshold implies that excessive merges occur, which can inhibit the algorithm from reaching correct termination.

3.8.6.3 Visibility on Edge Parameter

This parameter gives the ants the ability to determine the internal content of other ants. The more extended this visibility is, the greater is the number of ant encounters counted.

FIGURE 3.10: Results of varying the visibility range parameter are given as follows; figure (a) shows the average feature combinations carried by ants, figure (b) shows the distribution of ants in top N colonies versus other smaller colonies, figure (c) shows the repetition in traversed nodes, and figure (d) shows the progressive decline in the number of colonies present and the

termination criteria.

In this experiment three values are considered; (i) single visibility where ants can only see one step away, (ii) partial visibility where ants can see steps belonging to approximately half an edge length away, and finally (iii) complete visibility where ants can see all ants present on the edge.

Visibility elongation accelerates feature and colony merging, as the more ants are detected, the more frequently these operators take place [figure (3.10, a)].

Figure (3.10, b) shows that partial visibility takes longer to place ants within the top N colonies than full visibility, whilst single step visibility is considerably slower than both. Furthermore, figure (3.10, c) shows that both single visibility and partial visibility have similar repetitive traversals. This is likely to occur for different reasons. Single visibility operates on a single feature, much in the same way as when a high feature merging threshold is chosen, whilst partial visibility performs node traversals seeking feature combinations. On the other hand complete visibility tends to have lower repetitive traversals, which can be symptomatic of incorrect feature merges which do not create correct pheromone traversals to be followed. Thus, even if feature and colony merging is faster at the maximum value, the partial setting is operationally more coherent. A large visibility increases the ant encounters, which precipitates termination. 3.8.6.4 Time-window Parameter

This parameter has a primary impact on feature and colony merging, as the longer the time- window, the higher the rate of feature and colony merging should be, and vice-versa. This experiment demonstrates the variations of the time-window as this is increased at intervals, starting from 50, 100, 250 and 500 units. Experimentation shows that for this domain, the optimal value is around 100 time units.

Short time-windows imply a low feature merging, and respectively a low feature merge average, as per figure (3.11, a). A similar activity takes place as the lack of having a specific set of features, and the lack of historical ant encounters imply that colony formation takes longer to occur at this value [figure (3.11, b)]. As is shown in figures (3.11, a) and (3.11, b), as the time- window is gradually increased, feature merging increases, and so do the ants belonging in the top N colonies.

The disparity between ants depositing pheromone and those that are not, and even the random- ness in search is not particularly influenced by the time-window. This is because the likelihood of ants locating interesting nodes is unchanged [figure (3.9, c)]. Algorithm termination is di- rectly influenced by colony formation, hence a delay in colony formation consequently delays termination [figure (3.11, d)].

FIGURE 3.11: Results of varying the time-window parameter are given as follows; figure (a) shows the average feature combinations carried by ants, figure (b) shows the distribution of ants in top N colonies versus other smaller colonies, figure (c) shows the repetition in traversed nodes, and figure (d) shows the progressive decline in the number of colonies present and the

termination criteria.