Date: 07/08/05 (Algorithms)    Keywords: no keywords

I am having difficulty on how to do analysis to show the relationship between 2 algorithms, basically I am not sure what type of statistic, data to produce.  The problem is on the "movement" of agent-like system (Ant System, a bit diff from ACOhere ),  one algorithm is 'dependent'  movement and another is 'independent' movement. 

Dependent movement is at stage s,  agent(i) decision to move to a new place is based on the information obtained from agent(0:i-1)  .  (i.e when ants move, they lay pheremone and such).  Independent movement is agent(i) decision to move to a new place is independent from other agents, the decision is based on information on previous stage s-1. 

Imagine 2 ants at different places X , Y , try to decide if they should go to Z,  dependent movement is ant 1 makes decision first, it might move to Z, and thus ant 2 will be more likely to also choose Z since Z now has a stronger pheromone attaction.  Whereas independent movement is both ants will make the decision without regarding others's decision, so if ant 1 moves to Z that doesn't encourage ant 2 moves to Z since ant 2 is not aware of ant 1's decision. 

So clearly 2 algorithms are very different.  In my experiments, both of these algorithms give Equivalent results (i.e the solutions (on average) are equivalent). But I need to do a more detailed and formal analysis on Why 2 different behaviors yet producing same results (which is my goal actually, to show both algorithms will work).   I am not sure what kind of testing should I do, what statistic, numbers etc I want to obtain to show, also this is a heuristic kind of problem so things are generated randomly.   Any advice will be greatly appreciated.  Thanks in advance.

Source: http://www.livejournal.com/community/algorithms/59939.html