Friday, October 14, 2011

Long-distance convergence

The first picture tracks the achieved percentage reduction in a certain minimization objective function value (a shortest path distance) relative to it's initial value, over time.



Not monotone convergence, but still pretty good, and the relative gap finally goes close enough to zero (within a tolerance of 0.5%). Most would be happy to see this solution performance on any O.R decision problem instance in practice.

The next picture tracks the raw values corresponding to the first plot - the shortest path in miles, between the location of my ORMS job and that of my wife's (non ORMS job). The time scale is in years. This also happens to be the commute distance (logarithmic scale).



Average convergence rate = 581 miles/year
Total cost incurred = 27,500 mile-years (counting from year "-2")

Sometimes, superlinear convergence feels terribly slow, but in this era of labor restrictions, we'll chalk this down in the 'wins' column.

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