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    <p>I think it depends on how you define 'best'. For instance, if you wanted tasks to run every m seconds "on average", there's an easy way to do it using the same sort of algorithm as the Bresenham method to draw lines (a task that's 'n seconds every m seconds' is much like scattering n vertical steps among m horizontal steps when drawing a line). Assign each task a counter and a step value (for "1 second every 3 seconds" the step would be 1/3). Then add the step to the counter every 'cycle' through. When a counter goes above zero that task should run (and subtract 1 from the counter). If you have several counters above zero, choose the largest one. That may give you a solution that is "good enough" for the slightly more complex form as well.</p> <p>The "1/4" and "1/3" example though sounds like you have a requirement to run the tasks "exactly" m seconds apart. Starting from a list and adding a new task to maximize the count is not a difficult search problem - but I do not think this is what you need. The A(1/4) B(1/4) C(1/2) example would give A B x x A B x x after adding A then B. Then C could not be added,</p> <p>I think there are obvious candidates for fitness functions - a table of n,m,start can have a fitness function which is the portion of the time where no more than one task is scheduled. GA/annealing would have a good chance of finding a steady state solution if one exists. But in cases like (1/4), (1/3) wwhere there appears to be no steady state solution, defining 'best' should also define your fitness function.</p>
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