Fitness

No, it's not a New Year's Resolution that I'm talking about today. It's a set of thoughts that I'm having about how to measure the fitness of a solution to a difficult problem.

Let's imagine that we have a set of four tasks to do, and ten workers who can do them. Each worker has a skill rating at each of those four tasks, a cost to employ them to do the task, a reliability rating to see if they actually show up for the task, and maybe a few other attributes as well.

We're going to start by randomly assigning workers to tasks, and see how good those solutions are. So how do you measure the fitness of a given solution to the task at hand?

Well, we'll start by assigning positive or negative qualifiers to the different attributes of the workers:
Skill rating; reliability rating: these should clearly be maximised for any given task.
Cost: this should clearly be minimised for any given task.

Then we'll let the manager decide which of attributes is the most important, either by simply ranking them in order, or by assigning percentages to each one. (eg: they could decide that the priority should be 50% based on cost, 40% based on reliability, and 10% based on skill rating)

And now comes the hard part: normalisation! Let's say that we measure the time taken to complete the task in hours, the cost to complete the task in pounds, and the reliability of the worker as a percentage. How do we unite those completely different measurements?

Well, I've a few ideas, and they start with some kind of normalisation.

1) Normalise each value and then multiply by prioritisation:
- let's look over all of the values for a particular attribute (say skill), and then divide all of those attributes by the highest one. We'll end up with the highest skilled worker being rated with a skill of 1, and everyone else rated between 0 and 1.
- Repeat that for all of the other attributes available.
- multiply each of the attributes by the ranking factor, or the priority percentage.

2) Distance from average:
- again, we'll pick a particular attribute, and then calculate the average (mean) value of that attribute.
- Now, we'll calculate the distance from that average for every worker.
- Then, we'll normalise those distances to lie in the range -1 -- +1
- Finally, we can apply the priority factors.

Which of these would give a better set of results? Any gut feeling answers on a postcard?! In the meanwhile, I'm going to have a poke around in the literature to see if there are any recommendations there...