Defining a many-objective problem?

[Sam]

Dear all,

I have an optimization problem. Given x number of network devices. I need to group them into subgroups depending on the fitness of the group. I used NSGA-III and tried to define the problem as a 3 objective optimization, maximise the performance of group1, group2 and group3. This showed, performance of subgroups were not great, it would be better to divide the devices into more groups. I am now testing a 4-objective optimization using NSGA-III. However, I do not think this is a good way to solve the problem as I might need more than 4 subgroups. Is a there a better way to define and solve this problem.I would appreciate hearing your thoughts.

Thanks,

Sam

[Derek Tishler]

Hard to say without knowing more about the individual or how its evaluated. A figure or logs may show a big problem in convergence or other issues in the evo process.

Instead of selection, could the problem be an underlying issue in the fitness calc or the application of operators? This can make it hard to explore the solution space as a variety of individuals may not be producing a variety of meaningful fitness. Perhaps an individual can change via mutation but perhaps its fitness does not actually differ for example. Perhaps some individuals fitness is wrong for some cases and bad individuals are promoted despite the selection method.

NSGA-III will work up for 4+ subgroups and much higher dimensional spaces:
https://deap.readthedocs.io/en/master/examples/nsga3.html#higher-dimensional-objective-space

Depending on how your evo is progressing you may not necessarily get the desired difference in performance from just varying selection methods and breaking the fitness up from an aggregated value of 1 fitness dimension vs more. Here I tested that by using a base + 14 penalties as an example of similar results for an easy problem: