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If we want to optimize two characteristics of a result lets say Accuracy(maximize) and RMSE(minimize) simultaneously using an evolutionary optimization technique, how will the update condition work in the optimization algorithm?

In single-objective optimization, we can just check the previous best solution with the current and update accordingly.

if (current_best > global_best)
   global_best = current_best

But when it comes to multi-objective (in this case two objectives), how can we check both the conditions simultaneously?

if (global_acc < current_acc && global_rmse > current_rmse)
   update...???

This is a bit confusing. Can we even maximize and minimize simultaneously?

StormClouds
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  • If your data were discrete or both continuous and described by some function, you could form a pareto set and then choose among the candidate optimal solutions. Unless there exists a single most accurate and least RMSE point, you won't be able to choose a single optimal solution without more criteria. – David Diaz Oct 02 '20 at 16:51
  • In other words, if you're tied into your method, you could search for pareto improvements to your current best (an improvement of at least one condition without a decline in any condition). When you find an improvement, update. Eventually you will arrive at one of possibly many pareto optimal solutions. – David Diaz Oct 02 '20 at 17:08

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