I want to compare two multi-objective algorithms to optimize 2 objectives simultaneously. I used Hypervolume, Spread and Objective values for the analysis. However, one of them is better in terms of Hypervolume and the other one is better in Spread and tends to obtain lower objective values. Is this possible? How can I decide which one is better if they perform better in different metrics? Shouldn't Hypervolume already be related to the spread? Or not always better hypervolume means better spread?
We have pointed out that when evaluating an algorithm for noisy multi-objective optimisation, one should take into account the utility loss for a DM who may pick an inferior solution because the algorithm didn’t accurately predict the quality of the identified solutions. Based on this observa tion, we proposed modifications of the well-know R2 and IGD IGD+ metrics and demonstrated with an example that they have the desired property. As future work, it may be worthwhile to also develop an adaptation of the popular hypervolume metric to the noisy case.
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