An Assignment Problem Formulation for Dominance Move Indicator
This work addresses a computational bottleneck for researchers in multiobjective optimization, though it is incremental as it extends an existing indicator to higher dimensions.
The authors tackled the combinatorial calculation limitation of the Dominance Move (DoM) indicator in multiobjective optimization by proposing an assignment formulation to compute it for three or more objectives, validating it through experiments in biobjective and three-dimensional spaces.
Dominance move (DoM) is a binary quality indicator to compare solution sets in multiobjective optimization. The indicator allows a more natural and intuitive relation when comparing solution sets. It is Pareto compliant and does not demand any parameters or reference sets. In spite of its advantages, the combinatorial calculation nature is a limitation. The original formulation presents an efficient method to calculate it in a biobjective case only. This work presents an assignment formulation to calculate DoM in problems with three objectives or more. Some initial experiments, in the biobjective space, were done to present the model correctness. Next, other experiments, using three dimensions, were also done to show how DoM could be compared with other indicators: inverted generational distance (IGD) and hypervolume (HV). Results show the assignment formulation for DoM is valid for more than three objectives. However, there are some strengths and weaknesses, which are discussed and detailed. Some notes, considerations, and future research paths conclude this work.