Fréchet Similarity Metric in Multi-Objective Optimization
In one of our research directions in multi-objective optimization, we work on navigation algorithms. The challenge in such algorithms is to keep a diverse set of solutions in both objective and decision spaces. The diversity of solutions in the decision space is a challenging task, since the similarity of solutions should be measured along a list of waypoints. As shown in Figures below.
In one of our recent works, we have proposed to use the Fréchet distance measure, and we found out that we can significantly increase the diversity of solutions in the decision space. The concept of Fréchet distance measure is similar to the picture below (a man and a dog on the leash). The two data sets are considered to be the points visited by the man (set one) and the dog (set two).
More details can be found in our paper:
- Jens Weise and Sanaz Mostaghim
- Many-Objective Pathfinding based on Fréchet Similarity Metric
- Accepted at the 11th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2021), Shenzhen, China, 2021