Visualised Test Problems
M. Li, C. Grosan, S. Yang, X. Liu, X. Yao, Multi-line distance minimization: A visualized many-objective test problem suite. IEEE Transactions on Evolutionary Computation, 22(1) 2018. [PDF] [supplement] [C code] [Pareto front & Pareto set]
M. Li, C. Grosan, S. Yang, X. Liu, X. Yao, Multi-line distance minimization: A visualized many-objective test problem suite. IEEE Transactions on Evolutionary Computation, 22(1) 2018. [PDF] [supplement] [C code] [Pareto front & Pareto set]
M. Li, S. Yang, and X. Liu. A test problem for visual investigation of high-dimensional multi-objective search. IEEE Congress on Evolutionary Computation (CEC), 2140-2147, 2014. (Best Student Paper Award). [PDF] [C code]
M. Li, S. Yang, and X. Liu. A test problem for visual investigation of high-dimensional multi-objective search. IEEE Congress on Evolutionary Computation (CEC), 2140-2147, 2014. (Best Student Paper Award). [PDF] [C code]
Idea:
Idea:
A many-objective problem suite (called multi-line distance minimisation problem, ML-DMP) whose Pareto optimal solutions in the 2D decision space have similar distribution (in the sense of Euclidean geometry) to their images in the higher-dimensional objective space, thus allowing a direct observation of how the solution set are distributed in the high-dimensional space.
A many-objective problem suite (called multi-line distance minimisation problem, ML-DMP) whose Pareto optimal solutions in the 2D decision space have similar distribution (in the sense of Euclidean geometry) to their images in the higher-dimensional objective space, thus allowing a direct observation of how the solution set are distributed in the high-dimensional space.
Geometric similarity on a tri-objective instance, where a set of uniformly-distributed points over the regular triangle in the 2D decision space corresponds to a set of uniformly-distributed objective vectors.
Results:
Results:
The solution sets of 15 EMO algorithms on a 4-objective ML-DMP instance (medium difficulty)
The solution sets of 15 EMO algorithms on a 4-objective ML-DMP instance (medium difficulty)
The solution sets of 15 EMO algorithms on a 10-objective ML-DMP instance (very hard)
The solution sets of 15 EMO algorithms on a 10-objective ML-DMP instance (very hard)
