TY - GEN
T1 - Make Evolutionary Multiobjective Algorithms Scale Better with Advanced Data Structures
T2 - Van Emde Boas Tree for Non-dominated Sorting
AU - Buzdalov, Maxim
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019/2/4
Y1 - 2019/2/4
N2 - We improve the worst-case time complexity of non-dominated sorting, an operation frequently used in evolutionary multiobjective algorithms, to O(n·(log n)k-2 log log n), where n is the number of solutions, k is the number of objectives, and the random-access memory computation model is assumed. This improvement was possible thanks to the van Emde Boas tree, an “advanced” data structure which stores a set of non-negative integers less than n and supports many queries in O(log log n). This is not only a theoretical improvement, as we also provide an efficient implementation of the van Emde Boas tree, which resulted in a competitive algorithm that scales better than other algorithms when n grows, at least for small numbers of objectives greater than two.
AB - We improve the worst-case time complexity of non-dominated sorting, an operation frequently used in evolutionary multiobjective algorithms, to O(n·(log n)k-2 log log n), where n is the number of solutions, k is the number of objectives, and the random-access memory computation model is assumed. This improvement was possible thanks to the van Emde Boas tree, an “advanced” data structure which stores a set of non-negative integers less than n and supports many queries in O(log log n). This is not only a theoretical improvement, as we also provide an efficient implementation of the van Emde Boas tree, which resulted in a competitive algorithm that scales better than other algorithms when n grows, at least for small numbers of objectives greater than two.
KW - Large-scale optimization
KW - Non-dominated sorting
KW - vEB tree
UR - https://www.scopus.com/pages/publications/85063035224
U2 - 10.1007/978-3-030-12598-1_6
DO - 10.1007/978-3-030-12598-1_6
M3 - Conference Proceeding (ISBN)
SN - 9783030125974
T3 - Lecture Notes in Computer Science
SP - 66
EP - 77
BT - Evolutionary Multi-Criterion Optimization - 10th International Conference, EMO 2019, Proceedings
A2 - Klamroth, Kathrin
A2 - Reed, Patrick
A2 - Deb, Kalyanmoy
A2 - Goodman, Erik
A2 - Coello Coello, Carlos A.
A2 - Miettinen, Kaisa
A2 - Mostaghim, Sanaz
PB - Springer Nature
ER -