Opened 22 months ago
Last modified 22 months ago
#3055 accepted enhancement
S-Metric Selection Evolutionary Multi-objective Optimization Algorithm (SMS-EMOA)
Reported by: | kyang | Owned by: | kyang |
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Priority: | medium | Milestone: | |
Component: | Algorithms | Version: | branch |
Keywords: | MOO, Hypervolume Contribution, indicator-based | Cc: |
Description
- This algorithm is SMS-EMOA implementation on HL. The main structure and interfaces with HL are copied from MOEA/D on HL, which was written by Dr. Bogdan Burlacu. The S-metric (hypervolume contribution, HVC) selection operator was adapted from Kaifeng's MATLAB toolbox in SMS-EMOA. The computational complexity of HVC is AT LEAST $O (n^{2 \log n)$ in 2-D and 3-D cases. HVC should definitely be reduced to $\Theta (n \times \log n)$.
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- This algorithm assumes:
- 1. minimization problems. For maximization problems, it is better to add "-" symbol.
- This algorithm works on:
- 1. continuous, discrete, mixed-integer MOO problems. For different types of problems, the operators should be adjusted accordingly.
- 2. both multi-objective and many-objective problems. For many-objective problems, the bottleneck is the computational complexity of HV.
- This algorithm is the basic implementation of SMS-EMOA, proposed by Michael Emmerich et. al. Some potential improvements can be:
- 1. Dynamic reference point strategy
- 2. Normalized fitness value strategy ---- desirability function. See, Yali, Longmei, Kaifeng, Michael Emmerich CEC paper.
- 3. HVC calculation should definitely be improved, at least in the 2D and 3D cases.
- 4. multiple point strategy when $\lambda>1$
- 5. multiple reference points strategy, in ICNC 2016, Zhiwei Yang et. al.
- 6. HVC approximation by R2 for MANY OBJECTIVE cases, by Ishibushi 2019, IEEE TEC
- 7. Maybe: See maps
- Global parameters:
- 1. population
- Many thanks for Bogdan Burlacu and Johannes Karder, especially Bogdan for his explanation, help, and supports.
Change History (4)
comment:1 Changed 22 months ago by kyang
- Status changed from new to accepted
comment:2 Changed 22 months ago by kyang
comment:3 Changed 22 months ago by kyang
r17425: Added the first version of SMS-EMOA
comment:4 Changed 22 months ago by kyang
r17440: Fixed the bug of "no reference point" on non-scientific benchmarks (e.g., MOPs of symbolic regression).
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r17424: created branch for SMS-EMOA