S-Metric Selection Evolutionary Multi-objective Optimization Algorithm (SMS-EMOA)

[kyang]

• 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 $\Theta (n \times \log n)$.}
  • 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.

[kyang]

r17424: created branch for SMS-EMOA

[kyang]

r17425: Added the first version of SMS-EMOA

[kyang]

r17440: Fixed the bug of "no reference point" on non-scientific benchmarks (e.g., MOPs of symbolic regression).