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Opened 3 years ago

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

Reported by: Owned by: kyang kyang medium Algorithms branch MOO, Hypervolume Contribution, indicator-based

### 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 $O (n2 \log n)$ 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.

### comment:1 Changed 3 years ago by kyang

• Status changed from new to accepted

### comment:2 Changed 3 years ago by kyang

r17424: created branch for SMS-EMOA

### comment:3 Changed 3 years ago by kyang

r17425: Added the first version of SMS-EMOA

### comment:4 Changed 3 years 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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