Opened 5 months ago

Last modified 5 months ago

#3055 accepted enhancement

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

Reported by: kyang Owned by: kyang
Priority: medium Milestone:
Component: Algorithms Version: branch
Keywords: MOO, Hypervolume Contribution, indicator-based Cc:


  • 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.

Change History (4)

comment:1 Changed 5 months ago by kyang

  • Status changed from new to accepted

comment:2 Changed 5 months ago by kyang

r17424: created branch for SMS-EMOA

comment:3 Changed 5 months ago by kyang

r17425: Added the first version of SMS-EMOA

comment:4 Changed 5 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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