The standard, constrained and parallel multiobjective EGO algorithms
1. The unconstrained multiobjective EGO algorithm
The unconstrained multiobjective EGO algorithm using EIM (expected improvement matrix) criteria, which is significant cheaper to evaluate than the state-of-the-art multiobjective EI criteria. For detailed description about the EIM criteria, please refer to [1].
2. The constrained multiobjective EGO algorithm
The constrained multiobjective EGO algorithm using CEIM (constrained expected improvement matrix) criteria to solve expensive constrained multiobjective problems.
3. The parallel multiobjective EGO algorithm
The parallel multiobjective EGO algorithm using PEIM (Pseudo Expected Improvement Matrix) criteria, which is able to select multiple candidates in each cycle to evaluate in parallel [2].
4. The parallel constrained multiobjective EGO algorithm
The parallel constrained multiobjective EGO algorithm using PCEIM (Pseudo Constrained Expected Improvement Matrix) criteria, which is able to select multiple candidates in each cycle to evaluate in parallel [2].
5. Notes
The dace toolbox [3] is used for building the Kriging models in the implementations.
The non-dominated sorting method by Yi Cao [4] is used to identify the non-dominated fronts from all the design points.
The hypervolume indicators are calculated using the faster algorithm of [5] Nicola Beume et al. (2009).
Both the EIM and PEIM criteria are maximized by DE [6] algorithm.
Reference
- D. Zhan, Y. Cheng, J. Liu, Expected Improvement Matrix-based Infill Criteria for Expensive Multiobjective Optimization, IEEE Transactions on Evolutionary Computation, 2017, 21 (6): 956-975.
- D. Zhan, J. Qian, J. Liu, et al. Pseudo Expected Improvement Matrix Criteria for Parallel Expensive Multi-objective Optimization. In Advances in Structural and Multidisciplinary Optimization: Proceedings of the 12th World Congress of Structural and Multidisciplinary Optimization (WCSMO12), Schumacher, A.,Vietor, T.,Fiebig, S., et al., Eds. Springer International Publishing: Cham, 2018; 175-190.
- S. N. Lophaven, H. B. Nielsen, and J. Sodergaard, DACE - A MATLAB Kriging Toolbox, Technical Report IMM-TR-2002-12, Informatics and Mathematical Modelling, Technical University of Denmark, 2002. Available at: http://www2.imm.dtu.dk/projects/dace/.
- http://www.mathworks.com/matlabcentral/fileexchange/17251-pareto-front.
- N. Beume, C. M. Fonseca, M. Lopez-Ibanez, L. Paquete, J. Vahrenhold, On the Complexity of Computing the Hypervolume Indicator, IEEE Transactions on Evolutionary Computation 13(5) (2009) 1075-1082.
- K. Price, R. M. Storn, and J. A. Lampinen, Differential evolution: a practical approach to global optimization: Springer Science & Business Media, 2006. http://www.icsi.berkeley.edu/~storn/code.html