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M. Li, S. Yang, and X. Liu. Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Transactions on Evolutionary Computation, 18(3): 348-365, 2014. [PDF] [C code] [C code for WFG] [C++ code in OTL]
M. Li, S. Yang, and X. Liu. Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Transactions on Evolutionary Computation, 18(3): 348-365, 2014. [PDF] [C code] [C code for WFG] [C++ code in OTL]
Brief:
Brief:
A very little modification of density estimation in a Pareto-based algorithm (e.g. SPEA2) to make it suitable for many-objective optimisation. This modification needs tiny effort (often one line code change in the Pareto-based algorithm) but makes big difference to the algorithm's performance to many-objective problems.
A very little modification of density estimation in a Pareto-based algorithm (e.g. SPEA2) to make it suitable for many-objective optimisation. This modification needs tiny effort (often one line code change in the Pareto-based algorithm) but makes big difference to the algorithm's performance to many-objective problems.
Results:
Results:
Comparison of solution sets (shown in parallel coordinates) obtained by the original SPEA2 algorithm (left) and the SPEA2 working with SDE (right) on a tricky problem (10-objective DTLZ3) whose true Pareto front on each objective is in the range of [0,1].
Comparison of solution sets (in the decision space) obtained by SPEA2+SDE and other 14 multi-/many-objective algorithms on the 10-objective ML-DMP problem, where the Pareto optimal solutions in the 2D decision space have similar distribution to their images in the objective space, and the corresponding GD and IGD evaluation results.
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