Abstract
Multi-objective optimization is a challenging task in many disciplines. Although a number of algorithms have simplified this problem by degenerating redundant objectives into low-dimensional sets, there is currently no consensus method for evaluating their performance. In this paper, we propose an evaluation method that uses a spatial similarity ratio (SSR) to determine the quality of non-redundant objective sets (NRSs). We consider the reduction of all NRSs of three functions from 5D to 2D or 3D using our SSR-based method, and compare the results to those given by an inverted generational distance-based method. The results demonstrate that our method is more accurate, as it takes information from both the non-redundant and redundant objective sets into consideration. In addition, using the proposed SSR-based approach, no prior knowledge of the true Pareto set is required. Therefore, we can conclude that our SSR-based method is feasible for the assessment of non-redundant objective sets.
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Acknowledgments
The authors wish to thank the support of the Science and Technology Project of Hunan Province (Grant No. 2014GK3027), the National Natural Science Foundation of China (Grant No. 61379062, 61372049), the Science Research Project of the Education Office of Hunan Province (Grant No. 12A135, 12C0378), the Hunan Province Natural Science Foundation (Grant No. 14JJ2072, 13JJ8006), the Hunan Provincial Innovation Foundation For Postgraduate (Grant No. CX2013A011), and the Construct Program of the Key Discipline in Hunan Province.
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Communicated by V. Loia.
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Zou, J., Zheng, J., Deng, C. et al. An evaluation of non-redundant objective sets based on the spatial similarity ratio. Soft Comput 19, 2275–2286 (2015). https://doi.org/10.1007/s00500-014-1409-3
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DOI: https://doi.org/10.1007/s00500-014-1409-3