While traditional Pareto-based evolutionary multi-objective optimization (E-MO) algorithms have shown an excellent balance between convergence and diversity on a wide range of practical problems with two or three objectives in real applications, the decision maker (DM) is interested in a unique set of solutions rather than the the whole population on Pareto optimal front (POF).In addition, Pareto-based EMO algorithms have some shortcomings in dealing with many-objective problems because of insuffcient selection pressure toward trade-off solutions. Due to the above, it is crucial to incorporate DM preference information into EMO and seek a representative subset of Pareto optimal solutions with an increase in the number of objectives. This paper proposes a new dominance relationship, called Ra-dominance, which can improve diversity among the Pareto-equivalent solutions increase the selection presure in evolutionary process. It has the ability to guide the population toward areas more responsive to the needs of the DM according to a reference point and prefer-$ Fully documented templates are available in the elsarticle package on CTAN.

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Feature selection, which aims to improve the classification accuracy and reduce the size of the selected feature subset, is an important but challenging optimization problem in data mining. Particle swarm optimization (PSO) has shown promising performance in tackling feature selection problems, but still faces challenges in dealing with large-scale feature selection in big data environment because of the large search space. Hence, this paper proposes a bi-directional feature fixation (BDFF) framework for PSO and provides a novel idea to reduce the search space in large-scale feature selection. BDFF uses two opposite search directions to guide particles to adequately search for feature subsets with different sizes. Based on the two different search directions, BDFF can fix the selection states of some features and then focus on the others when updating particles, thus narrowing the large search space. Besides, a self-adaptive strategy is designed to help the swarm concentrate on a more promising direction for search in different stages of evolution and achieve a balance between exploration and exploitation. Experimental results on 12 widely-used public datasets show that BDFF can improve the performance of PSO on large-scale feature selection and obtain smaller feature subsets with higher classification accuracy.

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