Research On Evolutionary Optimization Algorithm For Multi-objective Attribute Reduction Problems

In the rough set theory,the minimum attribute reduction may not be able to derive the set of simplest decision rules.Therefore,in order to obtain the simpler set of decision rules from a decision table,we research the attribute reduction problem from the perspective of multiple objectives.First of all,we research a multi-objective attribute reduction problem by considering the least number of attributes and extractive decision rules simultaneously.And we propose its corresponding multi-objective evolutionary optimization algorithm based on the genetic algorithm.In this way,we can eliminate the redundant information in dataset from dimensions of the number of attributes and extractive decision rules respectively.After that,we introduce the concept of potential decision rules which is independent of data records in decision tables,and then solve the multi-objective attribute reduction problem which aims to get the least number of potential decision rules and attributes simultaneously.The main work in this paper is as follows:(1)We consider simplifying the set of decision rules in view of the number of extractive decision rules and attributes at the same time,and propose the multi-objective attribute reduction problem based on the optimization of' extractive decision rules.We also propose a multi-objective evolutionary optimization algorithm which has decentralized evolution strategy,elitism strategy and removing duplication strategy contrapuntally.The algorithm replaces the fitness function in the genetic algorithm by introducing the concept of Pareto and determines individual priority in a population by dominance relationship between multiple objectives.In the algorithm,decentralized evolution strategy balances the relationship between single objective and multiple objectives.Elitism strategy retains better individuals in the evolutionary process.And removing duplication strategy eliminates repeated individuals.These strategies enhance the diversity and convergence of the evolutionary population,and thus improve the efficiency of the algorithm.The experimental results show that compared with the traditional minimum attribute reduction which only considers the least number of attributes,the attribute reduction considering less number of extractive decision rules and attributes can obtain non-dominated reductions with multiple objectives,so that we can simplify the set of decision rules.On the other hand,compared with classical NSGA-?(Non-dominated Sorting Genetic Algorithm?),the algorithm proposed in this paper can gain more non-dominated multi-objective reductions,showing better ability to solve the multi-objective attribute reduction problem.(2)We propose the concept of potential decision rules which is independent of data records in decision tables and apply the above algorithm to solve the multi-objective attribute reduction problem based on the optimization of potential decision rules.Compared with extractive decision rules,the calculation of potential decision rules is related to conditional attributes of decision tables only and is more convenient with low computational complexity.The experimental results show that the multi-objective attribute reduction considering less number of potential decision rules and attributes can obtain non-dominated reductions with multiple objectives,so that we can simplify the set of decision rules effectively.And the optimization of potential decision rules can even complement the extractive decision rules to find the non-dominated reductions which are superior in the number of attributes,extractive decision rules and potential decision rules simultaneously.