A novel and better fitness evaluation for rough set based minimum attribute reduction problem

The minimum attribute reduction (MAR) problem in the context of rough set theory is known to be NP-hard. One popular way of dealing with this problem is to first transform it into a fitness maximization problem over a multi-dimensional Boolean space, and to then solve this problem using population-based stochastic optimization algorithms. It is therefore important to have an appropriate fitness function. In this paper, two examples are presented to show that existing fitness functions either do not guarantee optimality equivalence between the MAR problem and the transformed fitness maximization problem, or may produce the so-called overemphasis phenomenon that affects the performance of population-based stochastic optimization algorithms. To overcome these drawbacks, we propose a new fitness function that we prove both guarantees the optimality equivalence and reduces the overemphasis phenomenon. Experimental results show that the proposed fitness function is better than existing fitness functions in terms of solution quality.