In decision-theoretic rough set models, since decision regions (positive region or non-negative region) are defined by allowing some extent of misclassification, the monotonicity of decision regions with respect to attribute sets does not hold. The definition of attribute reduction based on the whole decision regions may change decision regions. In order not to change decision regions, the positive region and non-negative distribution preservation reduction are introduced into decision-theoretic rough set models. Moreover, due to the non-monotonicity of decision regions, attribute reduction algorithms must search all possible subsets of an attribute set. The positive region and non-negative region distribution condition information contents are presented to facilitate the design of heuristic algorithms for decision region distribution preservation reduction. In a bid to then solve the minimum attribute reduction problem, heuristic genetic algorithm is applied to decision region distribution preservation reduction. A new modify operator is constructed by using two kinds of decision region distribution condition information contents so that genetic algorithm can find decision region distribution preservation reduction. Experimental results verify the effectiveness of decision region distribution preservation reduction and show the efficiency of the genetic algorithm to solve the minimum attribute reduction problem.