The cost-minimizing inverse classification problem: a genetic algorithm approach

We consider the inverse problem in classification systems described as follows. Given a set of prototype cases representing a set of categories, a similarity function, and a new case classified in some category, find the cost minimizing changes to the attribute values such that the case is reclassified as a member of a (different) preferred category. The problem is “inverse” because the usual mapping is from a case to its unknown category. The increased application of classification systems in business suggests that this inverse problem can be of significant benefit to decision-makers as a form of sensitivity analysis. Analytic approaches to this inverse problem are difficult to formulate as the constraints are either not available or difficult to determine. To investigate this inverse problem, we develop several genetic algorithms and study their performance as problem difficulty increases. We develop a real genetic algorithm with feasibility control, a traditional binary genetic algorithm, and a steepest ascent hill-climbing algorithm. In a series of simulation experiments, we compare the performance of these algorithms to the optimal solution as the problem difficulty increases (more attributes and classes). In addition, we analyze certain algorithm effects (level of feasibility control, operator design, and fitness function) to determine the best approach. Our results indicate the viability of the real genetic algorithm and the importance of feasibility control as the problem difficulty increases.