Defect prediction models help software project teams to spot defect-prone source files of software systems. Software project teams can prioritize and put up rigorous quality assurance (QA) activities on these predicted defect-prone files to minimize post-release defects so that quality software can be delivered. Cross-version defect prediction is building a prediction model from the previous version of a software project to predict defects in the current version. This is more practical than the other two ways of building models, i.e., cross-project prediction model and cross- validation prediction models, as previous version of same software project will have similar parameter distribution among files. In this paper, we formulate cross-version defect prediction problem as a multi-objective optimization problem with two objective functions: (a) maximizing recall by minimizing misclassification cost and (b) maximizing recall by minimizing cost of QA activities on defect prone files. The two multi-objective defect prediction models are compared with four traditional machine learning algorithms, namely logistic regression, naïve Bayes, decision tree and random forest. We have used 11 projects from the PROMISE repository consisting of a total of 41 different versions of these projects. Our findings show that multi-objective logistic regression is more cost-effective than single-objective algorithms. © 2016, Springer-Verlag Berlin Heidelberg.