Regression testing is essential to ensure that the actual software product confirms the expected requirements following modification. However, it can be costly and time-consuming. To address this issue, various approaches have been proposed for selecting test cases that provide adequate coverage of the modified software. Nonetheless, problems related to omitting and/or rerunning unnecessary test cases continue to pose challenges, particularly with regard to technical debt (TD) resulting from code coverage shortcomings and/or overtesting. In the case of testing-related shortcomings, incurring TD may result in cost and time savings in the short run, but it can lead to future maintenance and testing expenses. Most prior studies have treated test case selection as a single-objective or two-objective optimization problem. This study introduces a multi-objective decision-making approach to quantify and evaluate TD in regression testing. The proposed approach combines the analytic-hierarchy-process (AHP) method and the technique of order preference by similarity to an ideal solution (TOPSIS) to select the most ideal test cases in terms of objective values defined by the test cost, code coverage, and test risk. This approach effectively manages the software regression testing problems. The AHP method was used to eliminate subjective bias when optimizing objective weights, while the TOPSIS method was employed to evaluate and select test-case alternatives based on TD. The effectiveness of this approach was compared to that of a specific multi-objective optimization method and a standard coverage methodology. Unlike other approaches, our proposed approach always accepts solutions based on balanced decisions by considering modifications and using risk analysis and testing costs against potential technical debt. The results demonstrate that our proposed approach reduces both TD and regression testing efforts.