The regression testing is a software-based testing approach executed to verify that changes made to the softwaredo not affect the existing functionality of the product. On account of the constraints of time and cost, it isimpractical to re-execute all the test cases for software whenever a change occurs. In order to overcome sucha problem in the selection of regression test cases, a prioritization technique should be employed. On the basisof some predefined criterion, the prioritization techniques create an execution schedule for the test cases, sothe higher priority test cases can be performed earlier than the lower priority test cases in order to improvethe efficiency of the software testing. Many prioritization criteria for regression test cases have been proposedin software testing literature; however, most of such techniques are code-based. Keeping in view this fact, thisresearch work has proposed a prioritization approach for regression test cases generated from software specificationswhich are based on the criterion of the Average Percentage Transition Coverage (APTC) by using arevised genetic algorithm. This criterion evaluates the rate of transitions coverage by incorporating knowledgeabout the significance of transitions between activates in the form of weights. APTC has been used as a fitnessevaluation function in a genetic algorithm to measure the effectiveness of a test cases sequence. Moreover, inorder to improve the coverage percentage, the proposed approach has revised the genetic algorithm by solvingthe problem of the optimal local solution. The experimental results show that the proposed approach demonstratesa good coverage performance with less execution time as compared to the standard genetic algorithmand some other prioritization techniques.