Changes in environment is common in daily activities and usually introduce new problems. To be adaptive to these changes, new solutions to the problems are to be found every time change occur. Our previous publication showed that centroid of non-dominated solutions associated with Multi-Objective Evolutionary Algorithm (MOEA) from previous changes enhances the search quality of solutions for the current change. However, the number of tasks in the test environment employed was fixed. In this two-part paper, we address the dynamic adaptation with time-varying task number. To cope with this variability, new components of the solution, corresponding to the new tasks, are inserted appropriately to all solutions of the previous changes. Then centroid of these modified solutions is recomputed. Further, to avoid confusion in solution presentation, the insertion of new tasks obliged the use of task ID number greater than the largest of the previous IDs. The first part of this paper will show that the resulting task numbering system will alter the centroid significantly which will degrade MOEA's search quality. To circumvent, task IDs are mapped to new values in order to minimize difference in IDs between adjacent solution components; an approach which significantly upgraded the search performance despite changes in task number as supported by the obtained results.