The requirements of multi-resolution models of feature-based solids, which represent an object at many levels of feature detail, are increasing for engineering purposes, such as analysis, network-based collaborative design, virtual prototyping and manufacturing. To provide multi-resolution models for various applications, it is essential to generate adequate solid models at varying levels of detail (LOD) after feature rearrangement, based on the LOD criteria. However, the non-commutative property of the union and subtraction Boolean operations is a severe obstacle to arbitrary feature rearrangement. To solve this problem we propose a new approach based on the non-manifold topological representation and the merge-and-select algorithm for non-manifold Boolean operations. In this approach, the merge-and-select algorithm is modified to satisfy the commutative law between union and subtraction operations by considering the history of the Boolean operations. Because this algorithm guarantees the same resulting shape as the original and reasonable shapes at the intermediate LODs for an arbitrary rearrangement of its features, various LOD criteria can be applied for multiresolution modeling in different applications.