We propose a new automatic method for generating LODs of a given polygonal model that is based on edge collapse simplification operation and exploits a variant of multiple choice optimization (MCO) framework [20]. In an edge collapse algorithm, the way how to measure the geometric deviation caused by an edge collapse transformation plays a key role. We introduce a new measure of local geometric deviation and a memory efficient method for its global evaluation; these local and global evaluation techniques are simple to implement, involve short execution times, and preserve geometric features and discontinuities automatically. Results and numerical comparisons show that our algorithm generates simplified models at different LODs of good visual fidelity, and consumes less memory and performs better in automatically preserving visually important features than other methods especially QSlim [6].