This paper presents an adaptive near-optimal scheduler for multimedia traffic for the 802.11e Enhanced Distributed Channel Access (EDCA) medium access control scheme. The scheduler exploits the ant colony optimization (ACO) meta heuristic to tackle the challenge of packet scheduling. ACO is a biologically inspired algorithm that is known to find near-optimal solutions for combinatorial optimization problems. Thus, we expect that ACO scheduling produces more efficient schedules than comparable deterministic scheduling approaches at the expenses of a computational overhead it introduces. We compare ACO scheduling relevant deterministic scheduling approaches, and in particular the MLLF scheduler that is specifically designed for the needs of compressed multimedia applications. The purpose of the evaluation is twofold. It allows to draw conclusions on the feasibility of ACO scheduling for multimedia traffic while it serves as a benchmark to determine to what extent deterministic schedulers fall short of a near-optimal solution.