This paper presents an optimization study of the single gantry high-speed rotary-head collect-and-place (CAP) surface mount device (SMD) machine. The rotary-head gantry-type CAP machine has the advantage of high flexibility and speed, which is widely used in the PCB assembly of smart phones, tablets, laptops, and monitors. However, the pick-and-place process in SMD machines is the most time-consuming stage that determines the cycle time of a PCB assembly lines. This single gantry optimization problem can be decomposed into nozzle assignment, feeder assignment, and component pick-and-place sequence problems. Because they are highly interrelated to each other, an integer programming model is developed to solve them simultaneously. Based on the operational characteristics of high-speed machines, an adaptive nearest neighbor tabu search (ANNTS) is proposed to integrate the solution processes of feeder assignment, pick-and-place sequence, and multiple nozzle types assignment. Compared to CPLEX results, the ANNTS finds all optimal solutions of 14 randomly generated small-sized data sets. Another 13 industrial data sets are used to test the variants of the ANNTS, which include different initial solutions and search heuristics. Compared to the large clusters of operations (LCO) heuristic (Kulak et al. Int J Prod Res 45(17): 3949–3969, 2007), the ANNTS yields a 23.32 % distance saving on average for the single nozzle type problems. The ANNTS improves the productivity by 5.79 % on average, compared to the industrial package results.