This paper considers single phase and three phase 55-level asymmetric cascaded multilevel inverters (ACMLIs), that consist of four H-bridges per phase, with dc sources E, 3E, 9E and 14E , where E is an arbitrarly chosen reference dc voltage value. An approach using a mixed integer linear programming (MILP) model is introduced to determine the switching angles of the inverter power switches that minimize the values of any undesired harmonics. The model is solved first to determine the number of harmonics to be minimized to obtain least value of the exact total harmonic distortion (%THDE) and least value of any undesired harmonic between all harmonics from the low order harmonics till the 199th harmonic relative to the main harmonic (%V LH) for an output voltage that is formed from all the 55 levels of the inverter. Then the model is solved aiming minimizing these harmonics for different output voltage amplitudes. For single phase case, output voltages amplitudes between 14E and 28E could be obtained with %V LH less than 1%, and between 20E and 28E with % V LH less than 0.5%. For three phase case, output phase voltages amplitudes between 12E and 32E could be obtained with %V LH less than 1 % and between 18E and 30E with %V LH less than 0.5%. In addition, the obtained values of %THDE and %VHmax agree with the IEEE standards 519-1992 for voltage distortion limits till 161kv for both single and three phase cases over wide voltage amplitude ranges.