In this paper, design of a time modulated linear array (TMLA) which is asymmetrically switched with minimum sideband power loss is investigated. Minimization of the total sideband power loss is calculated via recently appeared extended closed form equation. A 16 element equispaced linear Chebyshev array which is placed on positive z-axis is selected as the example. Differential evolution algorithm (DEA) is used as the optimization tool where the optimization is necessary. It is illustrated by an explanatory example that harmonic losses must also be taken into account in shifted pulse case (asymmetrically positioned pulse cases) designs.