A basin type solar still design problem is examined in the present work and the Levenberg-Marquardt Method is utilized to estimate the optimal inclination function for external reflector to obtain maximum daily distillate productivity. The design algorithm is to estimate the optimal design variables of inclination function for external reflector. Four different designs for time-dependent inclined angle of external reflector from vertical will be considered in the present study, and the resultant daily amount of distillate of the solar still for each design will be examined. Results indicate that using case 1 design the daily amount of distillate of the still would be about 27.8% greater than that with the vertical external reflector, and about 2.38 times as large as that of the still without the reflectors on a winter solstice day. The daily amount of distillate with case 2 design would be about 1.72% greater than that with case 1 design on a winter solstice day and the productivity of distillate is almost the same for case 2, case 3 and case 4 designs. The fact indicates that case 2 design should be recommended for use to produce the distillate of the solar still. (C) 2017 Elsevier Ltd. All rights reserved.