This paper deals with an optimal control for the reverse osmosis (RO) desalination process of a pilot desalination plant equipped with a high pressure pump and a retentate valve and operated by renewable solar energy. The goal of the optimal control is to maximize the permeate production, with constraints on the trans-membrane pressure on the RO membrane and the total dissolved solids of permeate, by joint control of the duty of the high pressure pump and the openness of the retentate valve. The trans-membrane pressure, the total dissolved solids of permeate, and the permeate production rate are empirically modeled by two-dimensional second order equations in terms of the duty and the openness. The duty and the openness providing the maximum permeate production rate with the constraints satisfied are found by the two-dimensional genetic algorithm (GA). This joint control is different from other existing approaches which separately control the duty and the openness. Time-varying behaviors of the trans-membrane pressure, the total dissolved solids of permeate, and the production rate obtained by the proportional-integral-derivative (PID) control are shown with those by the two-dimensional GA. The two-dimensional GA achieves maximum permeate production rate while satisfying the constraints, even when the PID control fails. (C) 2016 Elsevier B.V. All rights reserved.