A gradient-based stochastic search approach for optimal harvesting strategy in shrimp culture

This paper considers an optimal harvesting strategy problem arising in shrimp culture. The problem is formulated as an optimal control problem of nonlinear impulsive system. Since the impulsive switching constraints is very complex, the impulsive switching instants are unknown, and the objective function is not continuously differentiable, it is difficult to solve this problem by standard optimization methods. To overcome the difficulty, by introducing a novel binary variable for each sale price of shrimp, relaxing the binary variable, and imposing a penalty function on the relaxation term, the nonlinear impulsive system optimal control problem is transformed into a parameter optimization problem, which can be solved efficiently using any gradient-based optimization technique. Then, a gradient-based stochastic search approach is proposed for solving this problem. Finally, a harvesting strategy problem is presented to illustrate the efficiency of the approach proposed.