Optimization for pixel farming

Abstract

This thesis explores three optimization methods for pixel farming, a farming method that attempts to utilize the benefits of intercrop effects within a single field. By reducing a one dimensional version of the problem to finding Hamiltonian Paths, we demonstrate the NP-completeness of the general problem. Further we develop three methods for exploring the large search space. The first method relaxes the pixel farming problem to a fractional version and then uses gradient ascent to search for solutions. The second method leverages parallelism to improve on the known simulated annealing approach. The third method, through the use of a linear program, is able to determine the optimal way of swapping multiple crops at the same time. Iteratively applying the latter method in parallel resulted in an improvement over the state of the art.