Using genetic and evolutionary algorithms to solve boundary control problems in soil-water-plant interaction

In this thesis we investigate how modern artificial intelligent techniques, namely the genetic algorithm /evolutionary algorithm can be applied to find irrigation strategies for a cropped soil. We begin by providing an introductory chapter detailing the work that is to be carried out and the results obtained from research. In Chapter 2 we introduce some basic concepts of soil physics in order to give an understanding of the nature of soil composition and the movement of water within a cropped soil. We then summarise background research undertaken by Terry Janz in his Masters Thesis which shows how an irrigation schedule can be obtained using classical methods to solve the Richards' flow equation with realistic parameters and field data. Genetic and evolutionary algorithms are introduced in Chapter 3; their algorithmic structure is defined and contrasted with classic search techniques. In Chapter 4 we apply a genetic algorithm to the problem posed in Chapter 2 to obtain a schedule of irrigation defined as a sequence of irrigation on and irrigation off switches, to control moisture content at specific levels at certain depths within the soil, so that "nutrient uptake" by the root can be maximised. The problem posed is the classical optimal control problem in which the tracking of a desired set of final states is to be achieved. Finally in Chapter 5, we undertake an initial research study into how an evolutionary algorithm can be applied to solve the tracking problem associated with boundary control of a parabolic distributed process. The problem is first transformed into a classical optimal control problem with ordinary differential equations as differential constraints, by using the method of semi-discretisation, or method of lines. Our results are compared with classical techniques commonly used to solve this type of problem, including the finite element method which uses full discretisation of both the state and time variables. It is shown that it is feasible to apply evolutionary learning to problems of boundary control which arise in determining realistic irrigation strategies.