For the line-of-sight communications problem, the evaluation of the objective function
is a time consuming process. For example, if n communicator repeater robots are to be
positioned, there are 2n design variables, i.e. the x and y coordinates for each of the
repeater vehicles. Evaluating the objective function for each possible set of robot
positions requires calculating the total shadow area for this particular configuration,
which is a lengthy process. Since for this application the partial derivatives of the
objective function with respect to the design variables cannot be determined analytically,
many optimization approaches such as the steepest descent method must be ruled out.
For practical purposes, a random search algorithm must be implemented such as a
random search direction method, the Monte Carlo search method, or a genetic algorithm
approach method. This latter method was used in this problem and the next chapter will
describe the genetic algorithm approach.
This randomized approach will produce a near optimal solution. Although the optimal
solution is not necessarily obtained, the speed at which a solution is determined is greatly
reduced.