Results

Graphs of convergence are shown in the Appendix (figures 6 to 12). It can be seen that in general the mutation search method works as well or better, that is faster, than regular mutation. In certain circumstances, for example the first three fitness functions, convergence is achieved in a single iteration, indicating that for this kind of (essentially gradient descent) problem search mutation is extremely fast. In other unimodal problems it is generally much faster than regular mutation. It should be noted that because we used regular mutation every few iterations as well, also we benefited from a form of annealing.

• Sphere model, Schwefel's Problem No.1, Schwefel's Problem No.2. These were all optimised in a single population iteration using the the new mutation operator. There is no graph shown in the appendix.
• Sine Product Function. One optimum for this function was found after a single iteration in both the case of maximization and minimization. A graph of convergence is shown in figure 6 in the appendix. This graph is of interest because the relative time for convergence using the regular operator is much slower and it does not reach the optimum, only approaching it in 5000 iterations.
• Product Function. Given the same set of starting chromosomes, the new operator performs as expected and convergences relatively quickly. Shown in figure 7.
• Himmelblau Function. Another instance of single iteration convergence with the new operator. It should be mentioned that finding the global minimum in this experiment is luck, rather than a product of the methodology. Shown in figure 8.
• Six Hump Camel Function, . This result shows that this fitness function is particularly complex and varies very rapidly inside its domain limits. This kind of function is not well suited to the operator but it performed as well as the regular one. Both converged very quickly. Shown in figure 9.
• Generalized Rosenbrock's Function, . Both operators performed similarly but the space is very complex with rapid gradient changes. Various sizes of search window would probably have brought even greater benefits in this example. Shown in figure 10.
• Quartic Function with Noise, . Fast convergence was achieved with both operators. Notice that the noise causes even the same chromosome to have different evaluations with each iteration. Shown in figure 11.
• Generalized Rastrigin's Function, . The error converged relatively quickly and to a lower value than the canonical EA. Shown in figure 12.