The Hill Climber

Hill Climbing is a simple yet very useful mathematical concept that essentially boils down to the axiom of "always go to a better place". Hill Climbers do not have the social and shared behaviour of other swarm optimisation strategies. Rather, each particle will always attempt to optimise its own position regardless of the positions of its neighbours. The use of the swarm increases the chances of the particles finding an optimal solution. However, one important caveat exists: a hill climber particle will never go back to a position with a worse outcome. This important but simple rule means that they have a tendency to get "stuck" on positions that are locally, within the particle's search history, the best but may not be the actual best position available to them. Hill Climbing however remains a useful and important tool in optimisations for finding local optima.

Mutations and the Greedy Search

The hill climber does not have the cognitive and social components required by PSO to inform its new search directions. Rather, it makes use of a greedy search algorithm that relies on some degree of randomness or stochastic manipulation. A mutation rate for the position variables is combined in a formula that permuates the values within a range of some randomness. Regardless of this approach, Hill Climbing has proven very useful in solving optimisation problems that are convex in nature.