THE SHAPE of a soap bubble, the amount of inventory to keep in a shop,
and the most economical way to lay out a printed circuit board are all solutions
to problems of optimisation that both nature and human engineers often face.
In each case, you can think of the optimal solution as the least or greatest
value of a mathematical function describing how some variable behaves. The
soap bubble minimises its surface area, the correct amount of inventory
minimises cost, and the best printed circuit board layout is the one that
requires the least time to assemble.
During the past couple of decades, new techniques inspired by natural
systems in physics and biology have emerged for solving problems like these.
A key element in the success of these techniques aimed at optimisation is
randomness.
Optimisation is the problem of finding the best solution to a particular
problem. This is usually achieved by creating a what is called a ‘cost’
function, a term borrowed from economics. It measures how good any particular
solution is. The problem of finding the best solution then becomes one of
finding where this cost function is minimised.
If we think of the cost function as a landscape and altitude as a measure
of cost, then the optimal location in a landscape is where the deepest valley
has its bottom. This is called the global optimum, in order to distinguish
it from local optima, which are points at the bottom of smaller valleys
where the cost function is lower than at any immediately adjacent point
(see Figure 1a). The landscape of possible solutions is called…
