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what most people see when they look at a problem is only one face of an optimization landscape. that landscape can be divided into two general areas: one is the local optima, in which the good solution is achieved through a number of small increments that always narrow the gap to the goal. the other is the global optima, in which the good solution is achieved through a single big jump that always pushes the gap to the goal. in both cases, a good algorithm evaluates the different approaches and then chooses the best one. interestingly, the problem is not so much finding the optimal solution but finding the most efficient way to get there.


the computer can do this by constructing a landscape, but the search itself is a process of living in that landscape, using energy to climb different hills, being rewarded when you find a high point, and being punished when you fall into a deep valley. the landscape takes the problem into a different conceptual realm, where good is defined as a path up and down the mountain, efficient is defined as a path with low energy, and optimal is defined as the lowest possible energy.


this goal is nothing new. the ancient greeks used this approach and discovered that they were seeking the path of least resistance. the romans used it to design roads; the automobile uses it when it navigates traffic jams; and ants use it when finding a food source. in all of these cases, a self-reinforcing, collaborative, and innate process is always searching for the lowest-energy path.


the search engine that crawls through these landscapes looks for a path with the lowest possible energy. it uses both memory and random noise to move forward, but the search is always unbiased, which allows it to converge to the lowest energy state, not just the one that looks like the best solution. 3d9ccd7d82






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