In Search of Global Optimum

Many problems in science could be formulated as the search of global minimum (or maximum, but we only need to talk of one as the two are easily reversible). One such example is the protein folding problem where the goal is to find a 3D protein structure (given a 1D amino acid sequence) that has the lowest free energy. One can imagine such problem as trying to find the deepest valley in some rugged landscape, one spot at a time. Of course, the solution can be found when the size of the landscape is small, but becomes unsolvable when the landscape is vast. When it becomes unpractical to search everywhere for the optimum solution, heuristics that lead to ‘good enough’ solutions are often applied. However, one risks finding a solution that is only optimum locally instead of globally. Various methods that try to prevent the search from trapping in local minima have been devised, making it an active research area. I came to speculate recently, if our life were also like a search in such landscape, with the globally optimal solution as the “niche” best suited for a person. How many of us have actually hit that sweet spot, and how many of us are trapped in local minima? And how, if we may draw parallel from the search problem, can we utilize some heuristics to increase the chance at finding the global optimum solution?