DARPA’s Lagrange developing optimization algorithms for uncertain, dynamic, multiscale settings like Real time neuroimaging data

Mathematical optimization is a branch of applied mathematics that in the broadest senselooks for best solution with regard to some criterion from some set of available alternatives. The advent of the digital computer and a tremendous subsequent increase in our computational prowess has increased the impact of optimization in our lives. Today, tiny details such as airline schedules all the way to leaps and strides in medicine, physics and artificial intelligence, all rely on modern advances in optimization techniques.

There a two main approaches to solving an optimization problem. The first one is to formulate the problems as mathematical models and then solve them to optimality using exact algorithms or commercial optimization packages. The second one is simply to generate good solutions of the problems using metaheuristics. Although exact methods theoretically guarantee finding an optimal solution, in practice they only work in cases where optimization problem requires effort that grows polynomially in regards to the problem size. When optimization problem is NP-hard it might require exponential effort instead. In that case even medium sized problems may become unsolvable.

Thus it may be wise to look for heuristic solution to the problem. Heuristics don’t guarantee solution’s optimality, but can give a quality approximate solution with a reasonable effort. They often show good performance for many NP-complete problems and can therefore have practical relevance. Heuristic methods are usually problem-specific as they exploit properties of the problem