Real-time solving of computationally hard problems using optimal algorithm portfolios

Various hard real-time systems have a desired requirement which is impossible to fulfill: to solve a computationally hard optimization problem within a short and fixed amount of time T, e.g., T = 0.5 seconds. For such a task, the exact, exponential algorithms, as well as various Polynomial-Time Approximation Schemes, are irrelevant because they can exceed T. What is left in practice is to combine various anytime algorithms in a parallel portfolio. The question is how to build such an optimal portfolio, given a budget of K computing cores. It is certainly not as simple as choosing the K best performing algorithms, because their results are possibly correlated (e.g., there is no point in choosing two good algorithm for the portfolio if they win on a similar set of instances). We prove that the decision variant of this problem is NP-complete, and furthermore that the optimization problem is approximable. On the practical side, our main contribution is a solution of the optimization problem of choosing K algorithms out of n, for a machine with K computing cores, and the related problem of detecting the minimum number of required cores to achieve an optimal portfolio, with respect to a given training set of instances. As a benchmark, we took instances of a hard optimization problem that is prevalent in the real-time industry, in which the challenge is to decide on the best action within time T. We include the results of numerous experiments that compare the various methods. Hence, a side effect of our tests is that it gives the first systematic empirical evaluation of the relative success of various known stochastic-search algorithms in coping with a hard combinatorial optimization problems under a very short and fixed timeout.