Combining Parallel Algorithms Solving the Same Application: What is the Best Approach?

Given a hard computational problem and a pool of heuristics solving it, it is usual to have a subset of problem instances on which no heuristic outperforms all the others when measuring their runtimes on instances. This phenomenon motivated several studies whose goal was to design frameworks, that can automatically synthesize a set of heuristics solving the same problem for generating a superior one. The success of these investigations however introduced another combinatorial problem; indeed, given a basis of parallel heuristics, there are nowadays several frameworks that can be used for a synthesis: how to choose among them? This paper proposes a solution to this question considering three frameworks for heuristics synthesis, based on algorithm portfolio scheduling in parallel and homogeneous context. For choosing among the frameworks, we comparatively analyze two aspects: the runtime required for the heuristics synthesis within each framework and the performance that can be expected from the produced heuristics. We show that it is hard to make a clear distinction between the frameworks with respect to the runtime synthesis, since the key computational problem to solve here is on all frameworks, NP-complete. On the performance criterion, we show theoretically that from a knowledge of the parallel speedup distributions of the input heuristics, we can determine the framework that will lead to the best performance. The simulations on a SAT database confirm the theoretical results and give also insights into other parallel speed-up distributions that we did not analyze. Based on these results, we propose a preliminary conclusion on how to choose among the considered frameworks.