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Algorithms to solve hard combinatorial problems often exhibit complementary performance, i.e. where one algorithm fails, another shines. Algorithm portfolios and algorithm selection take advantage of this by running all algorithms in parallel or choosing the best one to run on a problem instance. In this paper, we show that neither of these approaches gives the best possible performance and propose the happy medium of running a subset of all algorithms in parallel. We propose a method to choose this subset automatically for each problem instance, and demonstrate empirical improvements of up to 19% in terms of runtime, 81% in terms of misclassification penalty, and 26% in terms of penalized averaged runtime on scenarios from the ASlib benchmark library. Unlike all other algorithm selection and scheduling approaches in the literature, our performance measures are based on the actual performance for algorithms running in parallel rather than assuming overhead-free parallelization based on sequential performance. Our approach is easy to apply in practice and does not require to solve hard problems to obtain a schedule, unlike other techniques in the literature, while still delivering superior performance. 

For many practical problems, there is more than one algorithm or approach to solve them. Such algorithms often have complementary performance – where one fails, another performs well, and vice versa. Per-instance algorithm selection leverages this by employing portfolios of complementary algorithms to solve sets of difficult problems, choosing the most appropriate algorithm for each problem instance. However, this requires complex models to effect this selection and introduces overhead to compute the data needed for those models. On the other hand, even basic hardware is more than capable of running several algorithms in parallel. We investigate the tradeoff between selecting a single algorithm and running multiple in parallel and incurring a slowdown because of contention for shared resources. Our results indicate that algorithm selection is worth it, especially for large portfolios.