Algorithm configuration landscapes: More benign than expected?

Abstract

Automated algorithm configuration procedures make use of powerful meta-heuristics to determine parameter settings that often substantially improve the performance of highly heuristic, state-of-the-art algorithms for prominent $$\mathcal {NP}$$ -hard problems, such as the TSP, SAT and mixed integer programming (MIP). These meta-heuristics were originally designed for combinatorial optimization problems with vast and challenging search landscapes. Their use in automated algorithm configuration implies that algorithm configuration landscapes are assumed to be similarly complex; however, to the best of our knowledge no work has been done to support or reject this hypothesis. We address this gap by investigating the response of varying individual numerical parameters while fixing the remaining parameters at optimized values. We present evidence that most parameters exhibit uni-modal and often even convex responses, indicating that algorithm configuration landscapes are likely much more benign than previously believed.