Unlimited Budget Analysis of Randomised Search Heuristics

Performance analysis of all kinds of randomised search heuristics is a rapidly growing and developing field. Run time and solution quality are two popular measures of the performance of these algorithms. The focus of this paper is on the solution quality an optimisation heuristic achieves, not on the time it takes to reach this goal, setting it far apart from runtime analysis. We contribute to its further development by introducing a novel analytical framework, called unlimited budget analysis, to derive the expected fitness value after arbitrary computational steps. It has its roots in the very recently introduced approximation error analysis and bears some similarity to fixed budget analysis. We present the framework, apply it to simple mutation-based algorithms, covering both, local and global search. We provide analytical results for a number of pseudo-Boolean functions for unlimited budget analysis and compare them to results derived within the fixed budget framework for the same algorithms and functions. There are also results of experiments to compare bounds obtained in the two different frameworks with the actual observed performance. The study show that unlimited budget analysis may lead to the same or more general estimation beyond fixed budget.