Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, December 18, 2014, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Nick Spooner

Fixed-Budget Performance of the (1+1)-EA on Linear Functions

The theoretical analysis of randomised search heuristics for discrete optimization problems has typically focused on the question of expected running time, i.e. the number of steps required on average to reach an optimal solution. In their seminal paper, Jansen and Zarges introduce a different perspective: so-called fixed budget' analysis. To measure the quality of an (evolutionary) algorithm on a specific problem, Jansen and Zarges ask two related, but not identical, questions. Firstly, given an predetermined number of iterations, or budget', what is the quality of the best solution found within this budget (a priori)? Secondly, if the algorithm has spent budget $B$, then how does the quality of the best solution found improve when the algorithm is allowed to continue searching for an additional budget $\Delta B$ (a posteriori)? We present a fixed budget analysis of the (1+1) evolutionary algorithm for general linear functions, attempting to answer both a priori and a posteriori questions.

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