On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
On the Choice of the Offspring Population Size in Evolutionary Algorithms
Evolutionary Computation
Runtime Analysis of the (μ+1) EA on Simple Pseudo-Boolean Functions
Evolutionary Computation
Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization
Theory of Computing Systems
Rigorous analyses of fitness-proportional selection for optimizing linear functions
Proceedings of the 10th annual conference on Genetic and evolutionary computation
On the choice of the parent population size*
Evolutionary Computation
Black-box search by elimination of fitness functions
Proceedings of the tenth ACM SIGEVO workshop on Foundations of genetic algorithms
Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers
Black-box search by unbiased variation
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Faster black-box algorithms through higher arity operators
Proceedings of the 11th workshop proceedings on Foundations of genetic algorithms
Black-box complexities of combinatorial problems
Proceedings of the 13th annual conference on Genetic and evolutionary computation
How crossover helps in pseudo-boolean optimization
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Towards a complexity theory of randomized search heuristics: ranking-based black-box complexity
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Crossover speeds up building-block assembly
Proceedings of the 14th annual conference on Genetic and evolutionary computation
On the analysis of the simple genetic algorithm
Proceedings of the 14th annual conference on Genetic and evolutionary computation
The choice of the offspring population size in the (1,λ) EA
Proceedings of the 14th annual conference on Genetic and evolutionary computation
Black-box complexity: from complexity theory to playing mastermind
Proceedings of the 15th annual conference companion on Genetic and evolutionary computation
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The recently active research area of black-box complexity revealed that for many optimization problems the best possible black-box optimization algorithm is significantly faster than all known evolutionary approaches. While it is not to be expected that a general-purpose heuristic competes with a problem-tailored algorithm, it still makes sense to look for the reasons for this discrepancy. In this work, we exhibit one possible reason---most optimal black-box algorithms profit also from solutions that are inferior to the previous-best one, whereas evolutionary approaches guided by the "survival of the fittest" paradigm often ignore such solutions. Trying to overcome this shortcoming, we design a simple genetic algorithm that first creates λ offspring from a single parent by mutation with a mutation probability that is k times larger than the usual one. From the best of these offspring (which often is worse than the parent) and the parent itself, we generate further offspring via a uniform crossover operator that takes bits from the winner offspring with probability 1/k only. A rigorous runtime analysis proves that our new algorithm for suitable parameter choices on the OneMax test function class is asymptotically faster (in terms of the number of fitness evaluations) than what has been shown for μ +, λ EAs. This is the first time that crossover is shown to give an advantage for the OneMax class that is larger than a constant factor. Using a fitness-dependent choice of k and λ, the optimization time can be reduced further to linear in n. Our experimental analysis on several test function classes shows advantages already for small problem sizes and broad parameter ranges. Also, a simple self-adaptive choice of these parameters gives surprisingly good results.