23 research outputs found
On the choice of the parameter control mechanism in the (1+(位, 位)) genetic algorithm
The self-adjusting (1 + (位, 位)) GA is the best known genetic algorithm for problems with a good fitness-distance correlation as in OneMax. It uses a parameter control mechanism for the parameter 位 that governs the mutation strength and the number of offspring. However, on multimodal problems, the parameter control mechanism tends to increase 位 uncontrollably.
We study this problem and possible solutions to it using rigorous runtime analysis for the standard Jumpk benchmark problem class. The original algorithm behaves like a (1+n) EA whenever the maximum value 位 = n is reached. This is ineffective for problems where large jumps are required. Capping 位 at smaller values is beneficial for such problems. Finally, resetting 位 to 1 allows the parameter to cycle through the parameter space. We show that this strategy is effective for all Jumpk problems: the (1 + (位, 位)) GA performs as well as the (1 + 1) EA with the optimal mutation rate and fast evolutionary algorithms, apart from a small polynomial overhead.
Along the way, we present new general methods for bounding the runtime of the (1 + (位, 位)) GA that allows to translate existing runtime bounds from the (1 + 1) EA to the self-adjusting (1 + (位, 位)) GA. Our methods are easy to use and give upper bounds for novel classes of functions
Complexity Theory for Discrete Black-Box Optimization Heuristics
A predominant topic in the theory of evolutionary algorithms and, more
generally, theory of randomized black-box optimization techniques is running
time analysis. Running time analysis aims at understanding the performance of a
given heuristic on a given problem by bounding the number of function
evaluations that are needed by the heuristic to identify a solution of a
desired quality. As in general algorithms theory, this running time perspective
is most useful when it is complemented by a meaningful complexity theory that
studies the limits of algorithmic solutions.
In the context of discrete black-box optimization, several black-box
complexity models have been developed to analyze the best possible performance
that a black-box optimization algorithm can achieve on a given problem. The
models differ in the classes of algorithms to which these lower bounds apply.
This way, black-box complexity contributes to a better understanding of how
certain algorithmic choices (such as the amount of memory used by a heuristic,
its selective pressure, or properties of the strategies that it uses to create
new solution candidates) influences performance.
In this chapter we review the different black-box complexity models that have
been proposed in the literature, survey the bounds that have been obtained for
these models, and discuss how the interplay of running time analysis and
black-box complexity can inspire new algorithmic solutions to well-researched
problems in evolutionary computation. We also discuss in this chapter several
interesting open questions for future work.Comment: This survey article is to appear (in a slightly modified form) in the
book "Theory of Randomized Search Heuristics in Discrete Search Spaces",
which will be published by Springer in 2018. The book is edited by Benjamin
Doerr and Frank Neumann. Missing numbers of pointers to other chapters of
this book will be added as soon as possibl