Related papers: Optimal Parameter Choices via Precise Black-Box An…
We propose a new black-box complexity model for search algorithms evaluating $\lambda$ search points in parallel. The parallel unary unbiased black-box complexity gives lower bounds on the number of function evaluations every parallel unary…
Black-box complexity studies lower bounds for the efficiency of general-purpose black-box optimization algorithms such as evolutionary algorithms and other search heuristics. Different models exist, each one being designed to analyze a…
Randomized search heuristics such as evolutionary algorithms, simulated annealing, and ant colony optimization are a broadly used class of general-purpose algorithms. Analyzing them via classical methods of theoretical computer science is a…
One important goal of black-box complexity theory is the development of complexity models allowing to derive meaningful lower bounds for whole classes of randomized search heuristics. Complementing classical runtime analysis, black-box…
Despite significant empirical and theoretically supported evidence that non-static parameter choices can be strongly beneficial in evolutionary computation, the question how to best adjust parameter values plays only a marginal role in…
It may seem very intuitive that for the maximization of the OneMax problem $\OM(x):=\sum_{i=1}^n{x_i}$ the best that an elitist unary unbiased search algorithm can do is to store a best so far solution, and to modify it with the operator…
We propose and analyze a self-adaptive version of the $(1,\lambda)$ evolutionary algorithm in which the current mutation rate is part of the individual and thus also subject to mutation. A rigorous runtime analysis on the OneMax benchmark…
In their GECCO'12 paper, Doerr and Doerr proved that the $k$-ary unbiased black-box complexity of OneMax on $n$ bits is $O(n/k)$ for $2\le k\le O(\log n)$. We propose an alternative strategy for achieving this unbiased black-box complexity…
We analyze the unbiased black-box complexity of jump functions with small, medium, and large sizes of the fitness plateau surrounding the optimal solution. Among other results, we show that when the jump size is $(1/2 - \varepsilon)n$, that…
A new class of test functions for black box optimization is introduced. Affine OneMax (AOM) functions are defined as compositions of OneMax and invertible affine maps on bit vectors. The black box complexity of the class is upper bounded by…
Choosing a suitable algorithm from the myriads of different search heuristics is difficult when faced with a novel optimization problem. In this work, we argue that the purely academic question of what could be the best possible algorithm…
We show that for all $1<k \leq \log n$ the $k$-ary unbiased black-box complexity of the $n$-dimensional $\onemax$ function class is $O(n/k)$. This indicates that the power of higher arity operators is much stronger than what the previous…
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…
The selection of the most appropriate algorithm to solve a given problem instance, known as algorithm selection, is driven by the potential to capitalize on the complementary performance of different algorithms across sets of problem…
The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible…
Meta-heuristics are powerful tools for solving optimization problems whose structural properties are unknown or cannot be exploited algorithmically. We propose such a meta-heuristic for a large class of optimization problems over discrete…
In a seminal paper in 2013, Witt showed that the (1+1) Evolutionary Algorithm with standard bit mutation needs time $(1+o(1))n \ln n/p_1$ to find the optimum of any linear function, as long as the probability $p_1$ to flip exactly one bit…
Feature-based algorithm selection aims to automatically find the best one from a portfolio of optimization algorithms on an unseen problem based on its landscape features. Feature-based algorithm selection has recently received attention in…
We show that the unrestricted black-box complexity of the $n$-dimensional XOR- and permutation-invariant LeadingOnes function class is $O(n \log (n) / \log \log n)$. This shows that the recent natural looking $O(n\log n)$ bound is not…
We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is…