Related papers: Runtime Analysis for Multi-Objective Evolutionary …
Theory of evolutionary computation (EC) aims at providing mathematically founded statements about the performance of evolutionary algorithms (EAs). The predominant topic in this research domain is runtime analysis, which studies the time it…
In this paper, we consider a fitness-level model of a non-elitist mutation-only evolutionary algorithm (EA) with tournament selection. The model provides upper and lower bounds for the expected proportion of the individuals with fitness…
With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LeadingOnes benchmark function in the desirable regime with low genetic drift. If the population size is…
While the theoretical analysis of evolutionary algorithms (EAs) has made significant progress for pseudo-Boolean optimization problems in the last 25 years, only sporadic theoretical results exist on how EAs solve permutation-based…
The decomposition-based multi-objective evolutionary algorithm (MOEA/D) does not directly optimize a given multi-objective function $f$, but instead optimizes $N + 1$ single-objective subproblems of $f$ in a co-evolutionary manner. It…
We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple box…
A key property underlying the success of evolutionary algorithms (EAs) is their global search behavior, which allows the algorithms to `jump' from a current state to other parts of the search space, thereby avoiding to get stuck in local…
Mutation has traditionally been regarded as an important operator in evolutionary algorithms. In particular, there have been many experimental studies which showed the effectiveness of adapting mutation rates for various static optimization…
Randomized search heuristics (RSHs) are known to have a certain robustness to noise. Mathematical analyses trying to quantify rigorously how robust RSHs are to a noisy access to the objective function typically assume that each solution is…
When globally optimal solutions of complicated optimization problems cannot be located by evolutionary algorithms (EAs) in polynomial expected running time, the hitting time/running time analysis is not flexible enough to accommodate the…
We study unbiased $(1+1)$ evolutionary algorithms on linear functions with an unknown number $n$ of bits with non-zero weight. Static algorithms achieve an optimal runtime of $O(n (\ln n)^{2+\epsilon})$, however, it remained unclear whether…
Given a point in $m$-dimensional objective space, any $\varepsilon$-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and…
We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current…
For genetic algorithms using a bit-string representation of length~$n$, the general recommendation is to take $1/n$ as mutation rate. In this work, we discuss whether this is really justified for multimodal functions. Taking jump functions…
The development, assessment, and comparison of randomized search algorithms heavily rely on benchmarking. Regarding the domain of constrained optimization, the number of currently available benchmark environments bears no relation to the…
Parameterized runtime analysis seeks to understand the influence of problem structure on algorithmic runtime. In this paper, we contribute to the theoretical understanding of evolutionary algorithms and carry out a parameterized analysis of…
The analysis of randomized search heuristics on classes of functions is fundamental for the understanding of the underlying stochastic process and the development of suitable proof techniques. Recently, remarkable progress has been made in…
The non-dominated sorting genetic algorithm~II (NSGA-II) is the most popular multi-objective optimization heuristic. Recent mathematical runtime analyses have detected two shortcomings in discrete search spaces, namely, that the NSGA-II has…
Higher-order mutation has the potential for improving major drawbacks of traditional first-order mutation, such as by simulating more realistic faults or improving test optimization techniques. Despite interest in studying promising…
Evolutionary algorithms are bio-inspired algorithms that can easily adapt to changing environments. Recent results in the area of runtime analysis have pointed out that algorithms such as the (1+1)~EA and Global SEMO can efficiently…