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Found 83 papers, 7 papers with code
Superior Genetic Algorithms for the Target Set Selection Problem Based on Power-Law Parameter Choices and Simple Greedy Heuristics
Besides providing a superior algorithm for the TSS problem, this work shows that randomized parameter choices and elementary greedy heuristics can give better results than complex algorithms and costly parameter tuning.
Fast Genetic Algorithms
We prove that the $(1+1)$ EA with this heavy-tailed mutation rate optimizes any $\jump_{m, n}$ function in a time that is only a small polynomial (in~$m$) factor above the one stemming from the optimal rate for this $m$.
A Mathematical Runtime Analysis of the Non-dominated Sorting Genetic Algorithm III (NSGA-III)
In this work, we provide the first mathematical runtime analysis of the NSGA-III, a refinement of the NSGA-II aimed at better handling more than two objectives.
Mathematical Runtime Analysis for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)
The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications.
Better Runtime Guarantees Via Stochastic Domination
Apart from few exceptions, the mathematical runtime analysis of evolutionary algorithms is mostly concerned with expected runtimes.
Probabilistic Tools for the Analysis of Randomized Optimization Heuristics
This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics.
Theory of Parameter Control for Discrete Black-Box Optimization: Provable Performance Gains Through Dynamic Parameter Choices
Parameter control aims at realizing performance gains through a dynamic choice of the parameters which determine the behavior of the underlying optimization algorithm.
Bounding Bloat in Genetic Programming
While many optimization problems work with a fixed number of decision variables and thus a fixed-length representation of possible solutions, genetic programming (GP) works on variable-length representations.
Precise Runtime Analysis for Plateau Functions
To gain a better theoretical understanding of how evolutionary algorithms (EAs) cope with plateaus of constant fitness, we propose the $n$-dimensional Plateau$_k$ function as natural benchmark and analyze how different variants of the $(1 + 1)$ EA optimize it.
The (1+$λ$) Evolutionary Algorithm with Self-Adjusting Mutation Rate
We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces.
An Elementary Analysis of the Probability That a Binomial Random Variable Exceeds Its Expectation
We give an elementary proof of the fact that a binomial random variable $X$ with parameters $n$ and $0. 29/n \le p < 1$ with probability at least $1/4$ strictly exceeds its expectation.
Runtime Analysis of the $(1+(λ,λ))$ Genetic Algorithm on Random Satisfiable 3-CNF Formulas
We show that this problem can be overcome by equipping the self-adjusting GA with an upper limit for the population size.
Optimal Parameter Settings for the $(1+(λ, λ))$ Genetic Algorithm
The $(1+(\lambda,\lambda))$ genetic algorithm is one of the few algorithms for which a super-constant speed-up through the use of crossover could be proven.
The Right Mutation Strength for Multi-Valued Decision Variables
The most common representation in evolutionary computation are bit strings.
A Tight Runtime Analysis of the $(1+(λ, λ))$ Genetic Algorithm on OneMax
We first improve the upper bound on the runtime to $O(\max\{n\log(n)/\lambda, n\lambda \log\log(\lambda)/\log(\lambda)\})$.
Solving Problems with Unknown Solution Length at (Almost) No Extra Cost
For their setting, in which the solution length is sampled from a geometric distribution, we provide mutation rates that yield an expected optimization time that is of the same order as that of the (1+1) EA knowing the solution length.
Optimising Spatial and Tonal Data for PDE-based Inpainting
Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED.
Optimal Parameter Choices Through Self-Adjustment: Applying the 1/5-th Rule in Discrete Settings
While evolutionary algorithms are known to be very successful for a broad range of applications, the algorithm designer is often left with many algorithmic choices, for example, the size of the population, the mutation rates, and the crossover rates of the algorithm.
Unbiased Black-Box Complexities of Jump Functions
We analyze the unbiased black-box complexity of jump functions with small, medium, and large sizes of the fitness plateau surrounding the optimal solution.
Collecting Coupons with Random Initial Stake
Motivated by a problem in the theory of randomized search heuristics, we give a very precise analysis for the coupon collector problem where the collector starts with a random set of coupons (chosen uniformly from all sets).
Significance-based Estimation-of-Distribution Algorithms
Estimation-of-distribution algorithms (EDAs) are randomized search heuristics that create a probabilistic model of the solution space, which is updated iteratively, based on the quality of the solutions sampled according to the model.
Optimal Parameter Choices via Precise Black-Box Analysis
It has been observed that some working principles of evolutionary algorithms, in particular, the influence of the parameters, cannot be understood from results on the asymptotic order of the runtime, but only from more precise results.
Runtime Analysis for Self-adaptive Mutation Rates
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.
Working Principles of Binary Differential Evolution
On the technical side, we observe that the strong stochastic dependencies in the random experiment describing a run of BDE prevent us from proving all desired results with the mathematical rigor that was successfully used in the analysis of other evolutionary algorithms.
The Query Complexity of a Permutation-Based Variant of Mastermind
We study the query complexity of a permutation-based variant of the guessing game Mastermind.
A Tight Runtime Analysis for the $(μ+ λ)$ EA
In this work, we analyze this long-standing problem and show the asymptotically tight result that the runtime $T$, the number of iterations until the optimum is found, satisfies \[E[T] = \Theta\bigg(\frac{n\log n}{\lambda}+\frac{n}{\lambda / \mu} + \frac{n\log^+\log^+ \lambda/ \mu}{\log^+ \lambda / \mu}\bigg),\] where $\log^+ x := \max\{1, \log x\}$ for all $x > 0$.
Fast Re-Optimization via Structural Diversity
We propose a simple diversity mechanism that prevents this behavior, thereby reducing the re-optimization time for LeadingOnes to $O(\gamma\delta n)$, where $\gamma$ is the population size used by the diversity mechanism and $\delta \le \gamma$ the Hamming distance of the new optimum from the previous solution.
Self-Adjusting Mutation Rates with Provably Optimal Success Rules
The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms.
A Tight Runtime Analysis for the cGA on Jump Functions---EDAs Can Cross Fitness Valleys at No Extra Cost
We prove that the compact genetic algorithm (cGA) with hypothetical population size $\mu = \Omega(\sqrt n \log n) \cap \text{poly}(n)$ with high probability finds the optimum of any $n$-dimensional jump function with jump size $k < \frac 1 {20} \ln n$ in $O(\mu \sqrt n)$ iterations.
Evolving Boolean Functions with Conjunctions and Disjunctions via Genetic Programming
Recently it has been proved that simple GP systems can efficiently evolve the conjunction of $n$ variables if they are equipped with the minimal required components.
Multiplicative Up-Drift
Drift analysis aims at translating the expected progress of an evolutionary algorithm (or more generally, a random process) into a probabilistic guarantee on its run time (hitting time).
The Efficiency Threshold for the Offspring Population Size of the ($μ$, $λ$) EA
Understanding when evolutionary algorithms are efficient or not, and how they efficiently solve problems, is one of the central research tasks in evolutionary computation.
An Exponential Lower Bound for the Runtime of the cGA on Jump Functions
In this work, we show that any choice of the hypothetical population size leads to a runtime that, with high probability, is at least exponential in the jump size.
The Runtime of the Compact Genetic Algorithm on Jump Functions
We prove that any choice of the hypothetical population size leads to a runtime that, with high probability, is at least exponential in the jump size $k$.
Sharp Bounds for Genetic Drift in Estimation of Distribution Algorithms
This paper further proves that for PBIL with parameters $\mu$, $\lambda$, and $\rho$, in an expected number of $\Theta(\mu/\rho^2)$ iterations the sampling frequency of a neutral bit leaves the interval $[\Theta(\rho/\mu), 1-\Theta(\rho/\mu)]$ and then always the same value is sampled for this bit, that is, the frequency approaches the corresponding boundary value with maximum speed.
Optimization of Chance-Constrained Submodular Functions
In this paper, we investigate submodular optimization problems with chance constraints.
Does Comma Selection Help To Cope With Local Optima
This is the first runtime result for a non-elitist algorithm on a multi-modal problem that is tight apart from lower order terms.
A Simplified Run Time Analysis of the Univariate Marginal Distribution Algorithm on LeadingOnes
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.
Exponential Upper Bounds for the Runtime of Randomized Search Heuristics
We argue that proven exponential upper bounds on runtimes, an established area in classic algorithms, are interesting also in heuristic search and we prove several such results.
A Rigorous Runtime Analysis of the $(1 + (λ, λ))$ GA on Jump Functions
In this work, we conduct the first runtime analysis of this algorithm on a multimodal problem class, the jump functions benchmark.
Fast Mutation in Crossover-based Algorithms
In this first runtime analysis of a crossover-based algorithm using a heavy-tailed choice of the mutation rate, we show an even stronger impact.
From Understanding Genetic Drift to a Smart-Restart Parameter-less Compact Genetic Algorithm
One of the key difficulties in using estimation-of-distribution algorithms is choosing the population size(s) appropriately: Too small values lead to genetic drift, which can cause enormous difficulties.
Fixed-Target Runtime Analysis
In this work, we conduct an in-depth study on the advantages and the limitations of fixed-target analyses.
Lower Bounds for Non-Elitist Evolutionary Algorithms via Negative Multiplicative Drift
We discuss in more detail Lehre's (PPSN 2010) \emph{negative drift in populations} method, one of the most general tools to prove lower bounds on the runtime of non-elitist mutation-based evolutionary algorithms for discrete search spaces.
Runtime Analysis of a Heavy-Tailed $(1+(λ,λ))$ Genetic Algorithm on Jump Functions
To obtain this performance, however, a non-standard parameter setting depending on the jump size $k$ was used.
Runtime Analysis of Evolutionary Algorithms via Symmetry Arguments
We use an elementary argument building on group actions to prove that the selection-free steady state genetic algorithm analyzed by Sutton and Witt (GECCO 2019) takes an expected number of $\Omega(2^n / \sqrt n)$ iterations to find any particular target search point.
Exploratory Landscape Analysis is Strongly Sensitive to the Sampling Strategy
While, not unexpectedly, increasing the number of sample points gives more robust estimates for the feature values, to our surprise we find that the feature value approximations for different sampling strategies do not converge to the same value.
First Steps Towards a Runtime Analysis When Starting With a Good Solution
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.
A Survey on Recent Progress in the Theory of Evolutionary Algorithms for Discrete Optimization
The theory of evolutionary computation for discrete search spaces has made significant progress in the last ten years.
The Univariate Marginal Distribution Algorithm Copes Well With Deception and Epistasis
In their recent work, Lehre and Nguyen (FOGA 2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem.
Theoretical Analyses of Multiobjective Evolutionary Algorithms on Multimodal Objectives
As a first step towards a deeper understanding of how evolutionary algorithms solve multimodal multiobjective problems, we propose the OJZJ problem, a bi-objective problem composed of two objectives isomorphic to the classic jump function benchmark.
Towards Explainable Exploratory Landscape Analysis: Extreme Feature Selection for Classifying BBOB Functions
We show that the classification accuracy transfers to settings in which several instances are involved in training and testing.
Lower Bounds from Fitness Levels Made Easy
One of the first and easy to use techniques for proving run time bounds for evolutionary algorithms is the so-called method of fitness levels by Wegener.
Lazy Parameter Tuning and Control: Choosing All Parameters Randomly From a Power-Law Distribution
On the other hand, this algorithm is also very efficient on jump functions, where the best static parameters are very different from those necessary to optimize simple problems.
An Extended Jump Functions Benchmark for the Analysis of Randomized Search Heuristics
We prove that several previous results extend to this more general class: for all {$k \le \frac{n^{1/3}}{\ln{n}}$} and $\delta < k$, the optimal mutation rate for the $(1+1)$~EA is $\frac{\delta}{n}$, and the fast $(1+1)$~EA runs faster than the classical $(1+1)$~EA by a factor super-exponential in $\delta$.
Choosing the Right Algorithm With Hints From Complexity Theory
Our finding that the unary unbiased black-box complexity is only $O(n^2)$ suggests the Metropolis algorithm as an interesting candidate and we prove that it solves the DLB problem in quadratic time.
Stagnation Detection Meets Fast Mutation
Two mechanisms have recently been proposed that can significantly speed up finding distant improving solutions via mutation, namely using a random mutation rate drawn from a heavy-tailed distribution ("fast mutation", Doerr et al. (2017)) and increasing the mutation strength based on stagnation detection (Rajabi and Witt (2020)).
Approximation Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)
In this work, we study how well it approximates the Pareto front when the population size is smaller.
Simulated Annealing is a Polynomial-Time Approximation Scheme for the Minimum Spanning Tree Problem
We prove that Simulated Annealing with an appropriate cooling schedule computes arbitrarily tight constant-factor approximations to the minimum spanning tree problem in polynomial time.
Towards a Stronger Theory for Permutation-based Evolutionary Algorithms
We observe that it not only leads to simpler proofs, but also reduces the runtime on jump functions with odd jump size by a factor of $\Theta(n)$.
A First Runtime Analysis of the NSGA-II on a Multimodal Problem
Very recently, the first mathematical runtime analyses of the multi-objective evolutionary optimizer NSGA-II have been conducted.
Automated Algorithm Selection for Radar Network Configuration
The exact modeling of these instances is complex, as the quality of the configurations depends on a large number of parameters, on internal radar processing, and on the terrains on which the radars need to be placed.
From Understanding Genetic Drift to a Smart-Restart Mechanism for Estimation-of-Distribution Algorithms
Building on a recent quantitative analysis of how the population size leads to genetic drift, we design a smart-restart mechanism for EDAs.
General Univariate Estimation-of-Distribution Algorithms
We propose a general formulation of a univariate estimation-of-distribution algorithm (EDA).
Runtime Analysis for Permutation-based Evolutionary Algorithms
We observe that it not only leads to simpler proofs, but also reduces the runtime on jump functions with odd jump size by a factor of $\Theta(n)$.
Runtime Analysis for the NSGA-II: Provable Speed-Ups From Crossover
Very recently, the first mathematical runtime analyses for the NSGA-II, the most common multi-objective evolutionary algorithm, have been conducted.
From Understanding the Population Dynamics of the NSGA-II to the First Proven Lower Bounds
Due to the more complicated population dynamics of the NSGA-II, none of the existing runtime guarantees for this algorithm is accompanied by a non-trivial lower bound.
The $(1+(λ,λ))$ Global SEMO Algorithm
The $(1+(\lambda,\lambda))$ genetic algorithm is a recently proposed single-objective evolutionary algorithm with several interesting properties.
Runtime Analysis for the NSGA-II: Proving, Quantifying, and Explaining the Inefficiency For Many Objectives
The NSGA-II is one of the most prominent algorithms to solve multi-objective optimization problems.
Fourier Analysis Meets Runtime Analysis: Precise Runtimes on Plateaus
We also use this method to analyze the runtime of the $(1+1)$ evolutionary algorithm on a new benchmark consisting of $n/\ell$ plateaus of effective size $2^\ell-1$ which have to be optimized sequentially in a LeadingOnes fashion.
Lasting Diversity and Superior Runtime Guarantees for the $(μ+1)$ Genetic Algorithm
From this better understanding of the population diversity, we obtain stronger runtime guarantees, among them the statement that for all $c\ln(n)\le\mu \le n/\log n$, with $c$ a suitable constant, the runtime of the $(\mu+1)$ GA on $\mathrm{Jump}_k$, with $k \ge 3$, is $O(n^{k-1})$.
Estimation-of-Distribution Algorithms for Multi-Valued Decision Variables
Roughly speaking, when the variables take $r$ different values, the time for genetic drift to become significant is $r$ times shorter than in the binary case.
(1+1) Genetic Programming With Functionally Complete Instruction Sets Can Evolve Boolean Conjunctions and Disjunctions with Arbitrarily Small Error
Recently it has been proven that simple GP systems can efficiently evolve a conjunction of $n$ variables if they are equipped with the minimal required components.
How the Move Acceptance Hyper-Heuristic Copes With Local Optima: Drastic Differences Between Jumps and Cliffs
In recent work, Lissovoi, Oliveto, and Warwicker (Artificial Intelligence (2023)) proved that the Move Acceptance Hyper-Heuristic (MAHH) leaves the local optimum of the multimodal cliff benchmark with remarkable efficiency.
How Well Does the Metropolis Algorithm Cope With Local Optima?
Even with the optimal temperature (the only parameter of the MA), the MA optimizes most cliff functions less efficiently than simple elitist evolutionary algorithms (EAs), which can only leave the local optimum by generating a superior solution possibly far away.
Larger Offspring Populations Help the $(1 + (λ, λ))$ Genetic Algorithm to Overcome the Noise
Evolutionary algorithms are known to be robust to noise in the evaluation of the fitness.
Runtime Analyses of Multi-Objective Evolutionary Algorithms in the Presence of Noise
We prove that when bit-wise prior noise with rate $p \le \alpha/n$, $\alpha$ a suitable constant, is present, the \emph{simple evolutionary multi-objective optimizer} (SEMO) without any adjustments to cope with noise finds the Pareto front of the OneMinMax benchmark in time $O(n^2\log n)$, just as in the case without noise.
The First Proven Performance Guarantees for the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) on a Combinatorial Optimization Problem
Recently, the first mathematical runtime guarantees have been obtained for this algorithm, however only for synthetic benchmark problems.
Bivariate Estimation-of-Distribution Algorithms Can Find an Exponential Number of Optima
We show that the bivariate EDA mutual-information-maximizing input clustering, without any problem-specific modification, quickly generates a model that behaves very similarly to a theoretically ideal model for EBOM, which samples each of the exponentially many optima with the same maximal probability.
Runtime Analysis of the SMS-EMOA for Many-Objective Optimization
To this aim, we first propose a many-objective counterpart, the m-objective mOJZJ problem, of the bi-objective OJZJ benchmark, which is the first many-objective multimodal benchmark used in a mathematical runtime analysis.
The Runtime of Random Local Search on the Generalized Needle Problem
In their recent work, C. Doerr and Krejca (Transactions on Evolutionary Computation, 2023) proved upper bounds on the expected runtime of the randomized local search heuristic on generalized Needle functions.
Already Moderate Population Sizes Provably Yield Strong Robustness to Noise
The only previous result in this direction regarded the less realistic one-bit noise model, required a population size super-linear in the problem size, and proved a runtime guarantee roughly cubic in the noiseless runtime for the OneMax benchmark.
A Block-Coordinate Descent EMO Algorithm: Theoretical and Empirical Analysis
We consider whether conditions exist under which block-coordinate descent is asymptotically efficient in evolutionary multi-objective optimization, addressing an open problem.
