# OneMax in Black-Box Models with Several Restrictions

@article{Doerr2016OneMaxIB,
title={OneMax in Black-Box Models with Several Restrictions},
author={Carola Doerr and J. Lengler},
journal={Algorithmica},
year={2016},
volume={78},
pages={610-640}
}
• Published 2016
• Mathematics, Computer Science
• Algorithmica
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 different aspect of typical heuristics such as the memory size or the variation operators in use. While most of the previous works focus on one particular such aspect, we consider in this work how the combination of several algorithmic restrictions influence the… Expand
21 Citations
OneMax in Black-Box Models with Several Restrictions
• Computer Science, Mathematics
• GECCO
• 2015
This work shows that the (μ+λ) elitist memory-restricted ranking-based black-box complexity of OneMax is as small as (an advanced version of) the information-theoretic lower bound, and enlivens the quest for natural evolutionary algorithms optimizing OneMax in o(n log n) iterations. Expand
Elitist Black-Box Models: Analyzing the Impact of Elitist Selection on the Performance of Evolutionary Algorithms
• Computer Science, Mathematics
• GECCO
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This work proposes a new elitist black-box model, in which algorithms are required to base all decisions solely on (a fixed number of) the best search points sampled so far, and introduces the concept of $p-Monte Carlo black- box complexity, which measures the time it takes to optimize a problem with failure probability at most p. Expand The (1+1) Elitist Black-Box Complexity of LeadingOnes • Computer Science, Mathematics • GECCO • 2016 The permutation- and bit-invariant version of LeadingOnes is regarded and it is proved that its (1+1) elitist black-box complexity is Ω(n2), a bound that is matched by (1-1)-type evolutionary algorithms. Expand The $$(1+1)$$(1+1) Elitist Black-Box Complexity of LeadingOnes • Mathematics, Computer Science • Algorithmica • 2017 The permutation- and bit-invariant version of LeadingOnes is regarded and it is proved that its(1+1) elitist black-box complexity is VarOmega (n^2)Ω(n2), a bound that is matched by(1-1)-type evolutionary algorithms, a bound which shows that for LeadingOns the memory-restriction, together with the selection requirement, has a substantial impact on the best possible performance. Expand Introducing Elitist Black-Box Models: When Does Elitist Behavior Weaken the Performance of Evolutionary Algorithms? • Computer Science, Medicine • Evolutionary Computation • 2017 The elitist model is added, in which algorithms are required to base all decisions solely on (the relative performance of) a fixed number of the best search points sampled so far, and the concept of p-Monte Carlo black-box complexity is introduced, which measures the time it takes to optimize a problem with failure probability at most p. Expand Selecting a diverse set of benchmark instances from a tunable model problem for black-box discrete optimization algorithms • Computer Science • Appl. Soft Comput. • 2020 A machine learning methodology is developed and applied to automatically discover several clusters of optimization process runtime behaviors as well as their reasons grounded in the algorithm and model parameters, which confirm that the different model parameters allow us to generate problem instances of different hardness, but also find that the investigated algorithms struggle with different problem characteristics. Expand Complexity Theory for Discrete Black-Box Optimization Heuristics Running-time analysis is aimed 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. Expand Unbiasedness of estimation-of-distribution algorithms • Computer Science • Theor. Comput. Sci. • 2019 It is shown that an n-Bernoulli-λ-EDA is unbiased if and only if its probability distribution satisfies a certain invariance property under isometric automorphisms of [ 0 , 1 ] n . Expand On the Choice of the Update Strength in Estimation-of-Distribution Algorithms and Ant Colony Optimization • Mathematics, Computer Science • Algorithmica • 2018 A rigorous runtime analysis concerning the update strength, a vital parameter in PMBGAs such as the step size 1 / K in the so-called compact Genetic Algorithm and the evaporation factor $$\rho$$ρ in ant colony optimizers (ACO). Expand The linear hidden subset problem for the (1 + 1) EA with scheduled and adaptive mutation rates It is shown that no schedule admits a better runtime guarantee and that the optimal schedule is essentially unique, and the related model of initial segment uncertainty with static position-dependent mutation rates is derived and derived asymptotically optimal lower bounds. Expand #### References SHOWING 1-10 OF 34 REFERENCES OneMax in Black-Box Models with Several Restrictions • Computer Science, Mathematics • GECCO • 2015 This work shows that the (μ+λ) elitist memory-restricted ranking-based black-box complexity of OneMax is as small as (an advanced version of) the information-theoretic lower bound, and enlivens the quest for natural evolutionary algorithms optimizing OneMax in o(n log n) iterations. Expand Ranking-Based Black-Box Complexity • Mathematics, Computer Science • Algorithmica • 2012 A ranking-based black-box algorithm is presented that has a runtime of Θ(n/logn), which shows that the OneMax problem does not become harder with the additional ranking- basedness restriction. Expand Elitist Black-Box Models: Analyzing the Impact of Elitist Selection on the Performance of Evolutionary Algorithms • Computer Science, Mathematics • GECCO • 2015 This work proposes a new elitist black-box model, in which algorithms are required to base all decisions solely on (a fixed number of) the best search points sampled so far, and introduces the concept of$p-Monte Carlo black- box complexity, which measures the time it takes to optimize a problem with failure probability at most p. Expand
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This paper introduces a more restricted black-box model for optimisation of pseudo-Boolean functions which it is claimed captures the working principles of many randomised search heuristics including simulated annealing, evolutionary algorithms, randomised local search, and others. Expand
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This work designs a new crossover-based genetic algorithm that uses mutation with a higher-than-usual mutation probability to increase the exploration speed and crossover with the parent to repair losses incurred by the more aggressive mutation. Expand
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