Probabilistic Tools for the Analysis of Randomized Optimization Heuristics

Doerr, Benjamin

doi:10.1007/978-3-030-29414-4_1

Cited by 120 publications

(91 citation statements)

References 104 publications

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“…However, in some instances with particular δ = 50, the old model outperforms the new model. The solutions in NSGA-II with old and PS (10) and NSGA-II with new and PS (12) indicate that in most instances, the new model performs better than the old model when using the PS crossover operator.…”

Section: Experimental Results For Nsga-iimentioning

confidence: 99%

“…Chebyshev's inequality has a high utility because it can be applied to any probability distribution with known expectation and standard deviation of design variables. It also gives a tighter bound in comparison to the weaker tails such as Markov's inequality [12]. The standard Chebyshev's inequality is two-side and provides tails for upper and lower bounds [5].…”

Section: Surrogate Functions Based On Tail Boundsmentioning

confidence: 99%

“…Statistic results of NSGA-II with Chernoff bound for instance eil101 with 500 items capacity delta alpha NSGA-II with old and uniform (9) NSGA-II with old and PS (10) NSGA-II with new and uniform (11) NSGA-II with new and PS(12) …”

mentioning

confidence: 99%

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Evolutionary algorithms for the chance-constrained knapsack problem

Xie

Harper

Assimi

et al. 2019

Proceedings of the Genetic and Evolutionary Computation Conference

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The chance-constrained knapsack problem is a variant of the classical knapsack problem where each item has a weight distribution instead of a deterministic weight. The objective is to maximize the total profit of the selected items under the condition that the weight of the selected items only exceeds the given weight bound with a small probability of α. In this paper, consider problem-specific single-objective and multi-objective approaches for the problem. We examine the use of heavy-tail mutations and introduce a problem-specific crossover operator to deal with the chance-constrained knapsack problem. Empirical results for single-objective evolutionary algorithms show the effectiveness of our operators compared to the use of classical operators. Moreover, we introduce a new effective multi-objective model for the chance-constrained knapsack problem. We use this model in combination with the problem-specific crossover operator in multiobjective evolutionary algorithms to solve the problem. Our experimental results show that this leads to significant performance improvements when using the approach in evolutionary multi-objective algorithms such as GSEMO and NSGA-II.

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Section: Experimental Results For Nsga-iimentioning

confidence: 99%

Section: Surrogate Functions Based On Tail Boundsmentioning

confidence: 99%

See 1 more Smart Citation

Evolutionary algorithms for the chance-constrained knapsack problem

Xie

Harper

Assimi

et al. 2019

Proceedings of the Genetic and Evolutionary Computation Conference

View full text Add to dashboard Cite

show abstract

“…By assuming c ≤ 1 and using the elementary estimate e x ≤ 1 + 2x valid for x ∈ [0, 1], see, e.g., Lemma 4.2(b) in [Doe18b], we have 1 − P + P exp( c µ ) ≤ 1 + 2P ( c µ ). Hence with P ≤ 2 n , c ≤ 1, µ ≥ 1, and ℓ ≤ n 320 , we obtain…”

Section: Resultsmentioning

confidence: 99%

An exponential lower bound for the runtime of the compact genetic algorithm on jump functions

Doerr

2019

Proceedings of the 15th ACM/SIGEVO Conference on Foundations of Genetic Algorithms

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In the first runtime analysis of an estimation-of-distribution algorithm (EDA) on the multi-modal jump function class, Hasenöhrl and Sutton (GECCO 2018) proved that the runtime of the compact genetic algorithm with suitable parameter choice on jump functions with high probability is at most polynomial (in the dimension) if the jump size is at most logarithmic (in the dimension), and is at most exponential in the jump size if the jump size is super-logarithmic. The exponential runtime guarantee was achieved with a hypothetical population size that is also exponential in the jump size. Consequently, this setting cannot lead to a better runtime.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. This result might be the first non-trivial exponential lower bound for EDAs that holds for arbitrary parameter settings.

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“…where the last estimate stems from the additive Chernoff bound (e.g., Theorem 10.9 in [Doe18]). Using the estimates…”

Section: Summary Of Useful Toolsmentioning

confidence: 99%

Self-adjusting mutation rates with provably optimal success rules

Doerr

Lengler

2019

Proceedings of the Genetic and Evolutionary Computation Conference

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The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms. While it is often applied in the literal sense, a common interpretation sees the one-fifth success rule as a family of success-based updated rules that are determined by an update strength F and a success rate s. We analyze in this work how the performance of the (1+1) Evolutionary Algorithm (EA) on LeadingOnes depends on these two hyper-parameters. Our main result shows that the best performance is obtained for small update strengths F = 1 + o(1) and success rate 1/e. We also prove that the running time obtained by this parameter setting is asymptotically optimal among all dynamic choices of the mutation rate for the (1+1) EA, up to lower order error terms. We show similar results for the resampling variant of the (1+1) EA, which enforces to flip at least one bit per iteration.

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Probabilistic Tools for the Analysis of Randomized Optimization Heuristics

Cited by 120 publications

References 104 publications

Evolutionary algorithms for the chance-constrained knapsack problem

Evolutionary algorithms for the chance-constrained knapsack problem

An exponential lower bound for the runtime of the compact genetic algorithm on jump functions

Self-adjusting mutation rates with provably optimal success rules

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