Speeding Up Evolutionary Algorithms through Asymmetric Mutation Operators

Doerr, Benjamin; Hebbinghaus, Nils; Neumann, Franz‐Josef

doi:10.1162/evco.2007.15.4.401

Cited by 43 publications

(30 citation statements)

References 18 publications

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“…Moreover, our runtime bound is a √ m-factor slower than Papadimitriou-McDiarmid for reasons we discuss at the end of the section. Nevertheless, we consider these modifications in the context of tailored search operators [6,14,22]. Specifically, we want to show that even small modifications that incorporate problem-specific knowledge into the representation and variation operators can close a superpolynomial runtime gap.…”

Section: Lemmamentioning

confidence: 99%

“…This is common in applications, but has also been studied from a theoretical perspective. Doerr et al [6] proved that tailored mutation operators for the Eulerian cycle problem on a graph of m edges can improve the efficiency of randomized local search and the (1 + 1) EA resulting in an upper bound of O(m 3 ). This beats the upper bound for the general version of the (1 + 1) EA by a factor of m 2 .…”

Section: Introductionmentioning

confidence: 99%

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Superpolynomial Lower Bounds for the $$(1+1)$$ ( 1 + 1 ) EA on Some Easy Combinatorial Problems

Sutton

2015

Algorithmica

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The (1 + 1) EA is a simple evolutionary algorithm that is known to be efficient on linear functions and on some combinatorial optimization problems. In this paper, we rigorously study its behavior on three easy combinatorial problems: finding the 2-coloring of a class of bipartite graphs, solving a class of satisfiable 2-CNF formulas, and solving a class of satisfiable propositional Horn formulas. We prove that it is inefficient on all three problems in the sense that the number of iterations the algorithm needs to minimize the cost functions is superpolynomial with high probability. Our motivation is to better understand the influence of problem instance structure on the runtime character of a simple evolutionary algorithm. We are interested in what kind of structural features give rise to so-called metastable states at which, with probability 1 − o(1), the (1 + 1) EA becomes trapped and subsequently has difficulty leaving. Finally, we show how to modify the (1 + 1) EA slightly in order to obtain a polynomial-time performance guarantee on all three problems.

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Section: Lemmamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Superpolynomial Lower Bounds for the $$(1+1)$$ ( 1 + 1 ) EA on Some Easy Combinatorial Problems

Sutton

2015

Algorithmica

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“…The behavior of (1+1) EAs on plateaus of different structures has been studied in [10] by a rigorous runtime analysis. In the case of combinatorial optimization problems, it has been shown that evolutionary algorithms have to cope with plateaus of constant fitness for the Eulerian cycle problem [2,13] and the computation of maximum matchings [6].…”

Section: Constant Population Sizementioning

confidence: 99%

Comparison of simple diversity mechanisms on plateau functions

Friedrich

Hebbinghaus

Neumann

2009

Theoretical Computer Science

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a b s t r a c tIt is widely assumed and observed in experiments that the use of diversity mechanisms in evolutionary algorithms may have a great impact on its running time. Up to now there is no rigorous analysis pointing out how different diversity mechanisms influence the runtime behavior. We consider evolutionary algorithms that differ from each other in the way they ensure diversity and point out situations where the right mechanism is crucial for the success of the algorithm. The considered evolutionary algorithms either diversify the population with respect to the search points or with respect to function values. Investigating simple plateau functions, we show that using the ''right'' diversity strategy makes the difference between an exponential and a polynomial runtime. Later on, we examine how the drawback of the ''wrong'' diversity mechanism can be compensated by increasing the population size.

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“…In general, the use of modified op-erators in the evolutionary algorithms [5][6][7] allows having a reduction in the computational time, without losing complexity in the model of the problem to solve. However, the modification of the operators must be realized in every strategy, which requires profound knowledge and skills.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Stochastic Optimization of Dividing-wall Distillation Columns Using a Surrogate Model Based on Neural Networks

Gutiérrez‐Antonio

Briones-Ramírez²

2016

Chem. Biochem. Eng. Q.

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Surrogate models have been used for modelling and optimization of conventional chemical processes; among them, neural networks have a great potential to capture complex problems such as those found in chemical processes. However, the development of intensified processes has brought about important challenges in modelling and optimization, due to more complex interrelation between design variables. Among intensified processes, dividing-wall columns represent an interesting alternative for fluid mixtures separation, allowing savings in space requirements, energy and investments costs, in comparison with conventional sequences. In this work, we propose the optimization of dividing-wall columns, with a multiobjective genetic algorithm, through the use of neural networks as surrogate models. The contribution of this work is focused on the evaluation of both objectives and constraints functions with neural networks. The results show a significant reduction in computational time and the number of evaluations of objectives and constraints functions required to reaching the Pareto front.

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Speeding Up Evolutionary Algorithms through Asymmetric Mutation Operators

Cited by 43 publications

References 18 publications

Superpolynomial Lower Bounds for the $$(1+1)$$ ( 1 + 1 ) EA on Some Easy Combinatorial Problems

Superpolynomial Lower Bounds for the $$(1+1)$$ ( 1 + 1 ) EA on Some Easy Combinatorial Problems

Comparison of simple diversity mechanisms on plateau functions

Multiobjective Stochastic Optimization of Dividing-wall Distillation Columns Using a Surrogate Model Based on Neural Networks

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