Analysis of Evolutionary Algorithms in Dynamic and Stochastic Environments

Neumann, Franz‐Josef; Pourhassan, Mojgan; Roostapour, Vahid

doi:10.1007/978-3-030-29414-4_7

Cited by 15 publications

(8 citation statements)

References 29 publications

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“…Thus, we usually want to maintain the solution quality by modifying the current solution without completely recomputing it. As in [6,31], our main focus is the ability of an algorithm adapting to the change of the objective. That is, starting from a solution with a good approximation ratio for the old objective, we concern the running time of an algorithm until regaining a solution with the same approximation ratio for the new objective.…”

Section: Analysis Under Dynamic Environmentsmentioning

confidence: 99%

Result Diversification by Multi-objective Evolutionary Algorithms with Theoretical Guarantees

Qian¹,

Liu²,

Zhou³

2021

Preprint

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Given a ground set of items, the result diversification problem aims to select a subset with high "quality" and "diversity" while satisfying some constraints. It arises in various real-world artificial intelligence applications, such as web-based search, document summarization and feature selection, and also has applications in other areas, e.g., computational geometry, databases, finance and operations research. Previous algorithms are mainly based on greedy or local search. In this paper, we propose to reformulate the result diversification problem as a bi-objective maximization problem, and solve it by a multi-objective evolutionary algorithm (EA), i.e., the GSEMO. We theoretically prove that the GSEMO can achieve the (asymptotically) optimal theoretical guarantees under both static and dynamic environments. For cardinality constraints, the GSEMO can achieve the optimal polynomial-time approximation ratio, 1/2. For more general matroid constraints, the GSEMO can achieve the asymptotically optimal polynomial-time approximation ratio, 1/2 − /(4n). Furthermore, when the objective function (i.e., a linear combination of quality and diversity) changes dynamically, the GSEMO can maintain this approximation ratio in polynomial running time, addressing the open question proposed by Borodin et al. [6]. This also theoretically shows the superiority of EAs over local search for solving dynamic optimization problems for the first time, and discloses the robustness of the mutation operator of EAs against dynamic changes. Experiments on the applications of web-based search, multi-label feature selection and document summarization show the superior performance of the GSEMO over the state-of-the-art algorithms (i.e., the greedy algorithm and local search) under both static and dynamic environments.

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Section: Analysis Under Dynamic Environmentsmentioning

confidence: 99%

Result Diversification by Multi-objective Evolutionary Algorithms with Theoretical Guarantees

Qian¹,

Liu²,

Zhou³

2021

Preprint

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“…), and we react to this change not by optimizing the new problem from scratch, but by initializing the EA with solutions that were good in the original problem. While there is a decent amount of runtime analysis literature on how EAs cope with dynamic optimization problems, see [NPR20], almost all of them regard the situation that a dynamic change of the instance happens frequently and the question is how well the EA adjusts to these changes. The only mathematical runtime analysis of a true reoptimization problem we are aware of is [DDN19].…”

Section: Starting With Good Solutionsmentioning

confidence: 99%

First Steps Towards a Runtime Analysis When Starting With a Good Solution

Antipov¹,

Buzdalov²,

Doerr³

2020

Preprint

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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. In practical applications it may be possible to guess solutions that are better than random ones. We start a mathematical runtime analysis for such situations. We observe that different algorithms profit to a very different degree from a better initialization. We also show that the optimal parameterization of the algorithm can depend strongly on the quality of the initial solutions. To overcome this difficulty, self-adjusting and randomized heavy-tailed parameter choices can be profitable. Finally, we observe a larger gap between the performance of the best evolutionary algorithm we found and the corresponding black-box complexity. This could suggest that evolutionary algorithms better exploiting good initial solutions are still to be found. These first findings stem from analyzing the performance of the (1 + 1) evolutionary algorithm and the static, self-adjusting, and heavy-tailed (1 + (λ, λ)) GA on the OneMax benchmark, but we are optimistic that the question how to profit from good initial solutions is interesting beyond these first examples.

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“…If the fitness function changes slowly enough, then population-based optimization heuristics may still find the optimum, or track the optimum over time [2,7,11,12,[22][23][24][26][27][28]. We refrain from giving a detailed overview over the literature, since an excellent review has recently been given in [25]. All the settings have in common that either the fitness function changes with very low frequency, or it changes only by some small local differences, or both.…”

Section: Introductionmentioning

confidence: 99%

Runtime Analysis of the $$(\mu + 1)$$-EA on the Dynamic BinVal Function

Lengler

Riedi

2022

SN COMPUT. SCI.

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We study evolutionary algorithms in a dynamic setting, where for each generation a different fitness function is chosen, and selection is performed with respect to the current fitness function. Specifically, we consider Dynamic BinVal, in which the fitness functions for each generation is given by the linear function BinVal, but in each generation the order of bits is randomly permuted. For the $$(1 + 1)$$ ( 1 + 1 ) -EA it was known that there is an efficiency threshold $$c_0$$ c 0 for the mutation parameter, at which the runtime switches from quasilinear to exponential. Previous empirical evidence suggested that for larger population size $$\mu$$ μ , the threshold may increase. We prove that this is at least the case in an $$\varepsilon$$ ε -neighborhood around the optimum: the threshold of the $$(\mu + 1)$$ ( μ + 1 ) -EA becomes arbitrarily large if the $$\mu$$ μ is chosen large enough. However, the most surprising result is obtained by a second-order analysis for $$\mu =2$$ μ = 2 : the threshold increases with increasing proximity to the optimum. In particular, the hardest region for optimization is not around the optimum.

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Analysis of Evolutionary Algorithms in Dynamic and Stochastic Environments

Cited by 15 publications

References 29 publications

Result Diversification by Multi-objective Evolutionary Algorithms with Theoretical Guarantees

Result Diversification by Multi-objective Evolutionary Algorithms with Theoretical Guarantees

First Steps Towards a Runtime Analysis When Starting With a Good Solution

Runtime Analysis of the $$(\mu + 1)$$-EA on the Dynamic BinVal Function

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