The Benefits of Population Diversity in Evolutionary Algorithms: A Survey of Rigorous Runtime Analyses

Sudholt, Dirk

doi:10.1007/978-3-030-29414-4_8

Cited by 52 publications

(38 citation statements)

References 66 publications

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“…The offspring y replaces a worst individual z from the population if f (y) ≥ f (z) (see Algorithm 1). Table 1 summarises previous work for the (µ+1) EA with diversity mechanisms on TwoMax (details for each (µ+1) EA variant can be found in the respective publications and in [19]). Some mechanisms succeed in finding both optima on TwoMax efficiently, that is, in (expected) time O(µn log n).…”

Section: Diversity Mechanisms and Previous Results For Twomaxmentioning

confidence: 99%

“…This is challenging as the two optima have the maximum possible Hamming distance. Studying TwoMax led to insights into the capabilities and weaknesses of various diversity mechanisms (see Section 2 and Sudholt's survey [19]), however a question left open is how diversity mechanisms deal with many local optima.…”

Section: Introductionmentioning

confidence: 99%

“…In[6] an additional fitness value for 1 n was added to distinguish between a local optimum 0 n and a unique global optimum 1 n . The discussion of previous work from[6] is adapted to a TwoMax with two optima[1,2,13] (seeTable 1and[19]). …”

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confidence: 99%

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Empirical Analysis of Diversity-Preserving Mechanisms on Example Landscapes for Multimodal Optimisation

Osuna

Sudholt

2018

Lecture Notes in Computer Science

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Many diversity-preserving mechanisms have been developed to reduce the risk of premature convergence in evolutionary algorithms and it is not clear which mechanism is best. Most multimodal optimisation problems studied empirically are restricted to real-parameter problems and are not accessible to theoretical analysis, while theoreticians analyse the simple bimodal function TwoMax. This paper looks to narrow the gap between both approaches. We perform an extensive empirical study involving 9 common diversity mechanisms on Jansen-Zarges multimodal function classes (Jansen and Zarges, PPSN 2016) that allow to control important problem features while still being amenable to theoretical analysis. This allows us to study functions with various degrees of multimodality and to explain the results in the light of previous theoretical works. We show which mechanisms are able to find and maintain a large number of distant optima, escape from local optima, and which fail to locate even a single peak.

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Section: Diversity Mechanisms and Previous Results For Twomaxmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Empirical Analysis of Diversity-Preserving Mechanisms on Example Landscapes for Multimodal Optimisation

Osuna

Sudholt

2018

Lecture Notes in Computer Science

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“…Our aim is that the more local optima are identified by the algorithm, the more M expoHD approximates its ideal behaviour. However, we will show that this is not the case using the well-studied bimodal benchmark functions TwoMax (4) [11,16,19,20] as an example:…”

Section: Realistic Inefficient Behaviourmentioning

confidence: 91%

On inversely proportional hypermutations with mutation potential

Corus

Oliveto

Yazdani

2019

Proceedings of the Genetic and Evolutionary Computation Conference

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Artificial Immune Systems (AIS) employing hypermutations with linear static mutation potential have recently been shown to be very effective at escaping local optima of combinatorial optimisation problems at the expense of being slower during the exploitation phase compared to standard evolutionary algorithms. In this paper we prove that considerable speed-ups in the exploitation phase may be achieved with dynamic inversely proportional mutation potentials (IPM) and argue that the potential should decrease inversely to the distance to the optimum rather than to the difference in fitness. Afterwards we define a simple (1+1) Opt-IA, that uses IPM hypermutations and ageing, for realistic applications where optimal solutions are unknown. The aim of the AIS is to approximate the ideal behaviour of the inversely proportional hypermutations better and better as the search space is explored. We prove that such desired behaviour, and related speed-ups, occur for a well-studied bimodal benchmark function called TwoMax. Furthermore, we prove that the (1+1) Opt-IA with IPM efficiently optimises a third bimodal function, Cliff, by escaping its local optima while Opt-IA with static potential cannot, thus requires exponential expected runtime in the distance between the cliff and the optimum.1 Alternatively, the fitness of the best candidate solution is sometimes used and the mutation rate of the rest of the population is inversely proportional to the best.

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“…It enables crossover to work effectively, improves performance and robustness in dynamic optimization, and helps to search for the whole Pareto front for evolutionary multiobjective optimization [6]. In the related studies of runtime analysis [5], diversity mechanisms proved to be highly effective for the considered problems, speeding up the optimization time by constant factors, polynomial factors, or even exponential factors.…”

Section: Introductionmentioning

confidence: 99%

On the Use of Diversity Mechanisms in Dynamic Constrained Continuous Optimization

Hasani-Shoreh

Neumann

2019

Neural Information Processing

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Population diversity plays a key role in evolutionary algorithms that enables global exploration and avoids premature convergence. This is especially more crucial in dynamic optimization in which diversity can ensure that the population keeps track of the global optimum by adapting to the changing environment. Dynamic constrained optimization problems (DCOPs) have been the target for many researchers in recent years as they comprehend many of the current real-world problems. Regardless of the importance of diversity in dynamic optimization, there is not an extensive study investigating the effects of diversity promotion techniques in DCOPs so far. To address this gap, this paper aims to investigate how the use of different diversity mechanisms may influence the behavior of algorithms in DCOPs. To achieve this goal, we apply and adapt the most common diversity promotion mechanisms for dynamic environments using differential evolution (DE) as our base algorithm. The results show that applying diversity techniques to solve DCOPs in most test cases lead to significant enhancement in the baseline algorithm in terms of modified offline error values.

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The Benefits of Population Diversity in Evolutionary Algorithms: A Survey of Rigorous Runtime Analyses

Cited by 52 publications

References 66 publications

Empirical Analysis of Diversity-Preserving Mechanisms on Example Landscapes for Multimodal Optimisation

Empirical Analysis of Diversity-Preserving Mechanisms on Example Landscapes for Multimodal Optimisation

On inversely proportional hypermutations with mutation potential

On the Use of Diversity Mechanisms in Dynamic Constrained Continuous Optimization

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