Escaping Local Optima Using Crossover With Emergent Diversity

Dang, Duc-Cuong; Friedrich, Tobias; Kötzing, Timo; Krejca, Martin S.; Lehre, Per Kristian; Oliveto, Pietro S.; Sudholt, Dirk; Sutton, Andrew M.

doi:10.1109/tevc.2017.2724201

Cited by 143 publications

(94 citation statements)

References 42 publications

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“…Now, with overwhelming probability the number of global optima is bounded by the number of search points with Hamming distance less than n δ / log 3 n from x * . By (8), this number is exp(o(n δ / log n)).…”

Section: Black-box Complexity Lower Bounds For Functions With Many Opmentioning

confidence: 99%

“…Example applications include functions with exp(o(n δ / log n)) local optima, including those where all local optima have at most n δ / log 3 n ones or at most n δ / log 3 n zeros. The latter function class includes the well-known Jump k functions [8,26], where a gap of Hamming distance k has to be "jumped" to reach a global optimum, with parameter k ≤ n δ / log 3 n: here all search points with k zeros are local optima, in addition to the global optimum 1 n . A similar function class Cliff d was used in [5,37,50], where the same holds for d in lieu of k; the difference between these two functions is that in the region "between" local and global optima Jump k has a gradient pointing back towards the local optima whereas Cliff d points towards the global optimum 1 n .…”

Section: Lower Bounds On the Time To Reach Local Optimamentioning

confidence: 99%

“…We can even push our applications a bit further. Again using (8), there are at most exp(o(n δ / log n)) search points within a Hamming ball of radius n δ / log 3 n around any search point. If there are exp(o(n δ / log n)) global or local optima then the number of all search points within the union of Hamming balls around all these points is still exp(o(n δ / log n)) · exp(o(n δ / log n)) = exp(o(n δ / log n)).…”

Section: Twomaxmentioning

confidence: 99%

“…Partition instances having two symmetric optimal solutions (which almost surely applies to random instances) 8. Monotone polynomials with positive weights where all but o(n δ / log n) variables appear in at least one monomial.…”

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confidence: 99%

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Parallel Black-Box Complexity With Tail Bounds

Lehre

Sudholt

2020

IEEE Trans. Evol. Computat.

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We propose a new black-box complexity model for search algorithms evaluating λ search points in parallel. The parallel unary unbiased black-box complexity gives lower bounds on the number of function evaluations every parallel unary unbiased black-box algorithm needs to optimise a given problem. It captures the inertia caused by offspring populations in evolutionary algorithms and the total computational effort in parallel metaheuristics 1 We present complexity results for LeadingOnes and OneMax. Our main result is a general performance limit: we prove that on every function every λ-parallel unary unbiased algorithm needs at least Ω( λn ln λ + n log n) evaluations to find any desired target set of up to exponential size, with an overwhelming probability. This yields lower bounds for the typical optimisation time on unimodal and multimodal problems, for the time to find any local optimum, and for the time to even get close to any optimum. The power and versatility of this approach is shown for a wide range of illustrative problems from combinatorial optimisation. Our performance limits can guide parameter choice and algorithm design; we demonstrate the latter by presenting an optimal λ-parallel algorithm for OneMax that uses parallelism most effectively.

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Section: Black-box Complexity Lower Bounds For Functions With Many Opmentioning

confidence: 99%

Section: Lower Bounds On the Time To Reach Local Optimamentioning

confidence: 99%

Section: Twomaxmentioning

confidence: 99%

mentioning

confidence: 99%

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Parallel Black-Box Complexity With Tail Bounds

Lehre

Sudholt

2020

IEEE Trans. Evol. Computat.

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“…Recently it has been shown how both the hypermutations with mutation potential and the ageing operator of Opt-IA can lead to considerable speed-ups compared to the performance of well-studied EAs using SBM for standard benchmark functions used in the evolutionary computation community such as Jump, Cliff or Trap [11]. While the performance of hypermutation operators to escape the local optima of these functions is comparable to that of the EAs with high mutation rates that have been increasingly gaining popularity since 2009 [12,13,14,15,16], ageing allows the optimisation of hard instances of Cliff in O(n log n) where n is the problem size. Such a runtime is required by all unbiased unary (mutation-based) randomised search heuristics to optimise any function with unique optimum [17].…”

Section: Introductionmentioning

confidence: 99%

Artificial immune systems can find arbitrarily good approximations for the NP-hard number partitioning problem

Corus

Oliveto

Yazdani

2019

Artificial Intelligence

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Typical artificial immune system (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which evolutionary algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial example functions constructed especially to show difficulties that EAs may encounter during the optimisation process. However, no evidence is available indicating that these two operators have similar behaviour also in more realistic problems. In this paper we perform an analysis for the standard NP-hard Partition problem from combinatorial optimisation and rigorously show that hypermutations and ageing allow AISs to efficiently escape from local optima where standard EAs require exponential time. As a result we prove that while EAs and random local search (RLS) may get trapped on 4/3 approximations, AISs find arbitrarily good approximate solutions of ratio (1+ ) within n( −(2/ )−1 )(1 − ) −2 e 3 2 2/ + 2n 3 2 2/ + 2n 3 function evaluations in expectation. This expectation is polynomial in the problem size and exponential only in 1/ . $ An extended abstract of this paper without proofs was presented at PPSN 2018 [1].

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Complexity Theory for Discrete Black-Box Optimization Heuristics

Doerr

2019

Natural Computing Series

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A predominant topic in the theory of evolutionary algorithms and, more generally, theory of randomized black-box optimization techniques is running time analysis. Running time analysis aims 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. As in general algorithms theory, this running time perspective is most useful when it is complemented by a meaningful complexity theory that studies the limits of algorithmic solutions.In the context of discrete black-box optimization, several black-box complexity models have been developed to analyze the best possible performance that a black-box optimization algorithm can achieve on a given problem. The models differ in the classes of algorithms to which these lower bounds apply. This way, black-box complexity contributes to a better understanding of how certain algorithmic choices (such as the amount of memory used by a heuristic, its selective pressure, or properties of the strategies that it uses to create new solution candidates) influences performance.In this chapter we review the different black-box complexity models that have been proposed in the literature, survey the bounds that have been obtained for these models, and discuss how the interplay of running time analysis and black-box complexity can inspire new algorithmic solutions to well-researched problems in evolutionary computation. We also discuss in this chapter several interesting open questions for future work.

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Escaping Local Optima Using Crossover With Emergent Diversity

Abstract: Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the

Cited by 143 publications

References 42 publications

Parallel Black-Box Complexity With Tail Bounds

Parallel Black-Box Complexity With Tail Bounds

Artificial immune systems can find arbitrarily good approximations for the NP-hard number partitioning problem

Complexity Theory for Discrete Black-Box Optimization Heuristics

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