How Crossover Speeds Up Evolutionary Algorithms for the Multi-criteria All-Pairs-Shortest-Path Problem

Neumann, Franz‐Josef; Theile, Madeleine

doi:10.1007/978-3-642-15844-5_67

Cited by 28 publications

(18 citation statements)

References 8 publications

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“…Thus, the empirical observations confirm that MOEA Through the analysis of MOEA onebit recomb and MOEA bitwise recomb for the artificial problems, we discover that the recombination operator works in the studied situation by accelerating the filling of the Pareto front through recombining the diverse optimal solutions that have been found. It is worth noting that this mechanism is different from that analyzed in [35], where the crossover operator works by its interplay with mutation. Moreover, this finding is unique to multi-objective optimization, as there is no Pareto front in single-objective situations.…”

Section: Our Contributionmentioning

confidence: 90%

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An analysis on recombination in multi-objective evolutionary optimization

Qian

Zhou

2013

Artificial Intelligence

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Evolutionary algorithms (EAs) are increasingly popular approaches to multi-objective optimization.One of their significant advantages is that they can directly optimize the Pareto front by evolving a population of solutions, where the recombination (also called crossover) operators are usually employed to reproduce new and potentially better solutions by mixing up solutions in the population.Recombination in multi-objective evolutionary algorithms is, however, mostly applied heuristically.In this paper, we investigate how from a theoretical viewpoint a recombination operator will affect a multi-objective EA. First, we employ artificial benchmark problems: the Weighted LPTNO problem (a generalization of the well-studied LOTZ problem), and the well-studied COCZ problem, for studying the effect of recombination. Our analysis discloses that recombination may accelerate the filling of the Pareto front by recombining diverse solutions and thus help solve multi-objective optimization. Because of this, for these two problems, we find that a multi-objective EA with recombination enabled achieves a better expected running time than any known EAs with recombination disabled.We further examine the effect of recombination on solving the multi-objective minimum spanning tree problem, which is an NP-Hard problem. Following our finding on the artificial problems, our analysis shows that recombination also helps accelerate filling the Pareto front and thus helps find approximate solutions faster.

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Section: Our Contributionmentioning

confidence: 90%

“…The recent work by Neumann and Theile [35] is, to the best of our knowledge, the first and only work analyzing crossover operators in MOEAs. They proved that a crossover operator can speed up evolutionary algorithms for the multi-criteria all-pairs-shortest-path problem.…”

Section: Original Name Unified Name Explanationmentioning

confidence: 99%

An analysis on recombination in multi-objective evolutionary optimization

Qian

Zhou

2013

Artificial Intelligence

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“…However, studies so far have eluded the most fundamental setting of building-block functions. Crossover was proven to be superior to mutation only on constructed artificial examples like Jump k [9,12] and "Real Royal Road" functions [10,18], the H-IFF problem [2], coloring problems inspired by the Ising model from physics [5,19], and the all-pairs shortest path problem [3,22,17]. H-IFF [2] and the Ising model on trees [19] consist of hierarchical building blocks.…”

Section: Introductionmentioning

confidence: 99%

Crossover speeds up building-block assembly

Sudholt

2012

Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation

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We re-investigate a fundamental question: how effective is crossover in combining building blocks? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter we prove that a simple GA with uniform crossover is twice as fast as the fastest EA using only standard bit mutation, up to small-order terms. The reason is that crossover effectively turns neutral mutations into improvements by combining the right building blocks at a later stage. Compared to mutation-based EAs, this makes multi-bit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from 1/n to (1 + √ 5)/2 · 1/n ≈ 1.618/n. Similar results are proved for k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building-block functions.

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“…Speedups by crossover could be shown for coloring problems inspired by the Ising model [8,21] and for the all-pairs shortest path problem [3,5,4,16,11]. In terms of pseudo-Boolean optimization, most results were actually limited to artificial functions [13,22,19,20] constructed such that a theoretical analysis was possible.…”

Section: Introductionmentioning

confidence: 98%

How crossover helps in pseudo-boolean optimization

Kötzing

Sudholt

Theile

2011

Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation

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Understanding the impact of crossover on performance is a major problem in the theory of genetic algorithms (GAs). We present new insight on working principles of crossover by analyzing the performance of crossover-based GAs on the simple functions OneMax and Jump.First, we assess the potential speedup by crossover when combined with a fitness-invariant bit shuffling operator that simulates a lineage of independent evolution on a function of unitation. Theoretical and empirical results show drastic speedups for both functions.Second, we consider a simple GA without shuffling and investigate the interplay of mutation and crossover on Jump. If the crossover probability is small, subsequent mutations create sufficient diversity, even for very small populations. Contrarily, with high crossover probabilities crossover tends to lose diversity more quickly than mutation can create it. This has a drastic impact on the performance on Jump. We complement our theoretical findings by Monte Carlo simulations on the population diversity.

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How Crossover Speeds Up Evolutionary Algorithms for the Multi-criteria All-Pairs-Shortest-Path Problem

Cited by 28 publications

References 8 publications

An analysis on recombination in multi-objective evolutionary optimization

An analysis on recombination in multi-objective evolutionary optimization

Crossover speeds up building-block assembly

How crossover helps in pseudo-boolean optimization

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