# Fast re-optimization via structural diversity

@article{Doerr2019FastRV, title={Fast re-optimization via structural diversity}, author={Benjamin Doerr and Carola Doerr and Frank Neumann}, journal={Proceedings of the Genetic and Evolutionary Computation Conference}, year={2019} }

When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that evolutionary algorithms, despite usually being robust problem solvers, can have unexpected difficulties to solve such re-optimization problems. When started with a random Hamming neighbor of the optimum, the (1+1) evolutionary algorithm takes Ω(n2) time to optimize…

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## References

SHOWING 1-10 OF 54 REFERENCES

A new analysis method for evolutionary optimization of dynamic and noisy objective functions

- Computer ScienceGECCO
- 2018

The results suggest that the typical way to find the optimum in such adverse settings is not via a steady approach of the optimum, but rather via an exceptionally fast approach after waiting for a rare phase of low dynamic changes or noise.

A Theory and Algorithms for Combinatorial Reoptimization

- Mathematics, Computer ScienceAlgorithmica
- 2017

A general framework for combinatorial repotimization is developed, encompassing classical objective functions as well as the goal of minimizing the transition cost from one solution to the other, distinguishing here for the first time between classes of reoptimization problems by their hardness status with respect to the objective of minimizing transition costs.

Reoptimization times of evolutionary algorithms on linear functions under dynamic uniform constraints

- Computer Science, MathematicsGECCO
- 2017

This paper studies the classical (1+1) EA and population-based algorithms and shows that they recompute an optimal solution very efficiently and that a variant of the (1+(λ, λ)) GA can recompute the optimal solution more efficiently in some cases.

Maintaining 2-Approximations for the Dynamic Vertex Cover Problem Using Evolutionary Algorithms

- Mathematics, Computer ScienceGECCO
- 2015

This paper examines a dynamic version of the classical vertex cover problem and analyse evolutionary algorithms with respect to their ability to maintain a 2-approximation and points out that the third approach is very effective in maintaining 2- approximations for the dynamic vertex coverproblem.

Runtime analysis of randomized search heuristics for the dynamic weighted vertex cover problem

- Computer ScienceGECCO
- 2018

A dynamic model of the classic Weighted Vertex Cover problem is presented and the performances of the two well-studied algorithms Randomized Local Search and (1+1) EA adapted to it are analyzed to contribute to the theoretical understanding of evolutionary computing for problems with dynamic changes.

Better Runtime Guarantees via Stochastic Domination

- Computer ScienceEvoCOP
- 2018

This work argues that stochastic domination is a notion that should be used more frequently in this area of runtime analysis, and proves a fitness level theorem which shows that the runtime is dominated by a sum of independent geometric random variables.

On the robustness of evolutionary algorithms to noise: refined results and an example where noise helps

- Mathematics, Computer ScienceGECCO
- 2018

The (1+1) EA on LeadingOnes is much more sensitive to noise than previously thought and offspring populations of size λ ≥ 3.42 log n can effectively deal with much higher noise than known before.

Design and analysis of migration in parallel evolutionary algorithms

- Computer ScienceSoft Comput.
- 2013

A first rigorous runtime analysis for island models is performed and a function where phases of independent evolution as well as communication among the islands are essential is constructed, leading to new insights into the usefulness of migration, how information is propagated in island models, and how to set parameters such as the migration interval.

On the Performance of Baseline Evolutionary Algorithms on the Dynamic Knapsack Problem

- Computer SciencePPSN
- 2018

The results show that the multi-objective approaches using a population that caters for dynamic changes have a clear advantage on many benchmarks scenarios when the frequency of changes is not too high.

Analyzing Evolutionary Algorithms

- Computer ScienceNatural Computing Series
- 2013

The author provides an introduction to the methods used to analyze evolutionary algorithms and other randomized search heuristics with a complexity-theoretical perspective, derives general limitations for black-box optimization, yielding lower bounds on the performance of evolutionary algorithms.