Stagnation detection meets fast mutation

Doerr, Benjamin; Rajabi, Amirhossein

doi:10.1016/j.tcs.2022.12.020

Cited by 12 publications

(2 citation statements)

References 27 publications

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“…For the bi-objective OJZJ benchmark, again a speed-up of k Ω(k) was proven when optimized via the GSEMO (Zheng and Doerr 2023d) and the NSGA-II (Doerr and Qu 2023a). Several other positive theoretical results exist for this heavy-tailed mutation, or more generally, other heavy-tailed parameter choices (Friedrich, Quinzan, and Wagner 2018;Wu, Qian, and Tang 2018;Quinzan et al 2021;Corus, Oliveto, and Yazdani 2021;Dang et al 2022;Antipov, Buzdalov, and Doerr 2022;Doerr, Ghannane, and Ibn Brahim 2022;Doerr and Rajabi 2023).…”

Section: Heavy-tailed Mutationmentioning

confidence: 92%

Runtime Analysis of the SMS-EMOA for Many-Objective Optimization

Zheng,

Doerr

2024

AAAI

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The widely used multiobjective optimizer NSGA-II was recently proven to have considerable difficulties in many-objective optimization. In contrast, experimental results in the literature show a good performance of the SMS-EMOA, which can be seen as a steady-state NSGA-II that uses the hypervolume contribution instead of the crowding distance as the second selection criterion. This paper conducts the first rigorous runtime analysis of the SMS-EMOA for many-objective optimization. To this aim, we first propose a many-objective counterpart, the m-objective mOJZJ problem, of the bi-objective OJZJ benchmark, which is the first many-objective multimodal benchmark used in a mathematical runtime analysis. We prove that SMS-EMOA computes the full Pareto front of this benchmark in an expected number of O(M^2 n^k) iterations, where n denotes the problem size (length of the bit-string representation), k the gap size (a difficulty parameter of the problem), and M=(2n/m-2k+3)^(m/2) the size of the Pareto front. This result together with the existing negative result on the original NSGA-II shows that in principle, the general approach of the NSGA-II is suitable for many-objective optimization, but the crowding distance as tie-breaker has deficiencies. We obtain three additional insights on the SMS-EMOA. Different from a recent result for the bi-objective OJZJ benchmark, the stochastic population update often does not help for mOJZJ. It results in a 1/Θ(min(Mk^(1/2)/2^(k/2),1)) speed-up, which is Θ(1) for large m such as m>k. On the positive side, we prove that heavy-tailed mutation still results in a speed-up of order k^(0.5+k-β). Finally, we conduct the first runtime analyses of the SMS-EMOA on the bi-objective OneMinMax and LOTZ benchmarks and show that it has a performance comparable to the GSEMO and the NSGA-II.

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Section: Heavy-tailed Mutationmentioning

confidence: 92%

Runtime Analysis of the SMS-EMOA for Many-Objective Optimization

Zheng,

Doerr

2024

AAAI

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“…The majority of results on evolutionary algorithms concern mutation-based algorithms. Results derived from the Jump benchmark suggest that higher mutation rates or a heavy-tailed random mutation rate [20] as well as a stagnation-detection mechanism [24,[54][55][56] can speed up leaving local optima. Some examples have been given where elitist crossover-based algorithms coped remarkably well with local optima [2,8,37,58], but it is not clear to what extent these results generalize [66].…”

Section: Previous Workmentioning

confidence: 99%

How Well Does the Metropolis Algorithm Cope With Local Optima?

Doerr

Houssaini

Rajabi

et al. 2023

Proceedings of the Genetic and Evolutionary Computation Conference

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The Metropolis algorithm (MA) is a classic stochastic local search heuristic. It avoids getting stuck in local optima by occasionally accepting inferior solutions. To better and in a rigorous manner understand this ability, we conduct a mathematical runtime analysis of the MA on the CLIFF benchmark. Apart from one local optimum, cliff functions are monotonically increasing towards the global optimum. Consequently, to optimize a cliff function, the MA only once needs to accept an inferior solution. Despite seemingly being an ideal benchmark for the MA to profit from its main working principle, our mathematical runtime analysis shows that this hope does not come true. Even with the optimal temperature (the only parameter of the MA), the MA optimizes most cliff functions less efficiently than simple elitist evolutionary algorithms (EAs), which can only leave the local optimum by generating a superior solution possibly far away. This result suggests that our understanding of why the MA is often very successful in practice is not yet complete. Our work also suggests to equip the MA with global mutation operators, an idea supported by our preliminary experiments. CCS CONCEPTS• Theory of computation → Theory of randomized search heuristics.

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