Tootfinder

Worst-Case Complexity of High-Order Algorithms for Pareto-Front Reconstruction
Andrea Cristofari, Marianna De Santis, Stefano Lucidi, Giampaolo Liuzzi
https://arxiv.org/abs/2506.11929

Worst-Case Complexity of High-Order Algorithms for Pareto-Front Reconstruction
In this paper, we are concerned with a worst-case complexity analysis of a-posteriori algorithms for unconstrained multiobjective optimization. Specifically, we propose an algorithmic framework that generates sets of points by means of $p$th-order models regularized with a power $p+1$ of the norm of the step. Through a tailored search procedure, several trial points are generated at each iteration and they can be added to the current set if a decrease is obtained for at least one objective func…

A First Runtime Analysis of the PAES-25: An Enhanced Variant of the Pareto Archived Evolution Strategy
Andre Opris
https://arxiv.org/abs/2507.03666 https:/…

A First Runtime Analysis of the PAES-25: An Enhanced Variant of the Pareto Archived Evolution Strategy
This paper presents a first mathematical runtime analysis of PAES-25, an enhanced version of the original Pareto Archived Evolution Strategy (PAES) coming from the study of telecommunication problems over two decades ago to understand the dynamics of local search of MOEAs on many-objective fitness landscapes. We derive tight expected runtime bounds of PAES-25 with one-bit mutation on $m$-LOTZ until the entire Pareto front is found: $Θ(n^3)$ iterations if $m=2$, $Θ(n^3 \log^2(n))$ iterations i…

Constraining Nuclear Mass Models Using r-process Observables with Multi-objective Optimization
Mengke Li, Matthew Mumpower, Nicole Vassh, William Samuel Porter, Rebecca Surman
https://arxiv.org/abs/2506.06464

Constraining Nuclear Mass Models Using r-process Observables with Multi-objective Optimization
Predicting nuclear masses is a longstanding challenge. One path forward is machine learning (ML) which trains on experimental data, but can suffer large errors when extrapolating toward neutron-rich species. In nature, such masses shape observables for the rapid neutron capture process (r-process), which in principle could inform ML models. Here we introduce a multi-objective optimization approach using the Pareto Front algorithm. We show that this technique, capable of identifying models which…

ROBBO: An Efficient Method for Pareto Front Estimation with Guaranteed Accuracy
Roberto Boffadossi, Marco Leonesio, Lorenzo Fagiano
https://arxiv.org/abs/2506.18004

ROBBO: An Efficient Method for Pareto Front Estimation with Guaranteed Accuracy
A new method to estimate the Pareto Front (PF) in bi-objective optimization problems is presented. Assuming a continuous PF, the approach, named ROBBO (RObust and Balanced Bi-objective Optimization), needs to sample at most a finite, pre-computed number of PF points. Upon termination, it guarantees that the worst-case approximation error lies within a desired tolerance range, predefined by the decision maker, for each of the two objective functions. Theoretical results are derived, about the wo…

This https://arxiv.org/abs/2312.10290 has been replaced.
link: https://scholar.google.com/scholar?q=a

Runtime Analysis of the SMS-EMOA for Many-Objective Optimization
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 of the bi-objective OJZJ benchmark. We prove that SMS-EMOA computes the full Pareto front of this benchmark in an expected number of $O(μM n^k)$ iterations, where $n$ denotes the problem size (length of the bit-string representation), $k$ the gap size (a difficulty parameter of the problem), $M=(2n/m-2k+3)^{m/2}$ the size of the Par…