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Bartosz Frej

Publications and source records attributed to Bartosz Frej.

9 recordsLinked to original sources
arXiv2026

The hop-like problem nature -- unveiling and modelling new features of real-world problems

Benchmarks are essential tools for the optimizer's development. Using them, we can check for what kind of problems a given optimizer is effective or not. Since the objective of the Evolutionary Computation field is to support the tools to solve hard, real-world problems, the benchmarks that resemble their features seem particularly valuable. Therefore, we propose a hop-based analysis of the optimization process. We apply this analysis to the NP-hard, large-scale real-world problem. Its results indicate the existence of some of the features of the well-known Leading Ones problem. To model these features well, we propose the Leading Blocks Problem (LBP), which is more general than Leading Ones and some of the benchmarks inspired by this problem. LBP allows for the assembly of new types of hard optimization problems that are not handled well by the considered state-of-the-art genetic algorithm (GA). Finally, the experiments reveal what kind of mechanisms must be proposed to improve GAs' effectiveness while solving LBP and the considered real-world problem.

cs.NE↗
arXiv2025

Availability of Perfect Decomposition in Statistical Linkage Learning for Unitation-based Function Concatenations

Statistical Linkage Learning (SLL) is a part of many state-of-the-art optimizers. The purpose of SLL is to discover variable interdependencies. It has been shown that the effectiveness of SLL-using optimizers is highly dependent on the quality of SLL-based problem decomposition. Thus, understanding what kind of problems are hard or easy to decompose by SLL is important for practice. In this work, we analytically estimate the size of a population sufficient for obtaining a perfect decomposition in case of concatenations of certain unitation-based functions. The experimental study confirms the accuracy of the proposed estimate. Finally, using the proposed estimate, we identify those problem types that may be considered hard for SLL-using optimizers.

cs.NE↗
arXiv2019

Extensions of Full Shifts with Group Actions

We give a sufficient condition for a symbolic topological dynamical system with action of a countable amenable group to be an extension of the full shift, a problem analogous to those studied by Ashley, Marcus, Johnson and others for actions of $\mathbb{Z}$ and $\mathbb{Z}^d$ .

math.DS↗
arXiv2019

Exploding Markov operators

A special class of doubly stochastic (Markov) operators is constructed. These operators come from measure preserving transformations and inherit some of their properties, namely ergodicity and positivity of entropy, yet they may have no pointwise factors.

math.DS↗
arXiv2019

A comment on ergodic theorem for amenable groups

We prove a version of ergodic theorem for an action of an amenable group, where a Fø lner sequence needs not to be tempered. Instead, it is assumed that a function satisfies certain mixing condition.

math.DS↗
arXiv2018

Doubly stochastic operators with zero entropy

We study doubly stochastic operators with zero entropy. We generalize three famous theorems: the Rokhlin's theorem on genericity of zero entropy, the Kushnirenko's theorem on equivalence of discrete spectrum and nullity and the Halmos-von Neumann's theorem on representation of maps with discrete spectrum as group rotations.

math.DS↗
arXiv2015

Shearer's inequality and Infimum Rule for Shannon entropy and topological entropy

We review subbadditivity properties of Shannon entropy, in particular, from the Shearer's inequality we derive the "infimum rule" for actions of amenable groups. We briefly discuss applicability of the "infimum formula" to actions of other groups. Then we pass to topological entropy of a cover. We prove Shearer's inequality for disjoint covers and give counterexamples otherwise. We also prove that, for actions of amenable groups, the supremum over all open covers of the "infimum fomula" gives correct value of topological entropy.

math.DS↗
arXiv2014

Minimal models for actions of amenable groups

We prove that on a metrizable, compact, zero-dimensional space every free action of an amenable group is measurably isomorphic to a minimal $G$-action with the same, i.e. affinely homeomorphic, simplex of measures.

math.DS↗