Work

Simplicity and Complexity in Combinatorial Optimization

Year: 2026

Type: article

Abstract: Many problems in physics and computer science can be framed in terms of combinatorial optimization. Due to this, it is interesting and important to study theoretical aspects of such optimization. Here, we study connections between Kolmogorov complexity, optima, and optimization. We argue that (1) optima and complexity are connected, with extrema being more likely to have low complexity (under certain circumstances); (2) optimization by sampling candidate solutions according to algorithmic probability may be an effective optimization method; and (3) coincidences in extrema to optimization problems are a priori more likely as compared to a purely random null model.

Source: Entropy

DOI: 10.3390/e28020226

Authors: Kamal Dingle, Marcus Hutter

Institutions: Gulf University for Science & Technology, Australian National University, Google DeepMind (United Kingdom)

Language: English

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: California Institute of Technology, Division of Mathematical Sciences