Optimization Strategies in Complex Systems

TL;DR

This paper analyzes the performance of different optimization algorithms in complex combinatorial systems across various scientific domains, focusing on their dynamics and system size effects.

Contribution

It introduces a comparative analysis of greedy, reluctant, and stochastic convex interpolation algorithms in complex systems, highlighting their performance characteristics.

Findings

Greedy algorithm decreases quickly along the gradient.

Reluctant algorithm decreases slowly near level curves.

Stochastic convex interpolation balances the two approaches.

Abstract

We consider a class of combinatorial optimization problems that emerge in a variety of domains among which: condensed matter physics, theory of financial risks, error correcting codes in information transmissions, molecular and protein conformation, image restoration. We show the performances of two algorithms, the``greedy'' (quick decrease along the gradient) and the``reluctant'' (slow decrease close to the level curves) as well as those of a``stochastic convex interpolation''of the two. Concepts like the average relaxation time and the wideness of the attraction basin are analyzed and their system size dependence illustrated.