.. _algorithms-chapter:

==========
Algorithms
==========

Argonaut supports three algorithm modes in the tested deployment.

Tree-Based Iterative
====================

Tree-Based Iterative runs an I-EPOS style tree topology based optimization. Agents are organized in a hierarchical communication tree and the branching factor controls the number of children per internal node.

This mode is intended for decentralized optimization without enumerating the full combinatorial decision space. It produces an execution trace across iterations rather than only a final solution.

Brute Force Exhaustive Search
=============================

Brute Force Exhaustive search enumerates all feasible collective solutions and evaluates their objective values. It is suitable for small datasets only. The simulator warns that brute force tests every plan combination and is suitable for small datasets, up to about 1 million combinations in the current UI warning.

For the tested Gaussian subset, the decision space contained:

.. math::

   2 \times 2 \times 2 = 8

solutions.

The Brute Force log is divided into:

* Part 1: brute force enumeration of all solutions.
* Part 2: EPOS from all starting positions, which checks whether each start reaches the optimum.

Both Tree-Based + Brute Force
=============================

Both mode runs Tree-Based Iterative and Brute Force in one workflow. It is useful for small problem instances where users want to compare the tree based solution against the complete solution space and report its optimality rank.

For the tested case, Both mode displayed:

* Tree-Based final global cost, unfairness, local cost, and weighted total cost.
* Brute Force combinations tested, best global cost, best local cost, success rate, and optimal selection.
* A combined log containing I-EPOS logs followed by Brute Force logs.
* A Tree-Based visualizer with Brute Force comparison fields, including ``Best BF GC`` and ``GC Rank``.