# Metaheuristics for Min-Power Bounded-Hops Symmetric Connectivity Problem

## TL;DR

This paper addresses the NP-hard problem of constructing energy-efficient communication trees with bounded hops in Euclidean space, proposing heuristic algorithms based on metaheuristics and comparing their performance.

## Contribution

It introduces novel heuristic algorithms using genetic local search, variable neighborhood search, and ant colony optimization for the problem.

## Key findings

- Heuristic algorithms effectively approximate solutions for the NP-hard problem.
- Comparative analysis shows differences in performance among the proposed metaheuristics.
- Results demonstrate the practicality of metaheuristics in energy-efficient network design.

## Abstract

We consider a Min-Power Bounded-Hops Symmetric Connectivity problem that consists of the construction of communication spanning tree on a given graph, where the total energy consumption spent for the data transmission is minimized and the maximum number of edges between two nodes is bounded by some predefined constant. We focus on the planar Euclidian case of this problem where the nodes are placed at the random uniformly spread points on a square and the power cost necessary for the communication between two network elements is proportional to the squared distance between them. Since this is an NP-hard problem, we propose different heuristics based on the following metaheuristics: genetic local search, variable neighborhood search, and ant colony optimization. We perform a posteriori comparative analysis of the proposed algorithms and present the obtained results in this paper.