# Selection of Random Walkers that Optimizes the Global Mean First-Passage Time for Search in Complex Networks

## TL;DR

This paper presents a genetic algorithm-based method to optimize the placement of multiple random walkers in complex networks, minimizing search overlap and improving the efficiency of finding targets.

## Contribution

It introduces a novel optimization approach using genetic algorithms to select initial positions of walkers, reducing overlap and enhancing search performance in complex networks.

## Key findings

- Effective reduction of overlap in random walkers' search paths.
- Successful application to WS and BA network models.
- Guidance for setting up multi-walker search strategies.

## Abstract

We design a method to optimize the global mean first-passage time (GMFPT) of multiple random walkers searching in complex networks for a general target, without specifying the property of the target node. According to the Laplace transformed formula of the GMFPT, we can equivalently minimize the overlap between the probability distribution of sites visited by the random walkers. We employ a mutation only genetic algorithm to solve this optimization problem using a population of walkers with different starting positions and a corresponding mutation matrix to modify them. The numerical experiments on two kinds of random networks (WS and BA) show satisfactory results in selecting the origins for the walkers to achieve minimum overlap. Our method thus provides guidance for setting up the search process by multiple random walkers on complex networks.