Load Balancing Based on Firefly and Ant Colony Optimization Algorithms for Parallel Computing
Abstract
:1. Introduction
2. Related Work
3. Background and Problem Statement
3.1. Background
3.1.1. Parallel Computing
3.1.2. Gragh and Bioinspired Algorithms
3.2. Problem Statement
4. Methods and Models
4.1. MultiLevel Algorithm for Partitioning Graphs
4.2. Firefly Algorithm
4.3. Ant Colony Optimization
5. Proposed Method
5.1. The FaCO Principle
5.2. Algorithm Flow
5.2.1. Algorithm Logic Diagram
5.2.2. Algorithm Pseudocode
Algorithm 1 FaCO algorithm. 
Input: m, I${}_{0}$, ${\beta}_{0}$, $\gamma $, p, Q, $\alpha $, $\beta $′, $\rho $, Max ▹ Initialization parameters Output: global extreme value points and optimal individual values

5.2.3. Algorithm Flow Chart
6. Experiment and Analysis
6.1. Parameter Setting
6.2. Experiment Analysis
7. Conclusions
8. Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Name of Parameter  Meaning of Parameters  Remarks  Experimental Values 

m  Firefly population size  1.5 times the number of cities  60 
I${}_{0}$  Absolute brightness of fireflies  Objective function value correlation; the better the value of the objective function, the higher the brightness of their own  Determined by the initial position of the firefly 
${\beta}_{0}$  The maximum attractiveness of fireflies  The maximum attractiveness of fireflies when $r=0$  Generally set to 1 
$\gamma $  Firefly light absorption coefficient  0.4  
p  Colony population size  1.5 times the number of cities  60 
Q  Colony pheromone constant  Usually takes the value of [10, 1000]  20 
$\alpha $  Colony pheromone factor  Range usually: [0.5, 1]  0.5 
$\beta $′  Ant colony heuristic function factor  Range of values: [0, 5]  2 
$\rho $  Ant colony pheromone volatility factor  Range of values usually: [0.4, 0.7]  0.69 
Max  Maximum number of iterations  1000  
r  Distance between two points  
${W}_{1}$  Ant colony position update weight  0.35  
${W}_{2}$  Firefly position update weight  0.65 
TSP Arithmetic Example  Firefly Algorithm Results  FaCO Algorithm Results  Particle Swarm Algorithm Results  Genetic Algorithm 

Burma14  44.129  30.8785  32.7  30.847 
Oliver30  956.26  864.37  897.4  906.57 
eil51  1436.788  807.175  823.6  842.1 
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Li, Y.; Li, J.; Sun, Y.; Li, H. Load Balancing Based on Firefly and Ant Colony Optimization Algorithms for Parallel Computing. Biomimetics 2022, 7, 168. https://doi.org/10.3390/biomimetics7040168
Li Y, Li J, Sun Y, Li H. Load Balancing Based on Firefly and Ant Colony Optimization Algorithms for Parallel Computing. Biomimetics. 2022; 7(4):168. https://doi.org/10.3390/biomimetics7040168
Chicago/Turabian StyleLi, Yong, Jinxing Li, Yu Sun, and Haisheng Li. 2022. "Load Balancing Based on Firefly and Ant Colony Optimization Algorithms for Parallel Computing" Biomimetics 7, no. 4: 168. https://doi.org/10.3390/biomimetics7040168