# Hunger Games Search Optimization Algorithm
## Hunger Games Search (HGS)

Hunger Games Search (HGS) was proposed in 2021. It is a performance-based swarm optimization method, which shows strong performance compared to various optimizers and DE variants in benchmark problems.

## Mathematical Model
### Approach Food

To express the approaching behavior mathematically, the following formulas are proposed to imitate the contraction mode:
${\vec {X}}(t+1)={\vec {X}}(t)\cdot \left(1+{\text{randn}}(1)\right),{\text{ if }}r_{1}<l$ ${\vec {X}}(t+1)={\vec {W}}_{1}\cdot {\vec {X}}_{b}+{\vec {R}}\cdot {\vec {W}}_{2}\cdot {\vec {X}}_{b}-{\vec {X}}(t),{\text{ if }}r_{1}>l{\text{ and }}r_{2}>E$ ${\vec {X}}(t+1)={\vec {W}}_{1}\cdot {\vec {X}}_{b}-{\vec {R}}\cdot {\vec {W}}_{2}\cdot {\vec {X}}_{b}-{\vec {X}}(t),{\text{ if }}r_{1}>l{\text{ and }}r_{2}\leq E$
where:
* ${\vec {X}}(t)$ – Position of the individual at iteration $t$
* ${\vec {W}}_{1}$ and ${\vec {W}}_{2}$ – Weights of hunger
* ${\vec {X}}_{b}$ – Location information of a random individual in all optimal individuals
* ${\text{randn}}(1)$ – Random number satisfying normal distribution
* $r_{1},r_{2}$ – Random numbers in the range $[0,1]$
* $l$ – Threshold value
* $E={\text{sech}}(|F(i)-BF|)$
The formula for $E$ is: $E={\text{sech}}(|F(i)-BF|)$ where:
* $F(i)$ – Fitness value of each individual
* $BF$ – Best fitness obtained in the current iteration
* ${\text{sech}}(x)={\frac {2}{e^{x}+e^{-x}}}$

### Hunger Role

The hunger characteristics of individuals are simulated mathematically.
The formula for ${\vec {W}}_{1}(i)$ is: ${\vec {W}}_{1}(i)={\begin{cases}{\text{hungry}}(i)\cdot {\frac {N}{\text{SHungry}}}\cdot r_{4},&{\text{if }}r_{3}<l\\1,&{\text{if }}r_{3}\geq l\end{cases}}$
The formula for ${\vec {W}}_{2}(i)$ is: ${\vec {W}}_{2}(i)=\left(1-\exp \left(-|{\text{hungry}}(i)-{\text{SHungry}}|\right)\right)\cdot r_{5}\cdot 2$
where:
* ${\text{hungry}}(i)$ – Hunger of individual $i$
* $N$ – Number of individuals
* ${\text{SHungry}}$ – Sum of hunger feelings of all individuals
* $r_{3},r_{4},r_{5}$ – Random numbers in the range $[0,1]$
The formula for ${\text{hungry}}(i)$ is: ${\text{hungry}}(i)={\begin{cases}0,&{\text{if }}{\text{AllFitness}}(i)=BF\\{\text{hungry}}(i)+H,&{\text{if }}{\text{AllFitness}}(i)\neq BF\end{cases}}$
The formula for $H$ is: $H={\frac {F(i)-BF}{WF-BF}}\cdot r_{6}\cdot 2\cdot ({\text{UB}}-{\text{LB}})$ $H={\begin{cases}{\text{LH}}\cdot (1+r),&{\text{if }}TH<{\text{LH}}\\TH,&{\text{if }}TH\geq {\text{LH}}\end{cases}}$ where:
* $r_{6}$ – Random number in the range $[0,1]$
* $F(i)$ – Fitness value of each individual
* $BF$ – Best fitness obtained in the current iteration
* $WF$ – Worst fitness obtained in the current iteration
* ${\text{UB}}$ and ${\text{LB}}$ – Upper and lower bounds of the search space
* ${\text{LH}}$ – Lower bound of hunger sensation

## = Algorithm

The pseudo-code for the HGS algorithm is as follows:

## Applications of Hunger Games Search Optimizer

The Hunger Games Search (HGS) optimizer has been applied in a variety of domains to enhance the performance of various systems and processes. Below are some notable applications:

### Modeling and Optimization

* Friction Stir Welding Process: AbuShanab et al. (2021) proposed a fine-tuned random vector functional link model enhanced by the Hunger Games Search optimizer to model the friction stir welding process of polymeric materials. This approach demonstrated improved accuracy in predicting the welding outcomes and process parameters.
* Photovoltaic Solar Cells: Xu et al. (2022) utilized a Quantum Nelder-Mead Hunger Games Search algorithm to optimize the performance of photovoltaic solar cells. This method achieved superior optimization results, enhancing the efficiency and performance of solar cell systems.

### Predictive Modeling

* Ground Vibration Intensity: Nguyen and Bui (2021) developed a Hunger Games Search Optimization-based artificial neural network to predict ground vibration intensity induced by mine blasting. This model provided more accurate predictions, benefiting the safety and planning of mining operations.
* Brain Tumor Classification: Emam et al. (2023) applied an improved Hunger Games Search Algorithm to optimize deep learning architectures for brain tumor classification. The optimized architecture led to enhanced classification accuracy, which is crucial for early diagnosis and treatment.

### Control Systems and Feature Selection

* Load Frequency Control: Fathy et al. (2022) designed a robust fractional-order PID controller for load frequency control using a modified Hunger Games Search optimizer. This approach improved the stability and performance of the power grid control systems.
* Feature Selection: Ma et al. (2022) employed a multi-strategy ensemble binary Hunger Games Search for feature selection. This method significantly enhanced the feature selection process, leading to better performance in machine learning applications.

### Environmental and Sustainability Applications

* Biomass Distributed Generators: Nassef et al. (2023) applied a modified Hunger Games Search to optimize the allocation of biomass distributed generators. This optimization aimed to reduce CO2 emissions, contributing to environmental sustainability.
* Shrinkage Prediction in SLS Parts: Zhang et al. (2022) integrated a novel hybrid improved Hunger Games Search optimizer with an extreme learning machine to predict shrinkage in Selective Laser Sintering (SLS) parts. This integration led to more accurate predictions and better quality control in manufacturing.

### Global Optimization and High-Dimensional Feature Selection

* Global Optimization: Chen et al. (2023) introduced an artificial bee bare-bone Hunger Games Search for global optimization and high-dimensional feature selection. This approach facilitated improved optimization results in complex, high-dimensional problems.