## 3 Proposed Improved Hybrid SSA with an EDO (ISSAEDO) Algorithm
### Exponential Distribution Optimization (EDO) Algorithm  
The exponential distribution model provided the basis for inspiration. Exponential distribution is a type of continuous probability distribution that is commonly used to model the time it takes for an event to happen. An algorithm, also referred to as an exponential distribution algorithm, is a set of instructions or a computer program specifically designed to produce random numbers following exponential distribution. Exponential distribution is a commonly employed probability distribution for modeling the time intervals between events that transpire at a consistent rate, in a random and independent manner. There exist multiple methodologies for generating random numbers that follow exponential distribution. The inverse transform method involves the generation of a random variable, \(u\), that follows a uniform distribution on the interval \([0,1]\). This random variable is subsequently transformed using the inverse cumulative distribution function (CDF) of exponential distribution. The CDF of an exponential distribution can be expressed as follows: \(F(x)=1-\exp^{(-\lambda x)}\), where \(\lambda\) represents the rate parameter and \(x\) denotes the time variable. The inverse of the CDF can be expressed as follows: \(F^{-1}(u)=-\log\Bigl{(}\frac{1-u}{\lambda}\Bigr{)}\), where \(u\) represents a random variable that follows a uniform distribution between 0 and 1. The aforementioned methodology has the potential to be perpetually extended in order to generate a set of random integers that adhere to exponential distribution. There are other methodologies available for generating random numbers that follow exponential distribution. Presented below are a few illustrations of various methodologies. * **Inverse Transform Method**: The CDF of an exponential distribution can be mathematically reversed to derive the corresponding quantile function, which serves as the fundamental principle for this approach. The quantile function is a mathematical tool that provides the value of a random variable at which a specified probability is surpassed. The quantile function for the exponential distribution can be expressed as \(Q(p)=-\log\Bigl{(}\frac{1-p}{\lambda}\Bigr{)}\), where \(p\) represents the probability and \(\lambda\) denotes the rate parameter. In order to generate a random number from an exponential distribution, the process involves generating a uniform random number, \(u\), that falls within the range of 0 to 1. Subsequently, the inverse quantile function formula is applied to derive the corresponding exponential random variable. The aforementioned methodology has the potential to be extended indefinitely in order to generate a random set of numbers that adhere to exponential distribution. * **Box-Muller Transform**: This approach is designed to produce random numbers from a normal distribution, but it can also be used to generate random numbers from exponential distribution. * **Acceptance-Rejection Method**: The proposed approach involves the generation of random numbers from a less complex distribution, followed by a decision-making process where these numbers are accepted or rejected based on a comparison with the probability density function (PDF) of the exponential distribution. One commonly chosen alternative for a simpler distribution is uniform distribution. The selection of these approaches may be influenced by the characteristics of the data and the computational resources at hand, leading to their preference in particular situations. The EDO algorithm operates in the following manner:  
* A pair of uniform random numbers \((u_{1},u_{2})\) is generated between 0 and 1. * Exponential random variable \(x\) can be computed as \(x=-\log\bigl{(}\frac{u_{1}}{\lambda}\bigr{)}\).