## 3 Proposed Improved Hybrid SSA with an EDO (ISSAEDO) Algorithm
### Exponential Distribution Optimization (EDO) Algorithm
* **Computational efficiency**: Exponential distribution is known for its rapid sampling and assessment capabilities, rendering it a valuable tool in simulation research and computational modeling. The inverse transform method is a technique that can be employed to generate samples from exponential distribution with low computational requirements. * **Parameter estimation**: The MLE is a straightforward approach utilized to estimate the parameters of exponential distribution based on observed data. The utilization of real-world data believed to be derived from an exponential distribution can be advantageous as it facilitates the estimation of distribution parameters based on the data. * **Relationship to other distributions**: Exponential distribution shows close relationships with other probability distributions, such as Gamma distribution and Weibull distribution. Exponential distribution can be utilized as a fundamental element in models that involve complex structures and incorporate several probability distributions. The proposed EDO utilizes the following methodologies in order to effectively investigate the global optimal search space. Initially, a collection of solutions is generated through a random process, encompassing a diverse spectrum of values. The search process can be described as having exponential distributions, which means that the positions of all solutions can be considered as random variables that follow exponential distribution. * To replicate the memoryless characteristic, a matrix is created and initialized with the identical value as the initial population. * By employing the exploratory and exploitative phases of the suggested approach, all solutions gradually converge towards the global optimum. * During the exploitation phase, the memoryless matrix is employed to simulate the memoryless property. This property allows for previously generated solutions, regardless of their past, to serve as influential members in updating new solutions, thereby preserving their established knowledge. Consequently, the responses are categorized into two distinct groups: those deemed as winners and those classified as losers. Furthermore, the utilization of the mean, exponential rate, and variance of the exponential distribution is observed in several contexts. The victorious entity progresses toward the guiding solution in order to explore the global optimum in its vicinity, whereas the defeated entity travels toward the victorious entity. * In order to enhance the exploration phase, the mean solution and two randomly chosen winners from the initial population are employed for the update process. The average response and variability exhibit significant deviation from the optimal global solution at the outset. The discrepancy between the average response and the universally optimal solution is progressively diminished through the process of optimization until it reaches a minimum value. The switch parameter mentioned above is employed with a probability of 0.5 to determine whether to execute the exploration phase or the exploitation phase. \[V_{i}^{time+1}=\left\{ \begin{array}{l}a\cdot(memoryless_{i}^{time}-\sigma^{2 })\\ +b\cdot Xguide^{time}\\ ifXwinners_{i}^{time}=memoryless_{i}^{time}\\ b\cdot(memoryless_{i}^{time}-\sigma^{2})\\ +\log(\phi)\cdot Xwinners_{i}^{time},\quad otherwise\\ Xwinners_{i}^{time}-M^{time}\\ +(c\cdot Z_{1}+(1-c)\cdot Z_{2})\quad,\;\;otherwise.\end{array} \right.\] (18)
* After being generated, the perimeter of each newly obtained solution is analyzed. The user's responses are then stored in a matrix with no memory. * The original population is updated by including new solutions obtained through the utilization of a greedy method during both exploitation and exploration stages. If the new solution proves to be successful, the original population undergoes updates. In the event that the newly proposed solution demonstrates efficacy, it results in the modification of the original population.