## 3 Proposed ATMALS-GSK Algorithm
### Atmals-Gsk  
As previously discussed, the original GSK algorithm is highly sensitive to a set of manually defined controllable parameters: \(K_{f}\), \(K_{r}\), \(K\), and \(P\). These parameters were originally set to fixed values based on empirical tuning as \(K\) = 10, \(K_{f}\) = 0.5, \(K_{r}\) = 0.9, and \(P\) = 0.1. However, this trial-and-error approach is not only time-consuming and tedious but also inconsistent and difficult to generalize across different problems. One of the key limitations of the original GSK is its reliance on these static parameter settings, which inherently restrict the ability of the algorithm to adaptively balance exploitation and exploration throughout the search process. This rigid configuration can result in suboptimal performance, particularly when tackling complex problems. Several underlying issues contribute to this limitation:  
* Lack of generalizability across problem domains: Fixed parameter values might yield strong results for a particular problem but often fail to perform well across different problem settings or objective landscapes. What works for a scheduling problem, for instance, may underperform in a continuous optimization task. * Inflexibility across search stages: The same parameter values are used throughout the entire execution of the algorithm, from the initial exploration phase to the final convergence phase. However, different phases of the search process typically benefit from different behaviors--strong exploration in early generations and refined exploitation in later ones. Static parameters fail to accommodate this shift, potentially leading to premature convergence or excessive wandering. * No feedback from historical performance: The original GSK lacks a learning mechanism to leverage past search experience. Without any form of memory or adaptive control, the algorithm is unable to assess the effectiveness of different parameter configurations over time. This absence of self-tuning prevents the algorithm from evolving and improving its own strategy dynamically. To overcome the mentioned challenges, there is a need to design an adaptive historical memory-based version of GSK that can iteratively adjust and update its parameters in response to the current state of the search process, based on the problem specifications. This kind of smart tuning would make the algorithm more flexible, robust, and capable of handling a wider range of problems more effectively. To fill this gap, the proposed ATMALS-GSK algorithm introduces a new framework that combines automatic parameter tuning, memory-based learning, and adaptive local search into the GSK structure. The key idea is to boost GSK's performance by learning from past experiences and adjusting its behavior accordingly. Unlike the original GSK algorithm, ATMALS-GSK does not rely on fixed parameter settings. Instead, it uses a Gaussian-based mechanism to dynamically update the selection probabilities of different parameter values, based on how well they have performed in the past. A memory-guided RWS method, using a weighted moving average, helps the algorithm gradually favor more effective parameter settings over time. It is important to note that the ATMALS-GSK algorithm uses a memory-guided RWS strategy to adapt parameter values--not to select individuals, as is typically performed in traditional algorithms like GA. Specifically, this RWS utilizes a Gaussian-weighted moving average to intelligently guide the selection of optimal values for five key parameters: \(K_{f}\), \(K_{r}\), \(K\), \(P\), and \(P_{LS}\). By integrating memory-driven adaptation into the parameter control process, the algorithm enhances its ability to fine-tune performance in a data-driven and responsive manner. In addition, ATMALS-GSK applies an adaptive local search to the top-performing (senior) solutions. This helps avoid getting stuck in local optima and ultimately leads to better results.