## 4 ITLCO Algorithm
### Improved Scheme
#### 4.2.2 Incremental Pheromone Update Model  
In the realm of dynamic optimization problems, such as the optimal scheduling of power systems, the static pheromone model inherent in the traditional TLCO algorithm confronts substantial challenges. Firstly, the fixed evaporation rate therein impedes the pheromones from promptly adapting to sudden alterations in the objective function. This limitation gives rise to the problem of environmental lag response, where the algorithm fails to promptly react to changes in the dynamic environment. Secondly, the persistence of old pheromone residues has the potential to misguide the search trajectory of the population. This phenomenon not only results in a decline of more than 50% in convergence efficiency but also entraps the algorithm in a situation where historical experience becomes obsolete. As a consequence, the algorithm's ability to efficiently explore and converge towards the optimal solution is severely compromised. (1) Design of incremental pheromone update model  
To enhance the performance of the TLCO algorithm in dynamic environments, a mechanism for detecting environmental changes is introduced to perceive the dynamic changes of the environment in real time. Based on the detected environmental change information, the evaporation rate of pheromones can be adaptively adjusted, and this adjustment is carried out in the form of dynamic evaporation rate regulation. \[\rho(\imath)=\rho_{\text{base}}+\alpha_{m}\cdot\frac{\Delta f_{\text{best}}}{f _{\text{best}}(\imath)} \tag{44}\]  
where \(\Delta f_{\text{best}}=|f_{\text{best}}(\imath)-f_{\text{best}}(\imath-\Delta \imath)|\) represents the change in the best fitness value and \(\alpha_{m}\) represents the sensitivity coefficient (the range of 0.1-0.5). When a drastic change is detected, the evaporation rate is triggered to double, written as follows:  
\[\rho(\imath)\leftarrow\min(0.99,2\rho(\imath)) \tag{45}\]  
After the dynamic evaporation rate adjustment, pheromone incremental deposition is carried out. The procedure involves using a sliding window mechanism, where only the information from the most recent \(\imath_{m}\) generations is retained. \[E_{\hbar\ell}(\imath)=\sum_{\imath_{\imath}=\imath-\imath_{m}+1}^{\imath} \Delta E_{\hbar\ell}(\imath_{n})\cdot e^{-\Gamma(\imath-\imath_{m})} \tag{46}\]  
where \(\Gamma\) is a decay factor (range: 0.05-0.2) and \(\Delta E_{\hbar\ell}(\imath_{n})\) is the pheromone increment of path \(\hbar\ell\) in the \(\imath_{n}\)-th generation. After completing the pheromone incremental deposition, monitor environmental mutations based on the entropy of the population fitness distribution. The formula is as follows:  
\[H(\imath)=-\sum_{i=1}^{N}p_{i}\log p_{i},p_{i}=\frac{f(X_{i})}{\sum f(X_{j})} \tag{47}\]When the condition \(\left|H(t)-H(t-\Delta t)\right|>0.6H(t-\Delta t)\) is met, it is determined that the environment has changed, and the pheromone reset is triggered. (2) Online learning architecture implementation  
After the incremental pheromone update model is designed, the online learning architecture is constructed next. It is divided into three steps: (1) real-time pheromone update; (2) environment perception and parameter adjustment; and (3) sliding window maintenance. The pseudocode for real-time pheromone updates is shown in Table 1.  
The pseudocode for environment perception and parameter adjustment is shown in Table 2.