# An Approach for Deployment of Service-Oriented Simulation Run-Time Resources
## 5 Simulation Run-Time Resources Deployment Algorithm
### The LGASRD Algorithm
#### 5.1.2 Elite Knowledge  
Elitist refers to the individual in a population that has the highest fitness value, e.g., the optimal objective function, from the start of evolution until now. It possesses the best genetic structure and excellent traits. To prevent the destruction or loss of elitists in the current population during subsequent iterative optimization processes, the elite retention strategy should be adopted, which involves adding an elitist from each generation to the Elite Population (EP). [PERSON] has theoretically proven that the standard genetic algorithm with elite retention strategy is globally convergent [34]. Therefore, we use the individuals in EP, called elite knowledge, to guide the subsequent optimization. There are two aspects to consider when using elite knowledge: updating EP and migrating elitists.  
The size of EP is \(\mathbb{E}\), and the top \(\mathbb{E}\) individuals from the first generation population can be selected to form the first generation EP. Starting from the second-generation population, if there is an individual A in the current population that is superior to one of the individuals in EP, we replace this elitist with A. In the multi-objective stage, we consider that individual A is superior to individual B if one of the following three conditions is met:  
* Condition 1: \[\begin{split} f_{1}(A)&\leq f_{1}(B)\\ f_{2}(A)&\leq f_{2}(B)\\ A&\
otin EP\end{split}\] (23)
* Condition 2: \[\begin{split} f_{1}(A)&<f_{1}(B)\\ f_{2}(A)&\geq f_{2}(B)\\ \frac{f_{1}(B)-f_{1}(A)}{f_{1}(B)}&>\frac{f_{2}(A)- f_{2}(B)}{f_{2}(B)}\\ randp&<1-\frac{f_{2}(A)-f_{2}(B)}{f_{2}(B)} \frac{f_{1}(B)}{f_{1}(B)-f_{1}(A)}\end{split}\] (24)* Condition 3: \[\begin{split}& f_{1}(A)\geq f_{1}(B)\\ & f_{2}(A)<f_{2}(B)\\ &\frac{f_{1}(A)-f_{1}(B)}{f_{1}(B)}<\frac{f_{2}(B)-f_{2}(A)}{f_{2}( B)}\\ & randp<1-\frac{f_{1}(A)-f_{1}(B)}{f_{1}(B)}\frac{f_{2}(B)}{f_{2}(B)-f_{2}(A)} \end{split}\] (25) where \(randp\) is a randomly generated probability. Equation (23) represents the case that A dominates B and no individual the same as A is in EP. Equations (24) and (25) mean that although A does not perform well in terms of \(f_{1}\) or \(f_{2}\), it performs exceptionally well in terms of another objective function. Take Equation (24) as an example, it indicates that although A is worse (larger) than B in terms of \(f_{2}\), it is better (smaller) than B in terms of \(f_{1}\) and the degree to which A is smaller than B for \(f_{1}\) is greater than the degree to which B is smaller than A for \(f_{2}\).  
In addition to trying to replace the inferior individuals in EP with outstanding ones in the current population to ensure the excellence of EP, we hope to use EP to guide the subsequent optimization process, e.g., elite migration. Every ten rounds of iteration in the second stage, we randomly select an elitist located in the top Pareto rank of EP and replace one individual in the lowest Pareto rank in the current population with it. This approach can bring the population closer to EP to some extent and accelerate the algorithm's convergence speed without too much loss of diversity within the population.