## 2 Literature Review
### Variants of ICA  
In the literature, many new operations have been proposed to enhance the basic operations in ICA. For example, [PERSON] [28] introduced three new features into the original ICA. In each generation, a portion of the colonies are replaced by the same number of randomly generated new candidate solutions, through the _revolution_ operation. When two imperialist are too close to each other,their empires are united as one, through the _unite_ operation. Finally, instead of competition in every generation, the frequency of competition among empires is reduced to avoid converging too quickly.  
Instead of using the revolution operation to replace a portion of colonies in every generation, [PERSON] _et al._[29] suggested monitoring the minimal cost and average cost of all countries, and if the minimal cost and the difference between the average cost and the minimal cost are below their respective user-specified thresholds, then a random number of countries in the population are replaced by new countries, generated using a chaotic sequence. [PERSON] and [PERSON] [30] suggested using a genetic algorithm to generate new countries for the revolution operation. [PERSON] _et al._[31] suggested applying genetic algorithm and ICA recursively to benefit from the search power of both algorithms.  
The assimilation operation of ICA often converges to a local optimum prematurely [29, 30, 32], and thus many attempts have been proposed to replace it with more powerful operations. For examples, [PERSON] _et al._[33] used a chaotic map to determine the moving direction for the assimilation operation. [PERSON] _et al._[34] defined the assimilation operation as a two-step process. First, each colony is moved precisely toward their imperialists. Then, some randomly chosen colonies are moved further in all dimensions to improve diversity. [PERSON] _et al._[35] replaced Equation (4) with Equation (8) below to allow some colonies moving away from their imperialists:  
\[\boldsymbol{p}^{c}=\boldsymbol{p}^{c}+(\beta\times\boldsymbol{\delta}- \boldsymbol{1})\times(\boldsymbol{p}^{i}-\boldsymbol{p}^{c}) \tag{8}\]  
They also suggested bouncing the out-of-bound values (e.g., \(x_{i}\) on the \(i\)-th dimension) into the feasible space using Equation (9), instead of sticking them to the nearest boundary.  
\[x_{i}=\begin{bmatrix}x_{i}&\boldsymbol{\text{if}}&L_{i}\leq x_{i}\leq U_{i} \\ 2U_{i}-(x_{i}-\left\lfloor\frac{x_{i}-U_{i}}{U_{i}-L_{i}}\right\rfloor(U_{i}-L _{i}))&\boldsymbol{\text{if}}&x_{i}>U_{i}\\ 2L_{i}-(x_{i}+\left\lfloor\frac{L_{i}-x_{i}}{U_{i}-L_{i}}\right\rfloor(U_{i}-L _{i}))&\boldsymbol{\text{if}}&x_{i}\leq L_{i}\end{bmatrix} \tag{9}\]  
[PERSON] _et al._[26] indicated that the assimilation operation is a primitive form of Particle Swarm Optimization (PSO), and thereby suggested replacing the assimilation operation with PSO. Similarly, [PERSON] _et al._[13] replaced the assimilation operation with an Electromagnetism-like Algorithm. [PERSON] and [PERSON] [36] applied ICA as the local search mechanism in a memetic algorithm. [PERSON] _et al._[37] proposed an assimilation operation adaptive to the distribution of colonies to balance between the exploration and exploitation abilities of ICA.