# Elite Opposition-Based Social Spider Optimization Algorithm for Global Function Optimization
## 2 The Social Spider Optimization Algorithm
### Computational Procedure
In proposing this technique, some definitions are clearly defined below:

### Opposite number

Let \(p\in[x,y]\) be a real number. The opposite number of \(p(p^{*})\) is defined by:

\[p^{*}=x+y-p \tag{14}\]

### Opposite point

Let \(p=(s_{1},s_{2},\ldots,s_{n})\) be a point in \(n\)-dimensional search space, where \(p_{r}\in[x_{r},y_{r}]\) and \(r=\{1,2,\ldots,n\}\). The opposite point is defined by

\[p_{r}^{*}=x_{r}+y_{r}-p_{r} \tag{15}\]

### Opposition based population initialization

By utilizing opposite points, a suitable starting candidate solution may be obtained even when there is not a priori knowledge about the solution. The main steps of the proposed approach are listed as follows:

**Step 1**: Initialize the population set in a random manner. **Step 2**: Calculate opposite population by:

\[op_{a,b}=x_{b}+y_{b}-p_{a,b} \tag{16}\]

where \(a=1,2,\ldots,N\), \(b=1,2,\ldots,n\) and \(p_{a,b}\) and \(op_{a,b}\) denote the \(b\)th variable of the \(a\)th vector of the population and opposite population, respectively. **Step 3**: Select the fittest \(N\) individuals from \(\{p\cup op\}\) as initial population. ### Opposition based generation jumping

If we apply similar approach to the current population, the whole evolutionary process can be forced to jump to a new solution candidate who is more suitable than the current one. From thiscomparison, the fittest \(N\) individuals are selected. In each generation, search space is reduced to calculate the opposite points, i.e.,

\[op_{a,b}=Min_{b}^{gn}+Max_{b}^{gn}-p_{a,b} \tag{17}\]

where \(a=1,2,\ldots,N\) and \(b=1,2,\ldots,n\). \([Min_{b}^{gn},Max_{b}^{gn}]\) is the current interval in the population which is becoming increasingly smaller than the corresponding initial range \([x_{b},y_{b}]\). ### Global Elite Opposition-Based Learning Strategy (GEOLS)

The Social Spider Optimization algorithm use cooperation among female groups in global search process. It is simulated by changes in the position of female spiders. As we know that it is a stochastic process, the probability of getting a good solution is relatively low. For increasing the probability of obtained a better solution to the problem in global search process and expand the searching space, this strategy is applied to the proposed EOSSO. Elite opposition-based Learning is a new technique in the field of intelligence computation. Its main ideology is: for a feasible solution, calculate and evaluate the opposite solution at the same time, and choose the better one as the individual of next generation. In this paper, individual with the best fitness value in the population is viewed as the elite individual. For explaining the definition of elite opposition-based solution, an example should be exhibited. If we suppose that the elite individual of the population is \(X_{e}=(x_{e,1},x_{e,2},\ldots,x_{e,n})\). For the individual \(X_{i}=(x_{i,1},x_{i,2},\ldots,x_{i,n})\), the elite opposition-based solution of \(X_{i}\) which can be defined as \(X_{i}^{*}=(x_{i,1}^{*},x_{i,2}^{*},\ldots,x_{i,n}^{*})\). In addition, it can be obtained by following equation:

\[r=\frac{\sum\limits_{j=1}^{n}p_{j}^{\mathit{high}}-p_{j}^{\mathit{low}}}{2n}\]0

where \(N\) is the population size, \(n\) is the dimension of \(X\), \(k\in U(0,1)\) and \((da_{j}db_{j})\) is the dynamic bound of \(j\)th decision variable. \(da_{j},db_{j}\) can be obtained by following equation:

\[r=\frac{\sum\limits_{j=1}^{n}p_{j}^{\mathit{high}}-p_{j}^{\mathit{low}}}{2n}\]1

As we know that the shrink of searching space may cause algorithm stuck in local minimal. Thus, in this proposed algorithm, we will update \(da_{j}\) and \(db_{j}\) every 50 generations. Dynamic bound is good at restoring searching experience. However, it can make \(x_{i,j}^{*}\) jump out of \((da_{j}db_{j})\), if that happened, equation below should be used to reset \(x_{i,j}^{*}\).