### State-of-the-Art
The current bit string is replaced by the new one if the fitness of the current bit string is not superior to the fitness of the new string. In their work, [PERSON] and [PERSON] made the study on performance of the \((1+1)\)-EA [79] and compared other evolutionary algorithms to the \((1+1)\)-EA [80]. In [80], the authors studied the conditions under which \((1+1)\)-EA is competitive with other evolutionary algorithms (EAs) in terms of the distribution of the fitness function at a given iteration and relative to the average optimization time. Their approach is applicable when the \((1+1)\)-EA mutation operator prevails in the reproduction operator of the evolutionary algorithm. In this case, the lower bounds obtained for the expected optimization time of \((1+1)\)-EA can be extended to other EAs based on the dominant operator. They proved that under the domination condition it is an optimal search technique with respect to the probability of finding solutions of sufficient quality after a given number of iterations. In the case of domination, the \((1+1)\)-EA is also preferable with respect to the expected fitness at any iteration and the expected optimization time. Reference [81] considers the scenario of the \((1+1)\)-EA and randomized local search (RLS) with memory. The authors present two new algorithms: \((1+1)\)-EA-m (with a raw list and hashtable option) and RLS-m+ (and RLS-m if the function is known in advance to be unimodal). These algorithms can be regarded as very simple forms of tabu search. Empirical results, with a reasonable fitness evaluation time assumption, verify that \((1+1)\)-EA-m and RLS-m+ are superior to their conventional counterparts. In paper [82], the authors investigate the \((1+1)\)-EA for optimizing functions over the space \(\{0,...,r\}^{n}\), where r is a positive integer. They show that for linear functions over \(\{0,1,2\}^{n}\), the ex pected runtime of this algorithm is \(O(n\)\(\log n)\). This result generalizes an existing result on pseudo-Boolean functions and is derived using drift analysis. They also show that for large values of \(r\), no upper bound for the runtime of the \((1+1)\)-EA for linear function on \(\{0,...,r\}^{n}\) can be obtained with this approach nor with any other approach based on drift analysis with weight-independent linear potential functions. In [83], the authors investigate the performance of the \((1+1)\)-EA, on the maximum independent set problem (MISP) from a theoretical point of view. They showed that the \((1+1)\)-EA can obtain an approximation ratio of \((\Delta+1)/2\) on this problem in expected time \(O(n^{4})\), where \(\Delta\) and \(n\) denote the maximum vertex degree and the number of nodes in a graph, respectively. They reveal that the \((1+1)\)-EA has better a performance than the local search algorithm on an instance of MISP and demonstrate that the local search algorithm with 3-flip neighborhood will be trapped in local optimum while the \((1+1)\)-EA can find the global optimum in expected running time \(O(n^{4})\). In [84], the authors theoretically investigate the approximation performance of the \((1+1)\)-EA, on the minimum degree spanning tree (MDST) problem which is a classical NP-hard optimization problem and show its capability of obtaining an approximate solution for the MDST problem with a limited maximum degree in expected polynomial time. In [85], the authors analyze the expected runtime of the \((1+1)\)-EA solving robust linear optimization problems (i.e., linear problems under robust scenarios) with a cardinality constraint. They consider two common robust scenarios, i.e., deletion-robust and worst-case, and disclose the potential of \((1+1)\)-EAs for robust optimization. An interesting approach was proposed in [86]. The authors propose a \((1+1)\)-fast evolutionary algorithm (\((1+1)\)-FEA) with an original approach to the adjustment of the mutation rate.