Erratum to "Dominance-Based Multiobjective Simulated Annealing"

For original paper see Z. Tu et al., ibid., vol. 8, no.5, p.456-70, (2004). We have recently discovered an error in the programming of the stochastic genetic algorithm (StGA). The main program was written in C++ except for a subroutine which was coded in MATLAB. This particular subroutine was used to generate the NS number of stochastic children for a chromosome. The NS stochastic children were stored in an array S (NS x N), where N is the dimension of a function. The array S was called into the main program in the form of a vector s with entries being taken column-wise from S (i.e., s[(j - 1) x NS + i] = S[i][j]). In the implementation of the local selection, the vector was supposed to be converted back to S in exactly the reverse manner. But unfortunately the statement was mistakenly written as S[i][j] = s[(i - 1) x N + j]. This error causes a distortion in the variable arrangement such that a typical stochastic child tends to have segments of similar values for different dimensions. Incidentally, for most of the 20 test functions, which have also been used by other researchers in a previous publication, the global optimum is at a position where all variables are equal. As a result, the StGA exhibited a false accelerated convergence speed in a surprisingly consistent manner in all the test cases. After the correction of the above programming error, the StGA as presented in the paper exhibits very different performance and in many cases could not achieve as satisfactory results.