Reply to the comments of Ganjavi et al

By picking a combination of four, three or two of these four restrictions, the following 11 cases are created: ð f1ðxÞ; f2ðxÞ; f3ðxÞ and f4ðxÞÞ; ð f1ðxÞ; f2ðxÞ and f3ðxÞÞ; ð f1ðxÞ; f2ðxÞ and f4ðxÞÞ; ð f1ðxÞ; f3ðxÞ and f4ðxÞÞ; ð f2ðxÞ; f3ðxÞ and f4ðxÞÞ; ð f1ðxÞ and f2ðxÞÞ; ð f1ðxÞ and f3ðxÞÞ; ð f1ðxÞ and f4ðxÞÞ; ð f2ðxÞ and f3ðxÞÞ; ð f2ðxÞ and f4ðxÞÞ and ð f3ðxÞ and f4ðxÞÞ: These 11 cases are examined and the results are presented in Table 1. Since Wi1⁄4 1 and Ki 1⁄4 b i ð8 i 2 I Þ; the ratio ðb i fiðxÞÞ=b i is computed as a measure of weighted and normalized deviation for all objectives of each case. It can be observed that for all six cases when two objectives are considered both ratios are the same. Out of four cases when three objectives are considered two cases result in a mismatch of ratios (ie the solution is not balanced). Finally, the only case with four objectives also resulted in a mismatch.