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Participants' problem-solving performance was operationalized by the sum of ratios of achieved scores to maximum scores (in terms of relative scores for each category).
The TCID50 titer was calculated by using KARBER statistical method: T TCID50 titer = 10×101 + d(S − 0.5)/ml, in which d is the log 10 of the dilution and S is the sum of ratios from the first dilution.
Tables 1 and 2 also provide 95% confidence intervals derived from Gaussian approximations of the distribution of the sum of strata frequencies or sum of ratios of strata frequencies.
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In this study, we propose a harmony search algorithm for solving a sum-of-ratios problem.
The sum-of-ratios problems have numerous applications in economy and engineering.
Jaberipour and Khorram (2010) proposed algorithm for the sum-of-ratios problem-based harmony search algorithm.
The sum-of-ratios problems are considered to be difficult, as these functions are highly nonconvex and multimodal.
Notice that the detailed complexity analysis of the proposed algorithm can be used as an indicator of the difficulty of some optimization problems, such as multiplicative programs, sum-of-ratios optimization, etc.
Multiplicative objective functions arise in a variety of practical applications, such as economic analysis [2], robust optimization [3], VLSI chip design [4], combination optimization [5], etc. Sum-of-ratios (SOR) optimization: SOR functions have the form (G y_{1},ldots,y_{p}) =sum_{i=1}^{p}y_{i}) with (y_{i}=frac{c_{i}^{top}x+c_{0i}}{d_{i}^{top}x+d_{0i}}).
Moreover, the sum-of-ratio form in the objective function (4) makes the problem more intractable.
Finally, for each category, each ratio is centred by the sum of all ratios.
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