Pareto ranking

Assign efficiency value to solutions based on Pareto-rank While Not Stop Condition ... 

Pareto-ranking. The individuals list of scores is subjected to a Pareto-ranking procedure to set the rank of each individual. According to this procedure the rank of an individual is set to the number of individuals that dominate it incremented by 1, thus, non-dominated individuals are assigned rank order 1. 

Fig. 2 Pareto ranking and dominance for a two-objective problem, minimising/ and/2. A non-dominated individual is one for which there is no other individual that is better in all objectives. In Pareto ranking, an individual s rank corresponds to the number of individuals in the current population by which it is dominated. Solutions A and B are given rank 0 since they are nondominated, whereas solution C is given rank 2 since it is dominated by both A and B...

In MoQSAR, MOGP [52, 54] is used to overcome the limitations of using a weighted-sum fitness function. The approach is similar to the MOGA approach described earlier where multiple objectives are handled independently without summation and without weights and Pareto ranking is used to identify a Pareto-optimal set of solutions. Pareto ranking was shown previously in Fig. 2. 

Multi-objective de novo design by Pareto-ranking and genetic operators on molecular graph-based chromosomes... 

In a more recent study, Hinchliffe and Willis (2003) model dynamic systems using genetic programming. The new approach is evaluated using two case studies, a test system with a time delay and an industrial cooking extruder. The objectives minimized are the root mean square error and the correlation and autocorrelations between residuals. The residuals of a model represent the difference between the predicted and actual values of the process output. In this work, two MOGPs are compared, one based on Pareto ranking but without preferences, and... 

FIGURE 9.5 Histogram of the average Pareto rank binned by the chronologically ordered date of experiment. The Pareto rank reaches lower (=better) values as the project proceeded in time (2004-2007), demonstrating that optimization was effective overall however, the candidate compound was a Pareto suboptimal solution. 

FIGURE 9.6 (a) Average Pareto rank binned by chronologically ordered chemical arrays,... 

Shifting the focus to chemotypes rather than arrays. Figure 9.6b summarizes the overall effectiveness of the six different chemotypes explored over the timeUne of Project A. This plot illustrates the chanotypes that gave consistently better Pareto ranks. For example, the exploration around the chanical classes C and E (colored in yellow and green, respectively) did not deliver and were therefore abandoned early in the project. Chemotype D gave comparatively better compounds but it was also abandoned after the discovery of chanotype A. Conversely, chemotypes A and B (red and bine) were consistently successful in terms of average Pareto ranks it is no surprise that the drug candidate came from chanotype A. 

Based on the Pareto ranking of effects on the objective function, the key decision variables are chosen. For the DME process, the methanol cost is high, but there are assumed to be no by-product reactions. The product DME is assumed to be at its purity specification. The only methanol loss is in the waste water thus, the purity of the bottoms product of T-202 could be a decision variable. At present, approximately 0.27% of the methanol feed leaves in the waste water. Thus, the target savings attainable can be calculated as 30,300/yr. 

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