### Table 2. Recognition rates (%) of feature extrction/selection methods on synthetic data sets with multi-objective (M.O.) annotations

in Vol. 23 no. 5 2007, pages 589–596 BIOINFORMATICS ORIGINAL PAPER doi:10.1093/bioinformatics/btl680

"... In PAGE 6: ...M.E.) situation. Recognition rates in Table2 are in general lower than those in Table 1. This shows the difficulty of building the automatic annotation system for fly embryo pattern images that are usually multi- objective.... ..."

### Table 1. An list of all objectives that are used for the multi-objective evolution of oscilla- tors from scratch. Zero crossings and am- plitudes are always measured relative to the mean output voltage. Occurring periods are calculated from those zero crossings.

in A Modular Framework for the Evolution of Circuits on Configurable Transistor Array Architectures.

### Table 4: Results for CVRP as a multi-objective problem.

"... In PAGE 24: ... This is the reason why we run 30 times our multi-objective GA (denoted as GAm), compute the average result and standard deviation for each instance, and compare them to the ones obtained with our single-objective GA. Results are shown in Table4 . For each method, the best result in all runs, the average of the best results, the standard deviation, and the relative difference between the best known result and the average of the best results are given.... ..."

### Table 4: Results of Multi-objective Experiments. Method Pareto

2007

"... In PAGE 6: ... Table 3: Results of Multimodal Experiments. Function SGA SGA with elite Tabu-GA Rastrigin 829/829/1 141/497/5 73/264/10 FMS- parameters -/-/0 126/282/2 143/608/10 Table4 shows the results of some multi-objective experiments, where Pareto is the number of Pareto optima and (n) is the tabu list size. While Ranking Selection GA gets six Pareto solutions on the frontier line of Pareto optima, Tabu-GA can get flexible and diverse Pareto solutions depending on a tabu list size.... ..."

### Table 2.1 2.3.2 Single- and Multi-Objective problems Quite often, the engineering problems require, that several contradicting criterions are satisfied simultaneously. Thus, it is suitable to refer to them as multi-objective problems. Example for such a problem in the Control Theory is the controller synthesis, where we want to have both minimal error between the set value and the system output, and control effort as small (economical) as possible.

### Table 3. Density estimation techniques in multi-objective evolutionary algorithms and operators used in this study.

2001

"... In PAGE 11: ... Many advanced multi-objective evolutionary algorithms use some form of density dependent selection. Furthermore, nearly all techniques can be expressed in terms of density estimation, a classification is given in Table3 . We will make use of this as a further step towards a common framework of evolutionary multi-objective optimizers, and present the relevant enhancement of the unified model.... ..."

Cited by 20

### Table 3. Density estimation techniques in multi-objective evolutionary algorithms and operators used in this study.

2001

"... In PAGE 11: ... Many advanced multi-objective evolutionary algorithms use some form of density dependent selection. Furthermore, nearly all techniques can be expressed in terms of density estimation, a classification is given in Table3 . We will make use of this as a further step towards a common framework of evolutionary multi-objective optimizers, and present the relevant enhancement of the unified model.... ..."

Cited by 20

### Table 4: Multi-objective search trace for the safety-critical example.

2000

"... In PAGE 22: ...Table 5: E ects of over-constraining in the control application. Table4 shows how the search progresses in the multi-objective optimization of the safety-critical application. In the table it can be seen that in the rst found solution, the load-balancing objective is estimated to have reached 92 percent of its optimal value while the lateness only has reached 10 percent.... In PAGE 23: ... It would be interesting to see if such reformulation is possible. As can be seen in Table4 , the multi-objective optimization strategy obtains an optimal value (20) of the communication. However, the estimated proximity of the communication in the optimal solution is only 66 percent.... ..."

Cited by 3

### Table 4. Fuzzy systems of nonlinear plant.

"... In PAGE 9: ... The interpretability-driven simplification methods and the multi-objective genetic algorithm are used to optimize the initial fuzzy system. The performance of the obtained four Pareto-optimal fuzzy systems is described in Table4 . The decision-marker can choose an appropriate fuzzy system according to a specific situation, either the one with higher interpretability (less number of fuzzy rules or/and fuzzy sets) or the one with less error.... In PAGE 9: ... The decision-marker can choose an appropriate fuzzy system according to a specific situation, either the one with higher interpretability (less number of fuzzy rules or/and fuzzy sets) or the one with less error. Table4 also shows the comparison with other published results, which indicates that the proposed -2 -1.5 -1 -0.... ..."

### Table 2. Results of the our proposed multi-objective approach after 1-hour runtime

2007

"... In PAGE 13: ...99 and the num ber of iterations within SA to be 1,000,000. Table2 lists the re- sults of using different evaluation functions on the obtained solutions. For the weighted-sum objective function, we use the sam e set of weight values as in formula (29), and list the num - ber of archived non-dom inated solutions (see colum n 2) and the best solution under this evaluation function (see colum n 3).... In PAGE 14: ...Table 2. Results of the our proposed multi-objective approach after 1-hour runtime A ccording to the results in Table2 , we can see that our proposed approach is very prom ising in solving the m ulti-objective nurse scheduling problem . In terms of the solution quality evaluated by the sam e objective function, our approach performs similar to the IP-based VNS, and significantly improve the best results of the hybrid genetic algorithm and the hybrid VNS by 25.... ..."