### 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 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.... ..."

### 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.... ..."

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### Table 2. Results comparison of game calculation and multi-objective optimization Objective function Design variable

2005

### Table 2 gives examples of block values and active blocks, where k = 4 and m = 3. The following multi-objective function is essentially OneMax defined on the active block, weighted differently with respect to each objective as to create different Pareto optimal solutions.

"... In PAGE 6: ...x |x|0 |x|1 |x|2 |x|3 j f(x) 000 000 000 000 0 0 0 0 0 (1, 512) 111 011 010 001 3 2 1 1 2 (128, 16) 010 111 011 001 1 3 2 1 0 (2, 1024) 111 111 111 110 3 3 3 2 3 (1563, 3) 111 110 111 111 3 2 3 3 1 (24, 192) 111 111 111 111 3 3 3 3 0 (4, 2048) Table2 . Examples of block values, active blocks (underlined), and objective function values.... ..."

### Table 2: Comparing run times of the multi-objective algo- rithms (in seconds)

"... In PAGE 5: ...orithms on kn500.2, kn750.2, kn750.3 and kn750.4. These plots provide very strong evidence in favour of the HISAM. Finally, Table2 shows very clearly that HISAM has a very much faster run time than either SEAMO2 or MOGLS. MOGLS is particularly slow because of its frequent need to re-evaluate all the members of CS, the current list of solutions, with respect to their weighted linear scalarizing functions.... ..."

### Table 3. The average time for obtaining a solution for the multi-objective optimization problems by using TGP. The results are averaged over 30 independent runs.

"... In PAGE 13: ...igure 5. Diversity metric computed at every 10 generations. The results are averaged over 30 independent runs. Numerical values of the convergence and diversity metrics for the last generation are also given in section 9. 8 Running time Table3 is meant to show the efiectiveness and simplicity of the TGP algorithm by giving the time needed for solving these problems using a PIII Celeron computer at 850 MHz. Table 3 shows that TGP without archive is very fast.... In PAGE 13: ... 8 Running time Table 3 is meant to show the efiectiveness and simplicity of the TGP algorithm by giving the time needed for solving these problems using a PIII Celeron computer at 850 MHz. Table3 shows that TGP without archive is very fast. An average of 0.... ..."

### Table 4. Total model size (number of nodes) for the different methods (SO Single- Objective, MO Multi-Objective; Bag Bagging, RF Random Forest).

"... In PAGE 6: ... While the number of trees will be smaller for ensembles of MODTs (with a factor equal to the number of targets), the effect on the total number of nodes of all trees is less obvious. Table4 presents the results. We see that ensembles of MODTs yield smaller models, with an increased difference in the presence of many target attributes.... ..."

### Table 1: Tracking results for meeting1, for our approach and a traditional multi-object PF. Results are shown for individual people, and averaged over all people.

2005

"... In PAGE 6: ... In this sequence, recorded with no visual background clutter, four seated speakers are engaged in a conversation and talk at a relaxed pace, tak- ing turns with little overlap, which occurs for instance when people laugh. The last row in Table1 (SGT ) indicates the proportion of time during which each person spoke in the sequence, as labeled in the speaking activity GT. Regarding visual tracking, the four objects were tracked with good quality and stably throughout the sequence for all runs (see SR, TR, and FT rows in Table 1, and video meeting1 mcmc 500:avi).... In PAGE 6: ... The last row in Table 1 (SGT ) indicates the proportion of time during which each person spoke in the sequence, as labeled in the speaking activity GT. Regarding visual tracking, the four objects were tracked with good quality and stably throughout the sequence for all runs (see SR, TR, and FT rows in Table1 , and video meeting1 mcmc 500:avi). The algorithm can handle partial visual self-occlusion (e.... In PAGE 6: ... With respect to speaking activity, our source localization method, combined with the AV calibration procedure, has shown to be able to estimate location reasonably well, and detect speaker turns with good accuracy and low latency, when people talk at the meeting table [6]. The audio ac- tivity inferred by the MCMC-PF preserves these properties for those segments where only one speaker takes the turn, while smoothing out very short speaker turns with the dy- namical model (see FS row in Table1 ). Although we use a 1www:idiap:ch= gatica=av-tracking-multiperson:html: a b c Figure 3: Multispeaker tracking results, meeting1.... In PAGE 6: ... To study the e ciency of the MCMC-PF, we compare it with a traditional joint multi-object PF, which uses IS in- stead of MCMC, while all other aspects and parameters of the lter remain xed. Results are computed using 20 runs, and are shown in Table1 and video meeting1 pf 500:avi. Clearly, our approach outperforms the traditional PF in both ability to track and estimation of the speaking sta- tus.... ..."

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