### 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 1. Formulation of the multi-objective problems used Problem Deflnition Constraints

2006

Cited by 1

### Table 3: Multi-objective optimisation algorithms based on simulated annealing. Dominance energy Volume energy

"... In PAGE 92: ...based or volume based) and whether the search is exploratory (computational temperature T gt; 0) or greedy (T = 0). Table3 summarises greedy and exploratory algorithms using dominance and volume energies, together with single solution and set states, which are described in this section; their performance on standard test problems is compared in section 4.4.... In PAGE 99: ... Results on MOSA and SAMOSA give a direct comparison of single solution states against set states, while dominance based and volume based energy measures are compared via the SAMOSA and VOLMOSA algorithms. As displayed in Table3 , the temperature zero versions of the algorithms are denoted by MOSA0 and SAMOSA0. Performance is evaluated on well-known test functions from the literature, namely the DTLZ test suite problems 1-6 [Deb et al.... ..."

### 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: 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 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.... ..."

Cited by 9

### Table 2. Dataset properties: domain name, number of instances (N), number of input attributes (Attr), number of target attributes (T), and whether used as multi-objective classification (Class) or regression (Regr) dataset.

"... In PAGE 4: ... 4.2 Datasets Table2 lists the datasets that we use, together with their properties. Most datasets are of ecological nature.... ..."