### Table 1. Results of the comparison between algorithms on a 64-bit H-IFF problem. Two of the algorithms are multi-objective and use the MH-IFF decomposition of the problem, namely PAES and PESA. The other three algorithms use the H-IFF objective function directly. Essentially the results compare two single-point hill-climbers, SHC and PAES, and two multi-point hill-climbers, DCGA and PESA. In both cases, the multi-objective algorithm signi cantly outperforms (using any statistical test) its SOO counterpart. The results of the simulated annealing algorithm (SA) act as a benchmark, indicating the level of performance that can be achieved when escape from local optima is made possible on the original landscape. The columns, `% one apos; and `% both apos;, indicate the percentage of the runs where respectively one of the optima and both optima were found over the thirty independent runs of each algorithm. Note that only PAES and PESA are able to nd both optima. Algorithm pm best mean % one % both

2001

"... In PAGE 10: ... For the simulated annealing algorithm, preliminary runs were performed and T0 and Tf were adjusted until the acceptance probabilities fell into the required ranges described in Section 3. Table1 shows the full set of results collected on the 64-bit H-IFF problem. In each case, the results were gathered from 30 independent runs of the algorithm.... ..."

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### TABLE II SET COVERAGE BETWEEN MOEA/D (A) AND MOGLS (B)

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### TABLE V SET COVERAGE BETWEEN NSGA-II AND MOEA/D

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### 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 3: Multi-objective oorplanning results with performance (P), maximum block tem- perature (T), area (A), wirelength (W), and runtime reported. The LP+SA-based oor- planner is used. Temperature is in C. Whitespace (WS) is reported as a percentage. 2D oorplan

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"... In PAGE 35: ... The weighting numbers used in [12] are unknown and so this accounts for the variation in these parameters. Table3 presents a comparison of the performance (P), temperature (T), area (A), wire- length (W), and runtime of 4 di erent objective functions for the 2D and 3D cases. All data in this table are taken from the combined LP+SA approach.... In PAGE 37: ...Table3 is the pipeline depth and whitespace percentages for the various objective functions. Pipeline depth is calculated by adding in the number of ip ops inserted between the major stages of the basic simplescalar pipeline.... In PAGE 37: ... One can observe that there is a 15% reduction in IPC and a 22% reduction in temperature between the performance-only objective (0) and the highest weight hybrid objective (20) for the 3D case. As expected and also shown in Table3 the multi-layer oorplans increase both the temperature and IPC over the single layer oorplans. Also of note is that the highest thermal weight multi-layer oorplan has a temperature close to that of the lowest thermal weight single layer oorplan while achieving a higher IPC.... ..."

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

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"... 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 I lists the value of N and H in MOEA/D for each test instance. For the instances with 2 objectives, the value N is the same as that of S in MOGLS. For all the instances with three objective, H = 25 and therefore N = 351. For all the instances with four objectives, H = 12 and then N = 455. Both of the algorithms stop after 500 S calls of the repair method. In our experimental studies, both gws and gte have been used in the repair method. In the following, W-MOEA/D (W- MOGLS) stands for MOEA/D (MOGLS) in which gws is used, while T-MOEA/D (T-MOGLS) represents MOEA/D (MOGLS) in which gte is used.

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### Table 3. Reservoir descriptions. Reservoir

"... In PAGE 7: ...able 2. Sacramento Basin regional precipitation............................................................................. 3 Table3 .... In PAGE 10: ... Table 1 lists the regions that the Sacramento River drains along with their approximate drainage areas. Table3 lists the drainage areas above each of the principal flood control reservoirs ... ..."

### 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.... ..."

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### 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.... ..."

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