### 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 1 Comparison of core/periphery fitness measures using Beck et al. (2003; ND) data

2004

"... In PAGE 5: ....P Boyd, W.J. Fitzgerald, R.J. Beck/Social Networks columns 4 and 5 of Table1 . Column 6 of Table 1 compares the results from the UCINET (Version 6.... In PAGE 5: ... For all 12 groups, all three of these algorithms matched the exhaustive search by consistently finding the global optimum from several starting configurations. [ Table1 about here] From the results in Table 1, the genetic algorithm in UCINET finds the global optimum in two out of our 12 cases. The UCINET fit statistic is among the five best for seven of the 12 cases, and among the ten best for nine of the 12 cases.... In PAGE 5: ... For all 12 groups, all three of these algorithms matched the exhaustive search by consistently finding the global optimum from several starting configurations. [Table 1 about here] From the results in Table1 , the genetic algorithm in UCINET finds the global optimum in two out of our 12 cases. The UCINET fit statistic is among the five best for seven of the 12 cases, and among the ten best for nine of the 12 cases.... In PAGE 7: ... A low probability along with an intuitively high observed fitness value suggests that the observed data may have a core/periphery structure. To illustrate this permutation test, we used Mathematica to program a random permutation generator based upon the observed within group distribution of messages for each of the 12 groups from Table1 . As with the observed data, diagonal cells were also ignored for these permutations.... In PAGE 7: ... For Group 1, for example, no random permutation in each of the 3 runs produced an optimal fitness value equal to or greater than the observed fitness value of 0.867 (see Table1 ). For Group 3, 43 of the random permutations in the first run produced optimal fitness values equal to or greater than the observed fitness value (0.... ..."

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### Table 2: Simulated annealing amp; genetic algorithm--constrained optimization

"... In PAGE 4: ... The confidence intervals for 95% confidence level were calculated for both the algorithms. Table2... ..."

### Table 3: Simulated annealing in connection with shift neighborhood.

2001

"... In PAGE 15: ... It is notable, that iterated steepest descent, even when restricted to a running time of 10 seconds, solves all problem instances with 20 jobs to optimality. Table3 shows the results of applying simulated annealing, in connection with the 8The running times for steepest descent, which are not shown in the table, are below one second for all but the largest problem instances. The running times for the instances with 200 jobs are about 10 seconds when starting from the identity permutation vs.... ..."

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### Table 3 Evaluation of simulated annealing for small networks (M = N = 9).

"... In PAGE 18: ... For this experiment, we set p = 1 and P = 0:5. In Table3 , we compare simulated annealing with the optimal solution. The results for simulated annealing are shown for di erent values of the repetition factor Repmax.... In PAGE 18: ... The results for simulated annealing are shown for di erent values of the repetition factor Repmax. The rst column of Table3 gives the value of the repetition factor. The second column gives the average deviation of simulated annealing results from the optimal solution, averaged over 100 repetitions of the exper- iment.... ..."

### TABLE VII. OVERALL RESULTS FOR THE MULTIOBJECTIVE OPTIMIZATION - AVERAGED BY

### Table 1: Number of Function Evaluations of selected problems using DE, DE-QN, SA and TS

"... In PAGE 11: ... By trial and error, incorporating QN into DE at 500 iterations was found to be the most computationally efficient. As seen from Table1 , the number of function evaluations required for solving the benchmark problems by DE-QN is considerably reduced compared to just using DE alone, indicating the local optimizer (QN) is able to locate the global minimum efficiently when DE has done the hard work at the beginning. Thus, DE is successfully combined with QN to reduce the computational time while maintaining the reliability.... ..."

### Table 17. Simulated Annealing

2006

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### Table 17. Simulated Annealing

### TABLE 1 Performances of SMC and simulated annealing (SA) optimization algorithms obtained over 50 iterations

2004

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