### Table 2. A schedule for the benchmark problem in Table 1 with the makespan = 293 In the next section, we introduce the three evolutionary based heuristics we implemented and ran with OSSP benchmark problems taken from a well known source of test problems. 3 Genetic Algorithms for OSSP In this work, we use three genetic algorithms. We start our discussion by pre- senting the Permutation GA and then turn our attention to the Hybrid GA.

"... In PAGE 3: ... Most benchmark problems in the literature of scheduling have this property. A schedule to the problem instance of Table 1 is given in Table2 . We note that the operations are not scheduled in their order of appearance in Table 1.... In PAGE 3: ... We note that the operations are not scheduled in their order of appearance in Table 1. Thus, operation O32, for instance, is scheduled at time 78 while operation O31 is scheduled at time 226, as can be seen in Table2 . Operation O22 is the last one to nish, with \end time quot; equal to 293, thus, the makespan of the schedule given in Table 2 is 293, which happens to be the optimal solution for this problem.... In PAGE 3: ... Thus, operation O32, for instance, is scheduled at time 78 while operation O31 is scheduled at time 226, as can be seen in Table 2. Operation O22 is the last one to nish, with \end time quot; equal to 293, thus, the makespan of the schedule given in Table2 is 293, which happens to be the optimal solution for this problem. Machines Job J1 Job J2 Job J3 Job J4 M1 85 23 39 55 M2 85 74 56 78 M3 3 96 92 11 M4 67 45 70 75 Table 1.... ..."

### Table 2 Summary of various genetic algorithm formulations. The references in the table are representative of the type of solution; this table does not contain an exhaustive list of published works. Most of the representations are order-based, i.e. the order in which the items appear in the list is a part of the problem structure.

1996

"... In PAGE 26: ... Parallelization by distributing computation will speed up execution, but additional evolutionary operations such as migration are required for improvements in solution quality. The applications of genetic algorithms to scheduling problems are summarized in Table2 . The diagrams in the first column illustrate the basic representation used in each case.... ..."

### Table 1* Back Propagation Genetic Algorithm

1995

"... In PAGE 11: ... In each case network architecture is that of Figure 1. The parameters used in the training of the network are given in Table1 . Two measures of fit, namely the sum of squares deviation (Ssq.... In PAGE 17: ... Table1 . The parameter settings to run the neural network using both the back propagation and the genetic algorithms to run all three problems are given.... ..."

### Table 1: The scheme of the genetic algorithm for the HIPP problem.

1997

Cited by 3

### Table 2: Subset Interconnection Design problem using Genetic Algorithms with uniform crossover, crossover rate 0.6, and adaptive mutation. A \* quot; indicates the best. [19] Darrell Whitley, T. Starkweather, and D. Fuquay. Scheduling problems and traveling salesman: The genetic edge recombination operator. In Scha er [17].

"... In PAGE 3: ... No- tice that the GA using adaptive mutation consistently performed better than xed mutation regardless of the crossover method used. Table2 shows the results for a total of 34 runs on eight di erent sets of vertices. The cardinalities of the eight sets of vertices range from n=5 to n=40 in increments of 5.... ..."

### Table 1. Genetic algorithms parameters.

"... In PAGE 9: ... Basically, the implementation of GA-Stacking combines two parts: a part coming from Weka that includes all the base learning algorithms and another part, which was integrated into Weka, that implements a GA. The parameters used for the GA in the experiments are shown in Table1 . The elite rate is the proportion of the population carried forward unchanged from each generation.... ..."

### 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.... ..."

Cited by 1

### Table 4: Genetic based algorithm results. GA (40 / 35) GA (60 / 40) GA (80 / 60)

"... In PAGE 8: ... In fact, in [ 4 ] the authors refer that they had to solve them in a VAX Alpha 2100 model 300 computer. Table4 presents the results for these problems obtained in a 200 Mhz Pentium MMX PC with 16 MB RAM. In this table column \sol* quot; gives the optimal solution (underlined), when known, or the best-published solution.... ..."

### Table 1 Results of the transformation compared to the genetic algorithm Problem parameters Genetic algorithm

2001

"... In PAGE 3: ... Firstly, we have solved to optimality a series of test problems from literature with an exact SPG- solver similar to that of Duin (1993). Table1 gives the results for the test problem set used in Dror et al. (2000).... ..."