### Table 3: Correlations with problem hardness

"... In PAGE 5: ... Problem hardness Problem hardness is taken to be the log of the number of search nodes required by satz. We present the most inter- esting correlations with problem hardness in Table3 , and discuss them in the text following. The strongest correlation with problem hardness we found was the size of the smallest strong backdoors.... ..."

### Table 3: Correlations with problem hardness

"... In PAGE 5: ... Problem hardness Problem hardness is taken to be the log of the number of search nodes required by satz. We present the most inter- esting correlations with problem hardness in Table3 , and discuss them in the text following. The strongest correlation with problem hardness we found was the size of the smallest strong backdoors.... ..."

### Table 1: Results on hard graph coloring problems

"... In PAGE 5: ... These problems have been shown to defeat many algorithmic complete search methods. Table1 shows the average timings required for each of our tested MGAs to solve these prob- lems. The MCH-MGA0 improved with popu learn and lazy look forward performs the best among the other MGAs since the lazy look-forward algorithm is invoked less frequently than the full look-forward algorithm.... ..."

### Table 1: Results on hard graph coloring problems

"... In PAGE 6: ... These problems have been shown to defeat many algorithmic complete search methods. Table1 shows the average timings required for each of our tested MGAs to solve these prob- lems. The MCH-MGA0 improved with popu learn and lazy look forward performs the best among the other MGAs since the lazy look-forward algorithm is invoked less frequently than the full look-forward algorithm.... ..."

### Table 1: Results on hard graph coloring problems

"... In PAGE 5: ... These problems have been shown to defeat many algorithmic complete search methods. Table1 shows the average timings required for each of our tested MGAs to solve these prob- lems. The MCH-MGA0 improved with popu learn and lazy look forward performs the best among the other MGAs since the lazy look-forward algorithm is invoked less frequently than the full look-forward algorithm.... ..."

### 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.... ..."

### Tables 2, 3 show that on hard random 3-SAT problems, Satz is faster than the above cited versions of C-SAT, Tableau and POSIT, Satz apos;s search tree size is the smallest, and Satz apos;s run time and search tree size grow more slowly. Table 4 shows the gain of Satz compared with the cited version of C-SAT, Tableau and POSIT at the ratio m=n=4.25. Each item is computed from Tables 2, 3 (average of all problems at a point) using the following equation: gain = (value(system)=value(Satz) ? 1) 100% 1 available via anonymous ftp to ftp.cis.upenn.edu in pub/freeman/

1997

Cited by 49

### Table 1: Computational results for hard single knapsack instances

2007

"... In PAGE 14: ... Multiple knapsack in- stances were generated in a similar way, by choosing a same capacity for all the containers. The results on hard single knapsack instances with 60 to 90 items are given in Table1 , where labels Dominance and Standard refer to the performance of our B amp;B scheme with and without the LD tests, and label Ratio refers to the ratios Standard/Dominance. The performance figures used in the comparison are the number of nodes of the resulting search tree and the computing time (in CPU seconds).... ..."

### Table 7. Effects of the resource strength RS on problem hardness

in Generation of Resource-Constrained Project Scheduling Problems with Minimal and Maximal Time Lags

1998

"... In PAGE 49: ...Table 7. Effects of the resource strength RS on problem hardness Table7 shows an interesting relationship between computation times and scarcity of (renewable) resources. In the interval [0.... ..."

Cited by 8

### Table 6. Performance data of PSATO on hard quasigroup problems. #P = number of machines. A work day equals 8 h. (*) means no idempotency.

1996

"... In PAGE 15: ... Since few heuristic methods can help to cut the search space, this requires an enormous amount of computing time. From Table6 , it is clear that the use of distributed programs on networked workstations is indispensable to our success. For instance, it would require approximately 240 days of continuous running on a single workstation to solve QG5(14) (without idempotency).... In PAGE 16: ... This empirical rule does not apply to satisfiable SAT problems. P-measures of all the problems in Table6 are given in the last column. Note that the P-measure of QG2(10) is 25.... ..."

Cited by 30