### Table 2. Approximate Solution

"... In PAGE 5: ... The last two columns show the results obtained using the Lindo package, which is based on a mathematical programming method known as Branch amp;Bound method. Table2 presents the results obtained using the Threshold Accepting Algorithm. Forty runs were made for each problem.... In PAGE 7: ...This paper shows the feasibility of using the Threshold Accepting algorithm, which showed good performance for small problems and demonstrated its ability to solve large problems. However, the solution tends to grow farther as the problem size increases ( Table2 and Fig. 1).... ..."

### Table 5. `1 errors for approximate solution.

1999

Cited by 21

### Table 6. `2 errors for approximate solution.

1999

Cited by 21

### Table 3: Results for the Combined Problem: exact and approximate solutions

2001

"... In PAGE 12: ... The two values of WBE that are obtained are almost identical, with the di erence so small as to be plausibly due to numerical errors. The results are in Table3 . Note the heavy usage of the residual network, which together with the uniformity of the earnings parameter constitute conditions in which we expect the approximate solution to be close to the optimum.... ..."

Cited by 6

### Table 1: approximate solution of the medical waste collection VRP

2005

"... In PAGE 7: ... Fig.3: The distribution graph of hospitals and clinics One approximate solution of this case study are shown in Table1 under difference confidence levels, providing the information on the customers assigned to the depot, the vehicle routes and the total travel time of all routes developed. No exact routing data are presented for proprietary reasons of the agency.... ..."

### Table 5.5. `1 errors for approximate solution.

1999

Cited by 21

### Table 5.6. `2 errors for approximate solution.

1999

Cited by 21

### Table 1. `2 errors for the approximate solution of (3) using hierarchy (2).

1999

"... In PAGE 4: ... We now compare collocation based on the C4-function 4;2. In the left half of Table1 we do not apply the smoothing, in the right half we do, i.e.... ..."

Cited by 15

### Table 2. `2 errors for the approximate solution of (3) using hierarchy (6).

1999

"... In PAGE 6: ... On the other hand Theorem 1 tells us how to select a family of functions which are obtained by repeated smoothing of one basic function. In particular, for the example in Table2 we used the functions 7;2(r) : = (1 ? r)9 +(80r2 + 27r + 3); 7;3(r) : = (1 ? r)10 + (320r3 + 197r2 + 50r + 5); 7;4(r) : = (1 ? r)11 + (128r4 + 121r3 + 51r2 + 11r + 1); 7;5(r) : = (1 ? r)12 + (2048r5 + 2697r4 + 1644r3 + 566r2 + 108r + 9); 7;6(r) : = (1 ? r)13 + (4096r6 + 7059r5 + 5751r4 + 2782r3 + 830r2 + 143r + 11): (6) As a by-product we mention that the recursive formula of Theorem 1 can be used to obtain explicit formulae for the functions `;k for xed values of k. Corollary 2.... ..."

Cited by 15

### Table 1: Average relative errors of approximate solution of algorithm based on y

"... In PAGE 115: ...swap push C8 BECZBV D1CPDC BG BF BG BF BK BJ C8 CZBV D1CPDC BE A0 BE D1B7BD BE A0 BE D1B7BD UB = BE A0 BE D1B7BD LB = BGD1 BFD1B7BD C9BECZBV D1CPDC BDB7 D4 BH BE BDB7 D4 BH BE D4 BDBJB7BD BG C9CZBV D1CPDC BDB7 D4 BGD1A0BF BE BDB7 D4 BGD1A0BF BE UB = BE A0 BE D1B7BD LB = BF BE A0 AF CABECZBV D1CPDC LB = D4 D1CPDC C7C8CC LB = D2 A0 BD undefined CACZBV D1CPDC LB = D4 D1CPDC C7C8CC LB = D4 D1CPDC A0BD C7C8CC undefined Table1 : performance guarantees: BV C4CB D1CPDC BPC7C8 CC same machine, then the swap neighborhood is empty; therefore, we define the swap neighborhood as one that consists of all possible jumps and all possible swaps. As can be seen in Table 1, the jump and swap neighborhoods have no constant performance guarantee for C9CZBV D1CPDC .... In PAGE 115: ...swap push C8 BECZBV D1CPDC BG BF BG BF BK BJ C8 CZBV D1CPDC BE A0 BE D1B7BD BE A0 BE D1B7BD UB = BE A0 BE D1B7BD LB = BGD1 BFD1B7BD C9BECZBV D1CPDC BDB7 D4 BH BE BDB7 D4 BH BE D4 BDBJB7BD BG C9CZBV D1CPDC BDB7 D4 BGD1A0BF BE BDB7 D4 BGD1A0BF BE UB = BE A0 BE D1B7BD LB = BF BE A0 AF CABECZBV D1CPDC LB = D4 D1CPDC C7C8CC LB = D2 A0 BD undefined CACZBV D1CPDC LB = D4 D1CPDC C7C8CC LB = D4 D1CPDC A0BD C7C8CC undefined Table 1: performance guarantees: BV C4CB D1CPDC BPC7C8 CC same machine, then the swap neighborhood is empty; therefore, we define the swap neighborhood as one that consists of all possible jumps and all possible swaps. As can be seen in Table1 , the jump and swap neighborhoods have no constant performance guarantee for C9CZBV D1CPDC . Therefore, we introduce a push neighborhood, for which any local optimum is at most a factor BE A0 BE D1B7BD of optimal for C9CZBV D1CPDC .... In PAGE 115: ... When pushing all jobs on the critical machines is unsuccessful, we are in a push optimal solution. In Table1 the performance guarantees for the various local optima and scheduling problems are given. UB = AQ denotes that AQ is a performance guarantee and LB = AQ denotes that the performance guarantee cannot be less than AQ; AQ denotes that UB = LB = AQ.... ..."