### Table 2 shows the difference among these hyper-heuristics and the variable neighborhood search approaches.

2004

"... In PAGE 29: ...AM-sdEmc3opt SD-LS+EMC-LS+3opt Accept all moves Random OI-sdEmc3opt SD-LS+EMC-LS+3opt Descent Random OICF- sdEmc3opt SD-LS+EMC-LS+3opt Descent Based on historical performance AMCF- sdEmc3opt SD-LS+EMC-LS+3opt Accept all moves Based on historical performance EMCQ- sdEmc3opt SD-LS+EMC-LS+3opt EMCQ Random AM-sd SD-LS Accept all moves Random OI-2opt 2-opt Descent Random OICF-2opt 2-opt Descent Based on historical performance EMCQ-2opt 2-opt EMCQ Random Table2 . A list of hyper-heuristics and VNS approaches with their local search (or LLH), acceptance criteria and calling sequence.... ..."

Cited by 3

### Table 1: Parameters for the neighborhood methods

"... In PAGE 4: ... The descent method (DN) was also run in a multi-start version (DN5), which means that the minimum out of 5 very short runs (4/5 seconds each) is considered as the result of a the whole 4 second run. The parameters for each method are summarized in Table1 and 2. For comparison purposes, we added results achieved by the Problem Space Genetic Algorithm (PSGA), one of the best available approaches for single machine scheduling problems, as reported in (Avci et al.... ..."

### Table 1: Parameters for the neighborhood methods

"... In PAGE 4: ... The descent method (DN) was also run in a multi-start version (DN5), which means that the minimum out of 5 very short runs (4/5 seconds each) is considered as the result of a the whole 4 second run. The parameters for each method are summarized in Table1 and 2. For comparison purposes, we added results achieved by the Problem Space Genetic Algorithm (PSGA), one of the best available approaches for single machine scheduling problems, as reported in (Avci et al.... ..."

### Table 6. Descent DA heuristics in 287-customer problem.

1997

"... In PAGE 20: ... We will report on only a few of the more promising combinations. Table6 provides results on four DA strategies for the 287-customer problem. The Av: column gives the average result from ten random restarts, while the next column lists the best result.... In PAGE 22: ... Summary results for local descent heuristics with Relocation neighbourhoods. The rst two heuristics in Table 7 are the apos;fast apos; versions of drop/add reported in Table6 . The next heuristic (referred to as CH for interchange) considers all possible location interchanges of a single facility from its current position to an unoccupied xed point.... ..."

Cited by 8

### Table 6. Comparisons of the approaches (Hybrid GA: genetic algorithm + local search; Hybrid VNS: iterated variable neighborhood search, and our approaches) on the problem. Hybrid GA Hybrid VNS Decomposition

2005

"... In PAGE 5: ...enalties are re-assigned and the descent local search is started again. See [10] for more details. Using the decomposition, construction and post-processing approach, we obtained a number of different schedules on the problem presented in Section 2. The best results out of 5 runs on each of the approaches, namely the hybrid genetic algorithm, the variable neighborhood search and our approach with and without the variable neighborhood search approach as the 3rd stage of post-processing, are presented in Table6 . The values in parentheses give the computational time of the corresponding approaches.... ..."

Cited by 3

### Table 6. Comparisons of the approaches (Hybrid GA: genetic algorithm + local search; Hybrid VNS: iterated variable neighborhood search, and our approaches) on the problem. Hybrid GA Hybrid VNS Decomposition

2005

"... In PAGE 5: ...enalties are re-assigned and the descent local search is started again. See [10] for more details. Using the decomposition, construction and post-processing approach, we obtained a number of different schedules on the problem presented in Section 2. The best results out of 5 runs on each of the approaches, namely the hybrid genetic algorithm, the variable neighborhood search and our approach with and without the variable neighborhood search approach as the 3rd stage of post-processing, are presented in Table6 . The values in parentheses give the computational time of the corresponding approaches.... ..."

Cited by 3

### Table 1: Heuristics for ESTP. Type classi cation and performance. An \- quot; in- dicates that no or insu cient data is available to give a reliable estimate of reduction over MST and/or running time complexity.

1997

"... In PAGE 16: ...Summary In Table1 we present a summary of heuristics for ESTP, by noting their local search type, average reduction over MST (when available) and running time complexity (when available). The type classi cation descent method in general stands for an iterative best improvement method.... ..."

Cited by 4

### Table 2: Branches explored and CPU time (seconds) used to nd a minimal length ruler (F) or prove that none shorter exists (P). A - means that the run was cut o after 105 branches. ing domain (SD); this heuristic has often been found to give good results, although mainly in binary constraint satisfaction problems. In one version of the smallest-domain heuristic, both the original and the auxiliary variables are used as search variables. In the other version (restricted SD) only the original variables are used as search variables. The lexicographic ordering selects the original variables in order, starting from x2 (since x1 is already assigned to 0). When all the original variables have been assigned, constraint propagation will have already assigned the auxiliary variables as well, and therefore a restricted form of this heuristic does exactly the same thing.

1999

"... In PAGE 7: ... We concen- trate on the auxiliary variable representation with the single all-di erent constraint as this is the most e cient in terms of CPU time, from those compared in Table 1. Table2 compares lexicographic ordering with two ver- sions of the heuristic which chooses next the variable with smallest remain-... In PAGE 8: ... Hence, lexicographic ordering of the auxiliary variables gives identical results to lexicographic ordering of the original variables, in both ternary representations. It is clear from Table2 that lexicographic ordering gives much better results than smallest domain ordering. With the smallest domain ordering, it is a good idea to search only on the original variables, and not on the auxiliary variables as well.... ..."

Cited by 25

### Table 1 An illustration of a quay crane schedule Quay Crane 1 Quay Crane 2

"... In PAGE 1: ... For instance, there are ten holds in a container vessel, and two quay cranes are allocated to handle the container vessel. Table1 illustrates a feasible quay crane schedule for this instance. It shows the handling sequence of holds for every quay crane, the processing time of each hold and the time schedule for handling every hold.... ..."

### Table 4. Experimental results on optimal test access architecture design under power constraints: (a) S 1 (b) S 2 .

"... In PAGE 5: ... G i can be obtained from power models for core i. Experimental results for power-constrained test access archi- tecture design for S 1 and S 2 are shown in Table4 . For our ex- periments, we approximated G i by the number of gates in core i.... In PAGE 5: ... On the other hand, for higher values of W, the testing time is affected substantially. For example, in Table4 (a), for W 24 and power budget of 300 units, the testing time does not decrease with an increase in W due to power constraints. In some cases, the ILP problem may even be infeasible for higher test widths, e.... In PAGE 5: ...g. in Table4 (b) with W =48 and power budget of 300 units for S 2 . Comparing with Table 2, we note that the width distribution is also significantly different due to power constraints.... In PAGE 5: ... This is achieved using a width distribution of (10,10) and test bus assignment (2,2,2,2,2,2,2,2,2,1). However, as seen from Table4 . for test width W =24, the test bus assignment has to be changed to meet power constraints, and the minimum testing time increases to 471900 cycles.... ..."