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Figure 12. Illustrative examples of the different possible variants of 5-edge-exchange moves

Figure 12 Illustrative examples of the different possible variants of 5-edge-exchange moves

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this type of moves. Note that the 2-exchange move is symmetric as p’ = p | move(i, j) > p=p' Li move(i, j). Figure 1. Illustrative example of the 2-edge-exchange move
this type of moves. Note that the 2-exchange move is symmetric as p’ = p | move(i, j) > p=p' Li move(i, j). Figure 1. Illustrative example of the 2-edge-exchange move
Figure 4. Graphical representation of the neighborhoods @, and @,,, the number of the sub-neighborhoods covered remains constant, the time complexity of the neighborhood exploration is proportional to O(n’), where n is the problem size. In the case of the fast local search, the complexity reduces to O(Kn), where K is the candidate list size.
Figure 4. Graphical representation of the neighborhoods @, and @,,, the number of the sub-neighborhoods covered remains constant, the time complexity of the neighborhood exploration is proportional to O(n’), where n is the problem size. In the case of the fast local search, the complexity reduces to O(Kn), where K is the candidate list size.
Figure 8. Graphical representation of the neighborhood 0,,,..: Figure 7. Graphical representation of the neighborhood @,,,.,
Figure 8. Graphical representation of the neighborhood 0,,,..: Figure 7. Graphical representation of the neighborhood @,,,.,
Figure 6. Graphical representation of the neighborhood 0,,,6.6
Figure 6. Graphical representation of the neighborhood 0,,,6.6
Figure 5. Graphical representation of the neighborhood 0,,,.,
Figure 5. Graphical representation of the neighborhood 0,,,.,
Figure 10. Illustrative example of the 3-edge-exchange move
Figure 10. Illustrative example of the 3-edge-exchange move
Figure 11. Illustrative examples of the different possible variants of 4-edge-exchange moves
Figure 11. Illustrative examples of the different possible variants of 4-edge-exchange moves
Figure 14. Time-to-target plots for the TSPLIB instance gr96 particular, the performance improvement factors PIF, here, fo. denotes the time needed to obtain the given target value with the probability 0.5. In Table 3, we present the approximate values of the performance improvement factors for the algorithms LS«@,), FLS(@,), IFLS(@2), and IEFLS( ©5926. )) In narticnlar the nerfarmance imnravement factare P/F,
Figure 14. Time-to-target plots for the TSPLIB instance gr96 particular, the performance improvement factors PIF, here, fo. denotes the time needed to obtain the given target value with the probability 0.5. In Table 3, we present the approximate values of the performance improvement factors for the algorithms LS«@,), FLS(@,), IFLS(@2), and IEFLS( ©5926. )) In narticnlar the nerfarmance imnravement factare P/F,
* the numeral in the instance name indicates the size of the problem, i.e. the number of cities. Table 1. Results of the experiments with the local search heuristics on TSPLIB instances
* the numeral in the instance name indicates the size of the problem, i.e. the number of cities. Table 1. Results of the experiments with the local search heuristics on TSPLIB instances
Table 2. Results of the comparison of different heuristic algorithms on TSPLIB instances corresponding optimal solution values for n < 300 and n > 300, respectively). From Table 3, it could be seen that the performance improvement factors of IEFLS to LS, IEFLS to FLS, and IEFLS to IFLS, averaged over 30 instances, are roughly equal to 6.6, 4.9, and 2.7,
Table 2. Results of the comparison of different heuristic algorithms on TSPLIB instances corresponding optimal solution values for n < 300 and n > 300, respectively). From Table 3, it could be seen that the performance improvement factors of IEFLS to LS, IEFLS to FLS, and IEFLS to IFLS, averaged over 30 instances, are roughly equal to 6.6, 4.9, and 2.7,
Table 3. Performance improvement factors for the local search heuristics on TSPLIB instances run time performance point of view. It has also been learned that, by integrating these modifications into the iterated local search framework, the performance is increased even more significantly. One more interesting observation is that the "breadth-first" like search appears to be preferable to the "depth-first" strategy at least for the TSP instances examined. 5. Concluding remarks
Table 3. Performance improvement factors for the local search heuristics on TSPLIB instances run time performance point of view. It has also been learned that, by integrating these modifications into the iterated local search framework, the performance is increased even more significantly. One more interesting observation is that the "breadth-first" like search appears to be preferable to the "depth-first" strategy at least for the TSP instances examined. 5. Concluding remarks
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