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By James A. Barnes

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28 C. Blum Fig. 2. Improvement of Cmsa over Greedy (in percent). Finally, we also present the size of the sub-instances that are generated (and maintained) within Cmsa in comparison to the size of the original problem instances. These sub-instance sizes are provided in a graphical way in Fig. 3. Note that these graphics show the sub-instance sizes averaged over all instances of the same alphabet size and the same value for ld . In all cases, the x-axis ranges from instances with a small base-length (n) at the left, to instance with a large base-length at the right.

For the PDPSTW, this step consists of removing a random number of routes (drawn uniformly between 1 and the number of routes in the solution) and a random number of additional customers 36 P. Mourdjis et al. (drawn between 1 and the number of customers left in the solution). The combined list of all removed customers is then re-inserted into the remaining routes, creating new additional routes if required. The scale of the destruction of the original solution normally results in a substantially different solution from which to restart the search, though we do not guarantee it is unique.

Number of Routes 20 19 18 2,800 Number of Routes LC 1-4-7 3,000 3,200 44 42 40 3,400 7,000 8,000 9,000 Distance Distance LR 1-2-9 LR 1-4-9 Number of Routes Number of Routes LC 1-2-9 17 16 15 4,500 30 29 28 27 10,000 5,000 10,000 10,300 10,600 10,900 11,200 11,500 Distance Distance RD BEBO VNDM QL Fig. 2. Number of routes versus cost for clustered (LC 1-2-9 and LC 1-4-7) and random (LR 1-2-9 and LR 1-4-9) benchmark instances. 34,000 RD BEBO VNDM QL Cost (£). 32,000 30,000 28,000 26,000 0 10 20 30 40 Time (mins).

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A Simulation of the Fluctuations of International Atomic Time by James A. Barnes

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