Montreal_Olli2

Montreal_Olli2 - A Fast Local Search Algorithm for the...

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Applied Mathematics A Fast Local Search Algorithm for the Vehicle Routing Problem with Time Windows OLLI BRÄYSY, GEIR HASLE SINTEF Applied Mathematics, Department of Optimisation, P.O. Box 124 Blindern, N-0314 Oslo, Norway {Olli.Braysy;Geir.Hasle}@math.sintef.no WOUT DULLAERT Ufsia-Ruca Faculty of Applied Economics, University of Antwerp Prinsstraat 13, 2000 Antwerp, Belgium wout.dullaert@ua.ac.be
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Applied Mathematics Introduction Development of a new fast local search heuristic for the VRPTW First application of Threshold Accepting as a post-optimization technique for the VRPTW A comprehensive computational study consisting of 358 benchmark problems from the literature New best-known solutions to both real-life problems of Russell (1995), and to 39% of the extended benchmarks by Gehring and Homberger (1999) Optimization Days, Montreal, Canada, May 6-8th
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Applied Mathematics Generation of the LS solution Reduce the number of routes Reduce distance Injection trees Modified Or-Opt and CROSS exchanges Build initial solutions Hybrid construction heuristic Optimization Days, Montreal, Canada, May 6-8th PROCESS METHOD
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Applied Mathematics Post-optimization by Threshold Accepting Intra-route distance improvement Inter-route distance improvement Initial solutions IOPT exchanges GENICROSS exchanges Generated by LS Optimization Days, Montreal, Canada, May 6-8th PROCESS METHOD
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Applied Mathematics Hybrid sequential insertion heuristic Initialization: seed customer randomly selected among the farthest from the depot Insert the cheapest customer in the best feasible insertion place Weighted cost function of additional detour and waiting time Subtract the distance of the customer to the depot Speed-up techniques: Only consider geographically close customers to the route for insertion Storage of arrival times and latest possible arrival times Calculate accumulated waiting time after each insertion place within the current route Result: Generate 5000 feasible solutions for Solomon’s 100 customer problem instances in 1 second on a 700 MHz PC Optimization Days, Montreal, Canada, May 6-8th
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Applied Mathematics Injection tree heuristic (1) GOAL: reduce number of routes Similarities with Ejection Chains (Glover, 1991 and 1992) Ejection Chains Injection Trees Eject a customer from a route to make room for a new customer Insert customer directly in target route, even if it lead to a violation of time or capacity constraints Remove a customer from the target route to make it feasible Remove an unlimited number of customers, provided that the removed customers can be inserted directly in a neighboring route (without removing a customer there) Optimization Days, Montreal, Canada, May 6-8th
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Applied Mathematics Injection tree heuristic (2) Implementation: Consider first the shortest routes for elimination Consider first insertions in geographically close routes, distant routes are
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Montreal_Olli2 - A Fast Local Search Algorithm for the...

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