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Rohit Kondekar BT08CSE053

A MapReduced Based Hybrid Genetic Algorithm Using Island Approach for Solving Large Scale Time Dependent Vehicle Routing Problem. Rohit Kondekar BT08CSE053. What is Vehicle Routing Problem?

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Rohit Kondekar BT08CSE053

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  1. A MapReduced Based Hybrid Genetic Algorithm Using Island Approach for Solving Large Scale Time Dependent Vehicle Routing Problem RohitKondekar BT08CSE053

  2. What is Vehicle Routing Problem? • Vehicle Routing Problem is a combinatorial optimization & integer programming problem seeking to service a number of customers with a fleet of vehicle. • Important problem in field of transportation, distribution & logistics. • Main points:- • There are a number of vehicles, each with an identical capacity. • There is a single depot, where each vehicle must start and end. • There are a number of customers, each in a different location, waiting for a certain time interval. • Each customer has a certain demand, which has to be satisfied by a delivery from just one of the vehicles.

  3. We know the distance between each customer, as well as the distance between the depot and each customer. • The total demands for the customers visited by one vehicle cannot exceed the capacity of the vehicle. • Different road types with varying Traffic Conditions, depending on day time interval. • To find best way to route vehicles, with minimum cost. Cost includes total time, distance & number of vehicles

  4. Dynamics of Road Network • A Step function of speed distribution to represent dynamic road networks. • A Step function of link travel speed gives a continuous function of link travel time. • Satisfies FIFO property.

  5. Objective Function Minimize - minZ= α1×K + α2×ST • ST : total schedule time • TT : total travel time • TSVT : total service time • Rij : travel time from node i to j at time interval m. • svti : service time of node i • ai : customer arrival time. • ti : arrival of vehicle at node i • xij : if a vehicle departs from node i to j

  6. Chromosome Representation

  7. What is an Island Approach and why to use it? • Can be easily depicted on a distributed platform. • Large number of population can be processed simultaneously. • Faster convergence.

  8. Hybrid Genetic Algorithm • To improve the probability of optimal solutions, hybrid approach is used. • It fuses the evolutionary GA with different population generation schemes & local search optimizations. • Population Generation :- • Generate M/4, using random method. • Generate M/4, using savings heuristics. • Generate M/4, using nearest neighbor search. • Local Optimizations :- • 2-opt optimization.

  9. Savings Heuristic s(i,j) = d(0,i) + d(0,j) – d(i,j) A link i-j is included if s(i,j)>0

  10. NNC Algorithm • NNC is an improved nearest neighbor algorithm, its route construction procedure is as follows: • Start every route by finding a non-routed customer closest to the depot. • At every subsequent iteration search for a customer closest to the last customer added into the route, and add it at the end of the route if it satisfies the time and capacity constraint. • A new route is started when it fails to find a feasible insertion place, unless there are no more non routed customers. • Here closeness is defined in terms of minimal travel time between two customer nodes.

  11. Fitness Function Selection • To avoid premature convergence, an adequate amount of selective pressure has to be maintained. • Due to the type of fitness function (which is scaled up), strong individuals have large fitness value as compared to weak individuals. • Therefore Ranking Method is used.

  12. Crossover • Maximal Route Preserving Crossover (MRPC) is applied to preserve maximal routes. • MRPC makes it possible to get feasible solutions without failure and has ability to preserve best routes from parent individuals. • 1) Find the maximal overlapping route from the two parent individuals, and copy it into the child. • 2) The maximal overlapping route can be obtained by: • a) Finding the route of maximum length. • b) If there are multiple maximal routes, then find the route which has maximum number of customers in the same route, in the other parent. • Mutation :- Exchange Mutation is applied.

  13. Local Search Optimization • The 2-opt algorithm, removes two edges from the route, and reconnects the two paths created. • This is done only if the new route is shorter.

  14. Thank You

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