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? 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.

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

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.

Objective Function Minimize - minZ = α 1 ×K + α 2 ×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

Chromosome Representation

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.

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.

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

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.

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.

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.

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.

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