Politecnico di Torino

Workgroup 20 for VRPTW

Roberto Tadei - Guido Perboli| Optimization methods and algorithms

Antonio Furnò – Raffaele Di Taranto – Filippo Magrì – Fernando Caponetto – Fabio Germano

Genetic Algorithmleads

the research

Tabu search explores search space, digging

the neighborhood

Genetic operators applied on population

Best solution repeated 6 times OR near to pass 5 min?

NO

YES

STOP

Our metaheuristic

Genetic Search based algorithm

Tabu Search based algorithm

Hybrid Approach Chromosome

Crossover

Mutation

Tabu Search operator

Basics blocks

Chromosome

Each chromosome is a list of numbers of customers where for each customer is associated a single route.

Crossover

Given two chromosomes we create two new elements given by half-part of the parents’ genetic.

Mutation

Mutation alters one or more gene(s) values in a chromosome from its initial state.

MyCrossover

It’s a crossover operator applied ‘size’ times, where the size is the number of population.

0 1 2 100

Basics block (cont.)

MyMutation

The logic is the same of MyCrossover but the difference is obviously in the meaning of the operator.

Tabu Search Operator

Inside the genetic algorithm we use the tabu seach approach like a genetic operator

When this operator will find a feasible solution it will be converted into a chromosome in order to continue the optimization with the genetic algorithm.

We apply seven operator: TabuOperator, MyCrossover, CrossoverOperator, MyMutation, SwappingMutationOperator, MyCrossover, MyMutation. When we will find a chromosome with smaller travel time, we will substitute this one with the worst element in the population that’s the element with the smaller fitness function.

Parameters tuning

Tested on the full instance set 10 times because of stochastic components

Max Evolutions: 1000

TabuSearch – Iterations : 17000

Population: 100

Crossover rate: 35 %

Mutation rate: 12 %

MyCrossover rate: 100 %

MyMutation rate: 100 %

TabuOperator rate: 1 %

Tenure TS: 5

Random generation inside, useful for the selection of the chromosome on which apply TS Operator

Results

InstanceOptimal Value Min OF

OPT GAP(min)% Mean OF Mean Time Vehicles

C101.txt 827,3 827,3 0 % 827,3 159,6 10

C208.txt 585,8 585,8 0 % 585,8 205,2 3

rC201.txt 1261.8 1265,6 0,30 % 1285,27 214,1 9

rC202.txt 1092.3 1096,7 0,40 % 1105,59 221,5 8

rC203.txt 923.7 933,1 1,01 % 946,44 204,2 5

rC204.txt 783.5 789,1 0,71 % 796,46 202,1 4

rC205.txt 1154 1162,7 0,75 % 1169,44 224,4 7

rC206.txt 1051.1 1055,4 0,40 % 1080,22 221,5 6

rC207.txt 962.9 968,4 0,57 % 985,3 213,8 6

rC208.txt 776.1 783,4 0,94 % 787,7 234,6 5

Results (cont.)

% Gap between our results and Optimal

Thank you for your attention