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
Top Related