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Route Optimization Algorithm

Route Optimization Algorithm

Presentation at Inter IIT Tech Meet 8.0

Venue: IIT Roorkee, India

Shreyas Bapat

December 22, 2019
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  1. Shreyas Bapat, Akash Dakoor, Palak Gupta
    {b16145, b17032, b16067}@students.iitmandi.ac.in
    BOSCH’s Route
    Optimization Algorithm
    Inter IIT Tech Meet 8.0

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  2. What we’ll
    cover
    PROBLEM ADDRESSED
    METHODS RESEARCHED
    01
    03
    02
    04
    05
    06
    APPROACH FOLLOWED
    ALGORITHM
    END RESULTS
    CHALLENGES FACED

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  3. PROBLEM ADDRESSED
    01

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  4. - A standard problem in domain of Heuristics.
    - The goal is to find optimal routes for multiple vehicles visiting a set of
    locations. (When there's only one vehicle, it reduces to the Traveling Salesman
    Problem)
    - NP-hard problem
    - For scheduling public buses, school buses in metro cities, delivery chains.
    Vehicle Routing Problem

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  5. - The current problem is a slight variant of the famous VRPTW.
    - Why capacitated? To control the overflow/overload of buses, trucks etc.
    - Lower bound on occupancy : This problem also has 85% as the lower bound on
    occupancy for maximum utilization of resources like bus seats and fuel
    - Time Windows : To deal with office/school opening times and strict delivery
    schedules. Making the problem more practical.
    - Cover maximum distance by a bus in a tour
    Capacitated Vehicle Routing
    Problem with Time Windows

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  6. Optimisation and Constraints
    - Total 4 constraints are given for the problem
    - 2 constraints need to be optimised, the total distance travelled by all the buses to
    solve the problem and number of buses used for the same. Both need to be
    minimised.
    - 2 constraints need to be just taken care of. The bus has to visit all the nodes on
    time always, and the bus capacity should be 85% at least to run the bus on that
    route.

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  7. METHODS RESEARCHED
    02

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  8. Reinforcement Learning with
    Beam Search
    - In this approach, the input is mapped to a high dimensional vector space and fed
    into an RNN decoder.
    - The decoder uses beam search which keeps track of the most probable paths
    and follows the one with minimum length.
    - An attention mechanism uses the RNN hidden state, along with the embedded
    inputs and gives a probability distribution over the next input- this repeats until a
    termination condition under the constraints is reached.

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  9. A MULTIPLE ANT COLONY SYSTEM FOR
    VEHICLE ROUTING PROBLEMS WITH
    TIME WINDOWS

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  10. APPROACH FOLLOWED
    03

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  11. MACS-VRPTW: A MULTIPLE ANT COLONY SYSTEM FOR
    VEHICLE ROUTING PROBLEMS WITH TIME WINDOWS
    MACS- VRPTW
    ACS for number of
    buses
    ACS for total distance
    The goal of the first colony, ACS-buses, is to try to diminish the number of buses used, while the second
    colony, ACS-distance, optimizes the feasible solutions found by ACS-buses. Both colonies use independent
    pheromone trails but collaborate by sharing the variable ψ(Total path) managed by MACS-VRPTW

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  12. Ant Colony Optimization
    ● Based on the ant’s capability of finding the shortest path from the nest to a food source.
    ● An ant repeatedly hops from one location to another to ultimately reach the destination (food).
    ● Ants deposit an organic compound called pheromones while tracing a path. The intensity of the
    pheromone is an indicator of the utility of that arc to build better solutions.

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  13. Ant Colony Optimization
    ● Pheromone levels in a path are updated as:
    where 0 ≤ ρ < 1 and 1 – p represent the pheromone evaporation rate, and Δτ
    ij
    is related to the
    performance of each ant.
    ● The probability of the kth ant at node i choosing node j using the pheromone trail τ
    ij
    is given
    by :

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  14. Algorithm In Depth!
    04

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  15. - We only pick the next node when:
    - Wait Time: When the bus reaches a node prior to it’s schedule time, we calculate
    it’s waiting time
    Wait time = max(Next Node’s departure time - Current time - distance between
    nodes / speed * 60 , 0)
    Current time + distance between nodes / speed * 60 + wait time + Distance of
    that node from Bosch Bidadi / speed * 60 <= Time to reach office
    Handling Time Windows

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  16. - Then the current time for the bus can be updated as:
    Current time += distance between nodes / speed * 60 + wait time
    - We have assumed the speed to be 60kmph in our program.
    Handling Time Windows

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  17. ACS-distance
    ● Compute a tour as short as possible
    ● m artificial ants are activated to construct m solutions
    ● Compared to current solution and, in case any one solution is better, it is sent to MACS-VRPTW
    ● MACS-VRPTW uses this solution to update the current tour
    ● After solutions generation, the global updates are performed
    ACS-buses
    ● Searches for a feasible solution by maximizing the number of visited nodes.
    ● Starts computation using v-1 vehicles (one vehicle less than the smallest number of vehicles in
    current feasible solution)
    ● Produces a solution only when the number of visited nodes in current best solution is increased

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  18. Find all the lat-long from
    Google Maps Geocode API
    (to be later used in algo
    easily)
    Populate a Distance Matrix
    based on the actual shortest
    distances between two Geo
    Locations using Google
    Maps Distance Matrix API.
    Otherwise, our algorithm
    guarantees > 85%
    occupancy all the times
    (as ants visit all the
    possible nodes once)
    Optimise the path for the
    given points, and find the
    number of buses used.
    No bus can run on that
    route (given the
    constraint of total
    travel distance per day)
    However, we still give
    the best number
    The complete workflow!
    < 85% bus
    occupancy
    on route
    Otherwise
    Current running time
    maintained for all the
    buses which helps
    understand which
    nodes to visit.

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  19. END RESULTS
    05

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  20. Total number of available buses with an organisation for
    managing the pickup-drop services.
    Due to budget limitations, parking place limitations, less
    management staff, the organisation might decide to use
    maximum of 5 buses, even if 7 are actually required!
    Adding one extra constraint (For
    practicality purposes)

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  21. A fully working code which takes
    prescribed input and gives a list of
    nodes followed by various buses in
    optimised order.

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  22. A visualisation, which shows
    animated path for the code
    Output path using the input data
    Some nodes
    are left out
    because that
    path does not
    have 85%
    occupancy
    Bus capacity: 20
    Total Customers: 30
    85% Bus Capacity: 17
    Best case remaining : 13
    (<17, hence another bus
    can’t run for remaining
    number)

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  23. CHALLENGES FACED
    06

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  24. It took us quite some time to
    understand that the problem
    can be solved using
    metaheuristic approaches,
    and can be modelled as a
    VRPTW problem.
    We tried clustering, and
    other approaches which
    didn’t work like
    metaheuristics.
    Hardships!
    Understanding what the
    problem demands
    Optimising two constraints
    at the same time
    We had earlier worked on
    problems like TSP etc, where
    only one constraint had to
    be optimised. It took us long
    enough to understand how
    to take care of two
    constraints at the same time
    efficiently
    Keeping the track of
    current time
    We assume the bus always
    run at speed 60km/h. Then
    we had to understand how
    to keep track of bus current
    time.

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  25. We request you to kindly pay attention to the screen as we are
    going to run the simulation for the data.
    References: http://people.idsia.ch/~luca/tr-idsia-06-99.pdf
    We have the code uploaded to GitHub :
    https://github.com/shreyasbapat/Route-Optimisation
    THANKS

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