Capacitated-vehicle-routing-problem-with-pick-up-and-delivery-Optimization-project

Problem statement:

There are N passengers whose are at places $1,2,...,N$ respectively. The $i$ passenger, who is currently at place $i$, wants to go to place $i+N$. There are $K$ buses are currently at place $0$. Bus $k$ can only contains $q_{k}$ number of passengers at the same time. Given the 2-dimensional array distance matrix $d$, where $d[i][j]$ is the distance of place $i$ to place $j$. Make an optimal route plan so that the total distance traveled by all buses is the shortest.

Input data:

• number of passengers: $N$
• number of buses: $K$
• distance matrix: 2D matrix d, where $d[i][j]$ = distance( $i$ $\rightarrow$ $j$ ) $\forall i , j$
• list of buses' capacity: 1D matrix q, where $q[k]$ is the number capacity of bus $k$

Ouput data:

• Route plan for $K$ buses
• Total cost

Terminology:

• place $0$: depot
• places $1$ $\rightarrow$ $N$: pickup places
• places $N+1$ $\rightarrow$ $2N$: destination places

Algorithms:

In this project, I use several algorithms to solve the problem:

• Branch and bound algorithm (Backtracking)
• Constraint programming (using ortools)
• Greedy search
• Uniform cost search
• Beam search
• Metaheuristic Hill Climbing (Hill Climbing)
• Randomized travel algorithm
• Genetic algorithm

Case study:

Description of dataset

I use dataset 609 cities of Vietnam. Hence, there are 304 pickup points and 304 destination points, each of them correspond to a passenger.

The dataset contains the name, latitude, longitude of 609 cities.

Here is the visualization of 609 cities of Vietnam:
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