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Traveling Salesman Problem (TSP)

创建日期：2024-07-05 17:13:41

所属分类：金融Finance

标签： TSP

Traveling Salesman Problem

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Assignment Description
Abstract: Traveling Salesman Problem (TSP) is a classical combinatorial problem that is
deceptively simple. This problem is about a salesman who wantsto visit n customers cyclically.
In one tour, the salesman must visit each customer just once and should finish up where he
started. Since each customer is situated in different locations, the distance between every
customer will be different. The objective is to find the shortest round-trip route that visits
each customer once and then returns to the starting customer. The dataset with 100
customers is provided in the zip file (‘TSPTW_dataset.txt’).
In this assignment, students are required to finish the following five tasks:
(1) Classical TSP
A genetic algorithm is used to find the shortest round-trip route of these 100 customers. The
locations of customers are given in TSPTW_dataset.txt. Students should visualize the roundtrip route and provide the total distance.
(2) Dynamic optimization problem
In the real-world TSP, the location and number of customers may vary with time, such a TSP
problem can be considered a dynamic optimization problem. Considering such a scenario:
For each environment ! = 0, … ,5, the first 50 + 10! customers are allowed to be visited.
Besides, the location of a customer varies with the environment !,
)!"# = ) + 2! ⋅ cos /
0
2 !1,
2!"# = 2 + 2! ⋅ sin /
0
2 !1,
where )!"# and 2!"# are the new X coordinate and Y coordinate at environment ! ,
respectively. ) and 2 are the X coordinate and Y coordinate provided in the
TSPTW_dataset.txt. Assuming that the environmental variable ! is changed every 100
generations, students should try to design a genetic algorithm to track the shortest roundtrip route for each environment ! by reusing the solutions from the last environment to
accelerate the search in the new environment and then compare the results from the genetic
algorithm without reusing the solutions from the last environment.
(3) Large-scale optimization problem
By adding 100 to the X coordinate for each customer in the TSPTW_dataset.txt, additional
100 customers can be formed. Regarding the newly formed 100 customers and the original
100 customers as a whole, the new problem can be regarded as a large-scale problem. For
this large-scale problem, the customers can be divided into several small-scale regions by
using clustering techniques, e.g., K-means. The salesman must finish visiting all the customers
within the region before visiting any other customers in other regions. In this task, students
are required to combine the clustering technique with a genetic algorithm to handle the largescale optimization problem.
(4) Multi-objective optimization problem
The salesman may consider more than one objective. For example, the salesman not only
wants to minimize the travel distance of the round-trip route but also maximize the sales
profit. Assume that the sales profit of each customer can be randomly generated between
[1,50], the two objective functions, (i.e., total travel distance 5$ and total sales profit 5%) may
be conflicting, that is, a solution cannot satisfy the maximal sales profit and minimal travel
distance at the same time. The multi-objective optimization problem can be formulated as
< min 5$ , max 5% >. An alternative approach is to change the multi-objective optimization
problem to a single-objective optimization problem by weighting the two objective functions,
min (5$ − ?5%),
where ? (? > 0) is the weight on 5%. Students can specify the ? value to get the optimal
solution.
In addition to the weighting objective functions-based method, students should develop a
Pareto dominance selection-based evolutionary algorithm to handle the multi-objective
optimization problem and discuss the advantages and disadvantages of the weighting
objective functions-based method and Pareto dominance selection-based method.
(5) Time window constraint problem
The salesman is required to visit a certain customer within a certain time window, i.e., the
salesman should visit the customer between “READY TIME” and “DUE TIME”, and the time
window for each customer is given in TSPTW_dataset.txt. The travel time between customers
is computed by the Euclidean distance between customers. Considering the time window as
an additional objective, students are required to develop a Pareto dominance selection-based
evolutionary algorithm to solve the problem by optimizing the following three objectives:
minimize total travel distance, maximize total sales profit, and minimize the total violation
value of the time window, where the total violation value of the time window is the
summation of the violation value of the time window for each customer. For example, “READY
TIME” and “DUE TIME” of the “CUST NO 3” are 2 and 61, respectively. If the salesman visits
the “CUST NO 3” at time 63, the violation value of the time window is 63-61=2. If the salesman
visits the “CUST NO 3” at time 1, the violation value of the time window is 2-1=1.
Discussion and analysis:
Students must give the details of the designed algorithms and perform sensitive studies for
the above tasks with the various parameters, for example, the crossover and mutation rates,
the population size, and the number of generations, and discuss the effects of changing these
parameters. Students need to show their results in various formats, such as tables, figures,
etc.

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