Assignment Description

Abstract:  Traveling  Salesman  Problem  (TSP)  is  a  classical  combinatorial  problem  that  is  deceptively simple. This problem is about a salesman who wants to 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 round- trip 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 e = 0, … ,5, the first 50 + 10e customers are allowed to be visited. Besides, the location of a customer varies with the environment e,

x!ew  = x + 2e ⋅ cos e1,

y!ew  = y + 2e ⋅ sin e1,

where x!ew   and  y!ew   are  the   new  X  coordinate  and  Y  coordinate  at  environment  e , respectively.   x   and   y    are    the   X    coordinate    and   Y    coordinate    provided    in    the TSPTW_dataset.txt.  Assuming  that  the   environmental  variable  e  is   changed   every  100 generations, students should try to design a genetic algorithm to track the shortest round- trip  route for each environment e 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 large- scale 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 f$  and total sales profit f% ) 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 f$ , max f% >. An alternative approach is to change the multi-objective optimization

problem to a single-objective optimization problem by weighting the two objective functions,

min (f$ − λf% ),

where λ (λ > 0) is the weight on f% .  Students  can specify the λ 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.