Subject Code : COMPSCI4095
Country : Australia
COMP SCI 4095 Multi Objective Evolution of Instances for the Traveling Salesperson Problem Computer Science Report Writing Assignment Help
Assignment Task:

1 Overview
Assignments should be done in groups consisting of 5-6 students. Each student has to take major responsibility for one of the exercises and collaborate with the team members on the remaining exercises. Each exercise needs one student taking major responsibility. The group has to make sure that the workload is evenly distributed. Programming has to be done in JAVA.

2 Assignment
In this assignment, you have to design multi-objective evolutionary algorithms that evolve Euclidean instances of the Traveling Salesperson (TSP) problem. An instance is given by n cities in the Euclidean plane. Each city i has coordinates (xi , yi), xi, yi ∈ [0, 20],1 ≤ i ≤ n. The distance between two cities is given by d(i, j) = q (xi − xj ) 2 + (yi − yj ) 2 which is the Euclidean distance between i and j. Given the n cities in [0, 20]2 , a TSP instance is fully specified based on the Euclidean distances between the cities. In the assignment, you have to evolve Euclidean instances that exhibit a significant performance difference for algorithms solving the Traveling Salesperson problem.

For all exercises of this assignment, you have to use implementations of 2-Opt Local Search (starting with a random initial solution), the Inver-over Algorithm (populations
size 10 and parameter setting as described in the original paper), and your own best performing evolutionary algorithm from Exercise 1 using a population size of 10. 2-opt
should run on each instance until it has obtained a local optimum and the evolutionary algorithms should run on each instance for 1000 generations.

Exercise 1 Your first multi-objective optimisation  Download and install JMetal. Run NSGA-II for 10.000 generations on the benchmark
functions ZDT 2 and ZDT 3 with population sizes 10, 100, and 1.000. Visualise the six final populations in your report.

Exercise 2 Discrete evolutionary multi-objective algorithms for TSP instances  Place a grid on the given area [0, 20]2 such that each cell has width and heights 1. In
total, you obtain a grid having 20 · 20 = 400 cells, Use an evolutionary algorithm that places each of the n cities in a different cell. The location for the city in a particular cell is the middle of this cell.

1. Design appropriate mutation and crossover operators that can be used in NSGA-II, SPEA2 and IBEA. Include a description in your report.

2. Apply the algorithms NSGA-II, SPEA2 and IBEA to maximize for each i ∈ {1, 2, 3} the two objectives pi,j (I) = fAj (I) − fAi (I) and pi,k(I) = fAk (I) − fAi
(I) where j 6∈ {k, i} and k 6∈ {i, j}, 1 ≤ j, k ≤ 3, and fA(I) as defined in Exercise 3 of Assignment 2. Include the results and your findings in your report.

 

Exercise 3 Continuous evolutionary multi-objective algorithms for TSP instances Cities can now have general coordinates and you are no longer bound by the grid structure. Use continuous evolutionary multi-objective algorithms to optimize the placement of the n coordinates of the cities. You have to make sure that your instances are feasible, i.e. each city is in [0, 20]2
.

1. Design appropriate mutation and crossover operators that can be used in NSGA-II, SPEA2 and IBEA. Include a description in your report.

2. Apply the algorithms NSGA-II, SPEA2 and IBEA to maximize for each i ∈ {1, 2, 3}
the two objectives pi,j (I) = fAj
(I) − fAi
(I) and pi,k(I) = fAk
(I) − fAi
(I) where
j 6∈ {k, i} and k 6∈ {i, j}, 1 ≤ j, k ≤ 3. Include the results and your findings in your
report.

Exercise 4 Mixed evolutionary multi-objective algorithms for TSP instances Combine the two previous approaches. A solution should consist of a placement according
to Exercise 2, but each cell may contain more than 1 city. Each city may be moved from the middle of the cell by a continuous algorithm. Cities that are placed in the same cell should have different offsets. A solution should be represented as a vector of length 3n where the first n entries are used to address the cells for the n cities and the remaining 2n entries are used to specify the offset for each city.

1. Design appropriate mutation and crossover operators that can be used in NSGA-II, SPEA2 and IBEA. Include a description in your report.

2. Apply the algorithms NSGA-II, SPEA2 and IBEA to maximize for each i ∈ {1, 2, 3} the two objectives pi,j (I) = fAj
(I) − fAi
(I) and pi,k(I) = fAk
(I) − fAi
(I) where
j 6∈ {k, i} and k 6∈ {i, j}, 1 ≤ j, k ≤ 3. For one fixed setting according to the grid (first n components), you should run a continuous multi-objective evolutionary algorithm that optimizes the placement of the turbines within this grid structure. This means that you are running a multi-objective algorithm ”inside” a multi-
objective algorithm. Use appropriate selection methods to merge this resulting population with the current parent population. Tune the algorithms such that they
perform as best as possible. Include the results and your findings in your report.

 

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