Advanced Aspects of Nature Inspired Search and Optimisation 2019/2020Lab 2 MSc: Time Series Prediction with GPNB! This coursework is only compulsory for MSc students taking the 20cr module.We released a different Lab 2 with an earlier deadline for UG students taking the20cr module.You need to implement one program that solves Exercises 1-3 using any programming language.In Exercise 5, you will run a set of experiments and describe the result using plots and a shortdiscussion.(In the following, replace abc123 with your username.) You need to submit one zip file withthe name niso3-abc123.zip. The zip file should contain one directory named niso3-abc123containing the following files:❼ the source code for your program❼ a Dockerfile (see the appendix for instructions)❼ a PDF file for Exercises 4 and 51In this lab, we will do a simple form of time series prediction. We assume that we are given somehistorical data, (e.g. bitcoin prices for each day over a year), and need to predict the next value inthe time series (e.g., tomorrow’s bitcoin value).We formulate the problem as a regression problem. The training data consists of a set of minput vectors X = (x(0), . . . , x(m−1)) representing historical data, and a set of m output valuesY = (x(0), . . . , x(m−1)), where for each 0 ≤ j ≤ m − 1, x(j) ∈ Rn and y(j) ∈ R. We will use geneticprogramming to evolve a prediction model f : Rn → R, such that f(x(j)) ≈ y(j).Candidate solutions, i.e. programs, will be represented as expressions, where each expression evaluatesto a value, which is considered the output of the program. When evaluating an expression,we assume that we are given a current input vector x = (x0, . . . , xn−1) ∈ Rn. Expressions and evaluationsare defined recursively. Any floating number is an expression which evaluates to the valueof the number. If e1, e2, e3, and e4 are expressions which evaluate to v1, v2, v3 and v4 respectively,then the following are also expressions❼ (add e1 e2) is addition which evaluates to v1 + v2, e.g. (add 1 2)≡ 3❼ (sub e1 e2) is subtraction which evaluates to v1 − v2, e.g. (sub 2 1)≡ 1❼ (mul e1 e2) is multiplication which evaluates to v1v2, e.g. (mul 2 1)≡ 2❼ (div e1 e2) is division which evaluates to v1/v2 if v2 6= 0 and 0 otherwise, e.g., (div 4 2)≡ 2,and (div 4 0)≡ 0,❼ (pow e1 e2) is power which evaluates to vv21, e.g., (pow 2 3)≡ 8❼ (sqrt e1) is the square root which evaluates to √v1, e.g.(sqrt 4)≡ 2❼ (log e1) is the logarithm base 2 which evaluates to log(v1), e.g. (log 8)≡ 3❼ (exp e1) is the exponential function which evaluates to ev1, e.g. (exp 2)≡ e2 ≈ 7.39❼ (max e1 e2) is the maximum which evaluates to max(v1, v2), e.g., (max 1 2)≡ 2❼ (ifleq e1 e2 e3 e4) is a branching statement which evaluates to v3 if v1 ≤ v2, otherwise theexpression evaluates to v4 e.g. (ifleq 1 2 3 4)≡ 3 and (ifleq 2 1 3 4)≡ 4❼ (data e1) is the j-th element xj of the input, where j ≡ |bv1c| mod n.❼ (diff e1 e2) is the difference xk − x` where k ≡ |bv1c| mod n and ` ≡ |bv2c| mod n❼ (avg e1 e2) is the average 1|k−`|Pmax(k,`)−1t=min(k,`)xt where k ≡ |bv1c| mod n and ` ≡ |bv2c|mod nIn all cases where the mathematical value of an expression is undefined or not a real number (e.g.,√−1, 1/0 or (avg 1 1)), the expression should evaluate to 0.We can build large expressions from the recursive definitions. For example, the expression(add (mul 2 3) (log 4))2evaluates to2 · 3 + log(4) = 6 + 2 = 8.To evaluate the fitness of an expression e on a training data (X , Y) of size m, we use the meansquare error is the value of the expression e when evaluated on the input vector x(j).3Exercise 1. (30 % of the marks)Implement a routine to parse and evaluate expressions. You can assume that the input describes asyntactically correct expression. Hint: Make use of a library for parsing s-expressions1, and ensurethat you evaluate expressions exactly as specified on page 2.Input arguments:❼ -expr an expression❼ -n the dimension of the input vector n❼ -x the input vectorOutput:❼ the value of the expressionExample:[pkl@phi ocamlec]$ niso_lab3 -question 1 -n 1 -x 1.0 \-expr (mul (add 1 2) (log 8))9.0[pkl@phi ocamlec]$ niso_lab3 -question 1 -n 2 -x 1.0 2.0 \-expr (max (data 0) (data 1))2.0Exercise 2. (10 % of the marks) Implement a routine which computes the fitness of an expressiongiven a training data set.Input arguments:❼ -expr an expression❼ -n the dimension of the input vector❼ -m the size of the training data (X , Y)❼ -data the name of a file containing the training da代写MSc留学生作业、代做Python编程语言作业、program课程作业代写、Python实验作业代做 帮做Hasketa in the form of m lines, where each linecontains n + 1 values separated by tab characters. The first n elements in a line representsan input vector x, and the last element in a line represents the output value y.Output:❼ The fitness of the expression, given the data.1See e.g. implementations here http://rosettacode.org/wiki/S-Expressions4Exercise 3. (30 % of the marks)Design a genetic programming algorithm to do time series forecasting. You can use any geneticoperators and selection mechanism you find suitable.Input arguments:❼ -lambda population size❼ -n the dimension of the input vector❼ -m the size of the training data (X , Y)❼ -data the name of a file containing training data in the form of m lines, where each linecontains n + 1 values separated by tab characters. The first n elements in a line representsan input vector x, and the last element in a line represents the output value y.❼ -time budget the number of seconds to run the algorithmOutput:❼ The fittest expression found within the time budget.Exercise 4. (10 % of the marks)Describe your algorithm from Exercise 3 in the form of pseudo-code. The pseudo-code should besufficiently detailed to allow an exact re-implementation.Exercise 5. (20 % of the marks)In this final task, you should try to determine parameter settings for your algorithm which lead toas fit expressions as possible.Your algorithm is likely to have several parameters, such as the population size, mutation rates,selection mechanism, and other mechanisms components, such as diversity mechanisms.Choose parameters which you think are essential for the behaviour of your algorithm. Run a set ofexperiments to determine the impact of these parameters on the solution quality. For each parametersetting, run 100 repetitions, and plot box plots of the fittest solution found within the time budget.5A. Docker HowtoFollow these steps exactly to build, test, save, and submit your Docker image. Please replace abc123in the text below with your username.1. Install Docker CE on your machine from the following website:https://www.docker.com/community-edition2. Copy the PDF file from Exercises 4 and 5 all required source files, and/or bytecode to anempty directory named niso2-abc123 (where you replace abc123 with your username).mkdir niso2 - abc123cd niso2 - abc123 /cp ../ exercise . pdf .cp ../ abc123 . py .3. Create a text file Dockerfile file in the same directory, following the instructions below.# Do not change the following line . It specifies the base image which# will be downloaded when you build your image .FROM pklehre / niso2020 - lab2 - msc# Add all the files you need for your submission into the Docker image ,# e . g . source code , Java bytecode , etc . In this example , we assume your# program is the Python code in the file abc123 . py . For simplicity , we# copy the file to the / bin directory in the Docker image . You can add# multiple files if needed .ADD abc123 . py / bin# Install all the software required to run your code . The Docker image# is derived from the Debian Linux distribution . You therefore need to# use the apt - get package manager to install software . You can install# e . g . java , python , ghc or whatever you need . You can also# compile your code if needed .# Note that Java and Python are already installed in the base image .# RUN apt - get update# RUN apt - get -y install python - numpy# The final line specifies your username and how to start your program .# Replace abc123 with your real username and python / bin / abc123 . py# with what is required to start your program .CMD [ - username , abc123 , - submission , python / bin / abc123 . py ]64. Build the Docker image as shown below. The base image pklehre/niso2019-lab3 will bedownloaded from Docker Hubdocker build . -t niso2 - abc1235. Run the docker image to test that your program starts. A battery of test cases will be executedto check your solution.docker run niso2 - abc1236. Once you are happy with your solution, compress the directory containing the Dockerfile asa zip-file. The directory should contain the source code, the Dockerfile, and the PDF file forExercise 4 and 5. The name of the zip-file should be niso2-abc123.zip (again, replace theabc123 with your username).Following the example above, the directory structure contained in the zip file should be asfollows:niso2-abc123/exercise.pdfniso2-abc123/abc123.pyniso2-abc123/DockerfileSubmissions which do not adhere to this directory structure will be rejected!7. Submit the zip file niso2-abc123.zip on Canvas.7转自：http://www.daixie0.com/contents/3/4877.html