Programming Assignment 1 - Particle Swarm Optimization

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Programming Assignment 1 - Particle Swarm Optimization
  Programming Assignment #2 : Differential Evolution 1. Refer to the Wikipedia page: https://en.wikipedia.org/wiki/Test_functions_for_optimization  (In another attachment the pdf version of that page is provided. Also the relevant sections of that page are copied in this assignment.) You need to develop your own program, in Python only (for consolidating skills for downstream assignments), that performs PSO optimization. The step-by-step process for this is given in the lecture slides as a high-level pseudo-code, along with the relevant equations and logic. Use this program to find the optima for two of the functions in that Wikipedia page  –  the Eggholder function , and the Holder Table function . The relevant section of the page is reproduced below: Function Name 3-D Plot Objective function  –  Note only 2 paras - (x, y) involved The range of parameters for the Eggholder function is: -512   x, y   512, while for the Holder Table function is -10   x, y   10. There are no explicit constraints in these problems. The same PSO program should work on both, as well as any other single-objective optimization problem you would like to solve. Your optimized values should match the values given in the link / pdf. You will need to make plots of the convergence history of the average (across all candidates) and the best (candidate) value of the objective function across all generations (gens. on x-axis). [Note that the identity of “best candidate” will change across generations; the plot should track the best value independent of candidate which will be the variable gbest  ]. Both these parameters should appear on the same plot; however, the two functions are to be plotted on two different plots. You need to experiment with two parameters  –  the population size and the max. number of generations for solution. Do you find similar trends for both functions? Continued in next page:  Ball-park figures for parameters: 1. Population size: 20, 50, 100, 200. 2. Num. of Iterations: 50, 100, 200. 3. Try out different values of Vmax. 4. Constants c1 (local effect) and c2 (global effect) should add up to 4. However, you can modulate their individual values within this constraint and observe the effects. Your submission should be a folder containing your code, and a word doc containing comparison of your optimized solution against the correct solution, as well as the plots for the given cases. Ideally all comparison cases, or at least some of them. BONUS : The CS member of your team should be having the corresponding solutions and plots from DE. You are encouraged to compare solutions from the two algorithms and report it, in particular the convergence histories of the best and average solutions (i.e. fitness value vs. iteration (generation) number) compared between the two algorithms, for the same population sizes.
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