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Preparing for 2K25 edition
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‎README.md

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# Operations Research 2K24
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# Operations Research 2K25
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This repository contains the Notebook used during the Operations Research (#orms) course at the [Department of Mathematics](https://matematica.unipv.it/) at the University of Pavia.
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| Data | Notebook | Link |
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|:-|:-|:-|
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|**[2024/05/10]**|*Traveling Student Problem (TSP)*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/TSP.ipynb)|
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|**[2024/04/19]**|*Training Binary Neural Networks*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/TrainingBNN.ipynb)|
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|**[2024/03/22]**|*Linear Regression with Gurobi*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/linear_regression.ipynb)|
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|**[2024/03/15]**|*Modeling exercises with Gurobi*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/Python_and_Gurobi.ipynb)|
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|**[2024/03/11]**|*Steel Production Planning (intro to Gurobi)*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/Steel_Planning.ipynb)|
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|**[2024/03/01]**|*Python in a Nutshell*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/Python_in_a_Nutshell.ipynb)|
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## Homeworks solutions
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| Data | Solution | Link |
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|:-|:-|:-|
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|**[2024/05/17]**|*Asymmetric TSP*|[atsp.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/atsp.py)|
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|**[2024/05/17]**|*Symmetric TSP*|[tsp.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/tsp.py)|
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|**[2024/05/03]**|*Training a BNN for the XOR logical function (non linearly separable*|[NN_xor.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/Xor_aula.py)|
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|**[2024/04/22]**|*Training a BNN for the AND logical function*|[NN_and.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/NN_and.py)|
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|**[2024/04/15]**|*Optimal Color Transfer*|[colorTransfer.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/colorTransfer.py)|
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|**[2024/04/12]**|*Linear regression Diabete dataset*|[regression_diabete.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/regression_diabete.py)|
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|**[2024/04/12]**|*Linear regression noisy $sin(x)$*|[regression_sin.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/regression_sin.py)|
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|**[2024/03/15]**|*Exercise 2.6: Square Magic*|[square_magic.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/square_magic.py)|
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|**[2024/03/15]**|*Exercise 2.5: Steel Recycle Bleending Problem*|[steel.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/steel.py)|
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|**[2024/03/01]**|*Python in a Nutshell: Solutions to exercises*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/Python_in_a_Nutshell_solutions.ipynb)|
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### License

‎aa2024/README.md

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# Operations Research 2K24
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This repository contains the Notebook used during the Operations Research (#orms) course at the [Department of Mathematics](https://matematica.unipv.it/) at the University of Pavia.
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Every notebook can be opened directly on the web using Google Colab, by clicking on the corresponding Colab icon.
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This repository is maintained by the [Computational Optimization Research Group](https://www.compopt.it/). You are welcome to contribute!
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## Python Notebooks
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| Data | Notebook | Link |
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|:-|:-|:-|
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|**[2024/05/10]**|*Traveling Student Problem (TSP)*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/TSP.ipynb)|
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|**[2024/04/19]**|*Training Binary Neural Networks*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/TrainingBNN.ipynb)|
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|**[2024/03/22]**|*Linear Regression with Gurobi*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/linear_regression.ipynb)|
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|**[2024/03/15]**|*Modeling exercises with Gurobi*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/Python_and_Gurobi.ipynb)|
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|**[2024/03/11]**|*Steel Production Planning (intro to Gurobi)*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/Steel_Planning.ipynb)|
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|**[2024/03/01]**|*Python in a Nutshell*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/Python_in_a_Nutshell.ipynb)|
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## Homeworks solutions
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| Data | Solution | Link |
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|:-|:-|:-|
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|**[2024/05/17]**|*Asymmetric TSP*|[atsp.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/atsp.py)|
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|**[2024/05/17]**|*Symmetric TSP*|[tsp.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/tsp.py)|
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|**[2024/05/03]**|*Training a BNN for the XOR logical function (non linearly separable*|[NN_xor.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/Xor_aula.py)|
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|**[2024/04/22]**|*Training a BNN for the AND logical function*|[NN_and.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/NN_and.py)|
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|**[2024/04/15]**|*Optimal Color Transfer*|[colorTransfer.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/colorTransfer.py)|
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|**[2024/04/12]**|*Linear regression Diabete dataset*|[regression_diabete.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/regression_diabete.py)|
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|**[2024/04/12]**|*Linear regression noisy $sin(x)$*|[regression_sin.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/regression_sin.py)|
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|**[2024/03/15]**|*Exercise 2.6: Square Magic*|[square_magic.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/square_magic.py)|
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|**[2024/03/15]**|*Exercise 2.5: Steel Recycle Bleending Problem*|[steel.py](https://github.com/mathcoding/opt4ds/blob/master/scripts/steel.py)|
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|**[2024/03/01]**|*Python in a Nutshell: Solutions to exercises*|[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/mathcoding/opt4ds/blob/master/notebooks/Python_in_a_Nutshell_solutions.ipynb)|
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### License
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<a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" property="dct:title"><b>#ORMS Notebooks</b></span> by <a xmlns:cc="http://creativecommons.org/ns#" href="http://matematica.unipv.it/gualandi" property="cc:attributionName" rel="cc:attributionURL">Stefano Gualandi</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://github.com/mathcoding/opt4ds" rel="dct:source">https://github.com/mathcoding/opt4ds</a>.

‎notebooks/Lego_Problems.ipynb renamed to ‎aa2024/notebooks/Lego_Problems.ipynb

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"id": "specified-functionality",
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"metadata": {},
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"source": [
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"<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\"><b>Solving the Lego Planning Problem with Pyomo and Glpk</b></span> by <a xmlns:cc=\"http://creativecommons.org/ns#\" href=\"http://mate.unipv.it/gualandi\" property=\"cc:attributionName\" rel=\"cc:attributionURL\">Stefano Gualandi</a> is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution 4.0 International License</a>. Based on a project at <a xmlns:dct=\"http://purl.org/dc/terms/\" href=\"https://github.com/mathcoding/opt4ds\" rel=\"dct:source\">https://github.com/mathcoding/opt4ds</a>."
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"<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by/4.0/88x31.png\" /></a><br /><span xmlns:dct=\"http://purl.org/dc/terms/\" property=\"dct:title\"><b>Solving the Lego Planning Problem with Gurobi</b></span> by <a xmlns:cc=\"http://creativecommons.org/ns#\" href=\"http://mate.unipv.it/gualandi\" property=\"cc:attributionName\" rel=\"cc:attributionURL\">Stefano Gualandi</a> is licensed under a <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\">Creative Commons Attribution 4.0 International License</a>. Based on a project at <a xmlns:dct=\"http://purl.org/dc/terms/\" href=\"https://github.com/mathcoding/opt4ds\" rel=\"dct:source\">https://github.com/mathcoding/opt4ds</a>."
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]
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},
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{

‎notebooks/linear_regression.ipynb renamed to ‎aa2024/notebooks/Linear_Regression.ipynb

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‎notebooks/Python_and_Gurobi.ipynb renamed to ‎aa2024/notebooks/Python_and_Gurobi.ipynb

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‎notebooks/Python_in_a_Nutshell.ipynb renamed to ‎aa2024/notebooks/Python_in_a_Nutshell.ipynb

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‎notebooks/Python_in_a_Nutshell_solutions.ipynb renamed to ‎aa2024/notebooks/Python_in_a_Nutshell_solutions.ipynb

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‎notebooks/Steel_Planning.ipynb renamed to ‎aa2024/notebooks/Steel_Planning.ipynb

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‎notebooks/TSP.ipynb renamed to ‎aa2024/notebooks/TSP.ipynb

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‎notebooks/TrainingBNN.ipynb renamed to ‎aa2024/notebooks/TrainingBNN.ipynb

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‎aa2024/scripts/B-SVM.py

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from gurobipy import Model, GRB, quicksum
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import numpy as np
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from math import sqrt
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import matplotlib.pyplot as plt
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import logging
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logging.basicConfig(filename='test-all.log',
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filemode='a',
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format='%(asctime)s,%(msecs)d %(message)s',
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datefmt='%H:%M:%S',
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level=logging.INFO)
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def Parse(filename):
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fh = open(filename, 'r')
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fh.readline()
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Xs, Ys = [], []
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for row in fh:
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line = row.replace('\n','').split(';')
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v = int(line[0])
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Ys.append(-1 if v == 4 else 1)
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Xs.append(list(map(int, line[1:])))
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n = len(Xs)
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Xs = np.matrix(Xs)/255
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return Xs, np.array(Ys)
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class BatchLearner(object):
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def __init__(self, Xtrain, Ytrain) -> None:
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self.Xtrain = Xtrain
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self.Ytrain = Ytrain
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self.mu = 0
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self.wp_hint = np.zeros(784)
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self.wn_hint = np.zeros(784)
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self.wbp_hint = 0
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self.wbn_hint = 0
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self.accuracy = 0.0
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self.Results = []
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self.Sol = []
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def evalTrain(self, F):
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Xs, Ys = self.Xtrain, self.Ytrain
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acc = 0
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n = len(Ys)
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for i in range(n):
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if F(Xs[i]) == Ys[i]:
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acc += 1
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return (acc/n*100)
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def solve(self, Xs, Ys, timelimit=10):
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model = Model()
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model.setParam(GRB.Param.OutputFlag, 0)
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model.setParam(GRB.Param.TimeLimit, timelimit)
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model.setParam(GRB.Param.BestObjStop, 1.00)
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#model.setParam(GRB.Param.Method, 2) # Barrier method
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#model.setParam(GRB.Param.Crossover, 0) # No crossover
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model.setParam(GRB.Param.Method, 1) # Dual Simplex
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# Number of samples
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n, m = Xs.shape
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N = int(sqrt(m))
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# Variables: w_ih weights
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wp, wn = {}, {}
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for i in range(m):
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wp[i] = model.addVar(obj=0.1, vtype=GRB.CONTINUOUS)
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wn[i] = model.addVar(obj=0.1, vtype=GRB.CONTINUOUS)
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# Bias variable
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wbp, wbn = {}, {}
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wbp = model.addVar(obj=0.1, vtype=GRB.CONTINUOUS)
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wbn = model.addVar(obj=0.1, vtype=GRB.CONTINUOUS)
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# Variable for margin
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z = [model.addVar(obj=1, lb=0.0, vtype=GRB.CONTINUOUS) for k in range(n)]
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# Constraints
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for k in range(n):
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model.addConstr(quicksum([Ys[k]*Xs[k,i]*(wp[i] - wn[i]) for i in range(m)]) + Ys[k]*(wbp - wbn) >= 1-z[k])
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model.update()
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# Set hint for variable
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if self.mu > 0:
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muWbar, muBias = self.meanWeights()
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if muBias >= 0.0001:
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wbp.VarHintVal = muBias
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wbn.VarHintVal = 0.0
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elif muBias <= -0.0001:
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wbp.VarHintVal = 0.0
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wbn.VarHintVal = -muBias
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else:
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wbp.VarHintVal = 0.0
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wbn.VarHintVal = 0.0
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for i in wp:
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if muWbar[i] >= 0.0001:
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wp[i].VarHintVal = muWbar[i]
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wn[i].VarHintVal = 0.0
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elif muWbar[i] <= -0.0001:
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wp[i].VarHintVal = 0.0
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wn[i].VarHintVal = -muWbar[i]
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else:
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wp[i].VarHintVal = 0.0
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wn[i].VarHintVal = 0.0
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if muBias >= 0.0001:
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wbp.PStart = muBias
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wbn.PStart = 0.0
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elif muBias <= -0.0001:
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wbp.PStart = 0.0
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wbn.PStart = -muBias
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else:
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wbp.PStart = 0.0
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wbn.PStart = 0.0
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for i in wp:
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if muWbar[i] >= 0.0001:
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wp[i].PStart = muWbar[i]
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wn[i].PStart = 0.0
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elif muWbar[i] <= -0.0001:
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wp[i].PStart = 0.0
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wn[i].PStart = -muWbar[i]
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else:
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wp[i].PStart = 0.0
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wn[i].PStart = 0.0
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model.optimize()
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if model.status != GRB.Status.OPTIMAL and model.status != GRB.TIME_LIMIT and model.status != GRB.USER_OBJ_LIMIT:
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return None
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if model.SolCount == 0:
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return None
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if model.status == GRB.USER_OBJ_LIMIT:
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model.setParam(GRB.Param.BestObjStop, 0.0)
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model.setParam(GRB.Param.TimeLimit, 5)
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model.optimize()
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# Build predictor function
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wbar = np.array([wp[i].x - wn[i].x for i in wp])
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wbias = wbp.x - wbn.x
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# Build predictor function
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def Predict(x):
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return 1 if (wbias + np.dot(x, wbar)) >= 0 else -1
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acc = self.evalTrain(Predict)
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# Update internal values
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print('accuracy:', round(acc, 3), 'obj:', round(model.objVal, 3), 'runtime', round(model.runtime, 2), 'status:', model.status)
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# Keep the best start solution
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if acc > self.accuracy:
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self.accuracy = acc
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self.Predict = Predict
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self.Results.append( (acc, model.objVal) )
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self.Sol.append( (wbar, wbias) )
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# Return prediction function
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return Predict
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def meanWeights(self):
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muWbar = np.zeros(784)
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muBias = 0.0
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for wbar, wbias in self.Sol:
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muWbar += wbar
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muBias += wbias
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muWbar = muWbar/len(self.Sol)
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muBias = muBias/len(self.Sol)
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return muWbar, muBias
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def meanPredict(self):
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muWbar, muBias = self.meanWeights()
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return lambda x: 1 if (muBias + np.dot(x, muWbar)) >= 0 else -1
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def showWeights(self):
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A = np.array([self.wp_start[i] - self.wn_start[i] for i in self.wp_start]).reshape(28,28)
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A[np.abs(A) < 1e-09] = np.nan
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plt.imshow(A, cmap='rainbow')
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plt.colorbar()
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plt.show()
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if __name__ == "__main__":
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import keras
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(x_train, y_train), (x_test, y_test) = keras.datasets.mnist.load_data()
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x_train = x_train.astype(float)/255
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x_train = x_train.reshape(x_train.shape[0],784)
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x_test = x_test.astype(float)/255
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x_test = x_test.reshape(x_test.shape[0],784)
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np.random.seed(13)
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batch_size = 512
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epochs = 30
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for a in range(10):
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for b in range(a+1, 10):
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I = np.where((y_train == a) | (y_train == b))
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Xs = x_train[I]
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Ys = y_train[I]
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DigitOne = Ys[0]
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Ys = np.where(Ys == DigitOne, 1, -1)
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n, m = Xs.shape
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bsvm = BatchLearner(Xs, Ys)
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from time import perf_counter
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time_start = perf_counter()
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for i in range(epochs):
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Sample = np.random.choice(n, n, replace=False)
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bsvm.solve(Xs[Sample], Ys[Sample], timelimit=3600)
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# record end time
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time_end = perf_counter()
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# calculate the duration
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tain_duration = time_end - time_start
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mu_acc, min_acc, max_acc = 0, 100, 0
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for acc, obj in bsvm.Results:
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mu_acc += acc
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min_acc = min(min_acc, acc)
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max_acc = max(max_acc, acc)
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if len(bsvm.Results) > 0:
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mu_acc = round(mu_acc/len(bsvm.Results), 3)
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# record end time
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time_end = perf_counter()
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# calculate the duration
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all_duration = time_end - time_start
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# bsvm.showWeights()
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print('LOG', a, b, 'END mu accuracy:', mu_acc, round(min_acc, 2), round(max_acc, 2), ' over', len(bsvm.Results), 'time:', round(all_duration,3), 'train time:', round(tain_duration, 3))
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I = np.where((y_test == a) | (y_test == b))
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Xs = x_test[I]
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Ys = y_test[I]
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Ys = np.where(Ys == DigitOne, 1, -1)
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acc = 0
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n = len(Ys)
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for i in range(n):
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if bsvm.Predict(Xs[i]) == Ys[i]:
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acc += 1
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acc = (acc/n*100)
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print('LOG', a, b, 'Best Test accuracy:', round(acc, 2))
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acc = 0
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n = len(Ys)
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F = bsvm.meanPredict()
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for i in range(n):
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if F(Xs[i]) == Ys[i]:
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acc += 1
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acc = (acc/n*100)
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print('LOG', a, b, 'Mean Test accuracy:', round(acc, 2))
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logging.info('LOG %d %d %d TestAccuracy %f MuAcc %f time %f t_train %f', a, b, batch_size, acc, mu_acc, all_duration, tain_duration)

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