/// <summary>
/// I used this Gurobi model to calculate the fixed point baseline.
/// </summary>
public mae_sdo()
{
string path = @"C:\Users\Roman Bolzern\Desktop\D4\neu\meta_data_training.csv";
var lines = File.ReadLines(path).ToArray();
GRBEnv env = new GRBEnv();
GRBModel m = new GRBModel(env);
var scale = 1e9;
var y = m.AddVar(1e-9 * scale, 1e-2 * scale, 0d, GRB.CONTINUOUS, "y");
var obj = new GRBLinExpr();
for (int i = 1; i < lines.Length; i++)
{
var diff = double.Parse(lines[i].Split(',')[3]) * scale - y;
var diffinput = m.AddVar(-1e-2 * scale, 1e-2 * scale, 0d, GRB.CONTINUOUS, "diffinput");
m.AddConstr(diffinput == diff);
var diffres = m.AddVar(0, 1e-2 * scale, 0d, GRB.CONTINUOUS, "diffres");
m.AddGenConstrAbs(diffres, diffinput, "diffAbs");
obj += diffres;
}
m.SetObjective(obj, GRB.MINIMIZE);
m.Optimize();
Console.WriteLine($"Objective: {((GRBLinExpr)m.GetObjective()).Value / scale}");
Console.WriteLine($"fixed point: {y.X / scale}");
}
public GurobiSolver(Crossword crossword)
{
var wordLengthHistogram = new Dictionary <int, int>()
{
{ 3, 18 },
{ 4, 24 },
{ 5, 20 },
{ 6, 18 },
{ 7, 12 },
{ 8, 4 },
{ 9, 4 },
};
const int maxWordLength = 9;
int sizeY = crossword.Grid.GetLength(0);
int sizeX = crossword.Grid.GetLength(1);
int amountQuestions = (int)Math.Round(0.22 * sizeX * sizeY);
GRBEnv env = new GRBEnv();
GRBModel m = new GRBModel(env);
// 0 = letter, 1 = question
GRBVar[,] fields = new GRBVar[sizeY, sizeX];
// 0 = right, 1 = down
GRBVar[,] questionType = new GRBVar[sizeY, sizeX];
for (int y = 0; y < sizeY; y++)
{
for (int x = 0; x < sizeX; x++)
{
// create a var for every non-blocked field
if (!(crossword.Grid[y, x] is Blocked))
{
fields[y, x] = m.AddVar(0, 1, 0, GRB.BINARY, "Field" + x + "_" + y);
questionType[y, x] = m.AddVar(0, 1, 0, GRB.BINARY, "QType" + x + "_" + y);
}
}
}
GRBLinExpr allFieldsSum = new GRBLinExpr();
// count word lengths (to compare with histogram)
var lengths = new Dictionary <int, GRBLinExpr>();
foreach (var l in wordLengthHistogram.Keys)
{
lengths.Add(l, new GRBLinExpr());
}
var partOfAWord = new GRBLinExpr[sizeY, sizeX];
for (int y = 0; y < sizeY; y++)
{
for (int x = 0; x < sizeX; x++)
{
partOfAWord[y, x] = new GRBLinExpr();
}
}
for (int y = 0; y < sizeY; y++)
{
for (int x = 0; x < sizeX; x++)
{
allFieldsSum += fields[y, x];
foreach (var l in wordLengthHistogram.Keys)
{
if (x + l < sizeX)
{
// + 1 if the following fields are all words and the last one is not a word (question or outside grid)
var wordCount = new GRBLinExpr();
for (int i = 1; i <= l; i++)
{
wordCount += fields[y, x + i];
}
// last field is question or outside?
var lastFieldIsNoWord = m.AddVar(0, 1, 0, GRB.BINARY, "lastFieldIsNoWord" + y + "_" + x + "_" + l);
if (x + l + 1 < sizeX)
{
m.AddConstr(lastFieldIsNoWord == fields[y, x + l + 1], "lastFieldIsInGridAndIsQuestion" + y + "_" + x + "_" + l);
}
else
{
m.AddConstr(lastFieldIsNoWord == 1, "lastFieldOutsideGrid" + y + "_" + x + "_" + l);
}
// https://cs.stackexchange.com/questions/51025/cast-to-boolean-for-integer-linear-programming
var hasCorrectWordCount = m.AddVar(0, 1, 0, GRB.BINARY, "hasCorrect" + y + "_" + x + "_" + l);
var hcTemp = m.AddVar(0, 1, 0, GRB.BINARY, "hasCorrectTemp" + y + "_" + x + "_" + l);
var worddiff = wordCount - l;
m.AddConstr(-sizeX * hasCorrectWordCount <= worddiff, "ToBoolean" + y + "_" + x + "_" + l + "_1");
m.AddConstr(worddiff <= sizeX * hasCorrectWordCount, "ToBoolean" + y + "_" + x + "_" + l + "_2");
m.AddConstr(0.001 * hasCorrectWordCount - (sizeX + 0.001) * hcTemp <= worddiff, "ToBoolean" + y + "_" + x + "_" + l + "_3");
m.AddConstr(worddiff <= -0.001 * hasCorrectWordCount + (sizeX + 0.001) * (1 - hcTemp), "ToBoolean" + y + "_" + x + "_" + l + "_4");
// firstFieldIsQuestion AND questionIsHorizontal AND hasCorrectWordCount AND lastFieldIsNoWord
var allConditionsMet = m.AddVar(0, 1, 0, GRB.BINARY, "allCondsMet" + y + "_" + x + "_" + l);
var condVal = fields[y, x] + (1 - questionType[y, x]) + hasCorrectWordCount + lastFieldIsNoWord - 3;
m.AddConstr(allConditionsMet >= condVal, "AllConditionsAND" + y + "_" + x + "_" + l + "_1");
m.AddConstr(allConditionsMet <= fields[y, x], "AllConditionsAND" + y + "_" + x + "_" + l + "_2");
m.AddConstr(allConditionsMet <= (1 - questionType[y, x]), "AllConditionsAND" + y + "_" + x + "_" + l + "_3");
m.AddConstr(allConditionsMet <= hasCorrectWordCount, "AllConditionsAND" + y + "_" + x + "_" + l + "_4");
m.AddConstr(allConditionsMet <= lastFieldIsNoWord, "AllConditionsAND" + y + "_" + x + "_" + l + "_5");
lengths[l] += allConditionsMet;
// If all conditions are met, all letters are part of a word
for (int i = 1; i <= l; i++)
{
partOfAWord[y, x + i] += allConditionsMet;
}
}
if (y + l < sizeY)
{
// + 1 if the following fields are all words and the last one is not a word (question or outside grid)
var wordCount = new GRBLinExpr();
for (int i = 1; i <= l; i++)
{
wordCount += fields[y + i, x];
}
// last field is question or outside?
var lastFieldIsNoWord = m.AddVar(0, 1, 0, GRB.BINARY, "lastFieldIsNoWord" + y + "_" + x + "_" + l);
if (y + l + 1 < sizeY)
{
m.AddConstr(lastFieldIsNoWord == fields[y + l + 1, x], "lastFieldIsInGridAndIsQuestion" + y + "_" + x + "_" + l);
}
else
{
m.AddConstr(lastFieldIsNoWord == 1, "lastFieldOutsideGrid" + y + "_" + x + "_" + l);
}
// https://cs.stackexchange.com/questions/51025/cast-to-boolean-for-integer-linear-programming
var hasCorrectWordCount = m.AddVar(0, 1, 0, GRB.BINARY, "hasCorrect" + y + "_" + x + "_" + l);
var hcTemp = m.AddVar(0, 1, 0, GRB.BINARY, "hasCorrectTemp" + y + "_" + x + "_" + l);
var worddiff = wordCount - l;
m.AddConstr(-sizeY * hasCorrectWordCount <= worddiff, "ToBoolean" + y + "_" + x + "_" + l + "_1");
m.AddConstr(worddiff <= sizeY * hasCorrectWordCount, "ToBoolean" + y + "_" + x + "_" + l + "_2");
m.AddConstr(0.001 * hasCorrectWordCount - (sizeY + 0.001) * hcTemp <= worddiff, "ToBoolean" + y + "_" + x + "_" + l + "_3");
m.AddConstr(worddiff <= -0.001 * hasCorrectWordCount + (sizeY + 0.001) * (1 - hcTemp), "ToBoolean" + y + "_" + x + "_" + l + "_4");
// firstFieldIsQuestion AND questionIsHorizontal AND hasCorrectWordCount AND lastFieldIsNoWord
var allConditionsMet = m.AddVar(0, 1, 0, GRB.BINARY, "allCondsMet" + y + "_" + x + "_" + l);
var condVal = fields[y, x] + (questionType[y, x]) + hasCorrectWordCount + lastFieldIsNoWord - 3;
m.AddConstr(allConditionsMet >= condVal, "AllConditionsAND" + y + "_" + x + "_" + l + "_1");
m.AddConstr(allConditionsMet <= fields[y, x], "AllConditionsAND" + y + "_" + x + "_" + l + "_2");
m.AddConstr(allConditionsMet <= (questionType[y, x]), "AllConditionsAND" + y + "_" + x + "_" + l + "_3");
m.AddConstr(allConditionsMet <= hasCorrectWordCount, "AllConditionsAND" + y + "_" + x + "_" + l + "_4");
m.AddConstr(allConditionsMet <= lastFieldIsNoWord, "AllConditionsAND" + y + "_" + x + "_" + l + "_5");
lengths[l] += allConditionsMet;
// If all conditions are met, all letters are part of a word
for (int i = 1; i <= l; i++)
{
partOfAWord[y + i, x] += allConditionsMet;
}
}
}
// max word count
if (x + maxWordLength < sizeX)
{
var maxWordCount = new GRBLinExpr();
var range = maxWordLength + 1;
if (x + range == sizeX)
{
range--;
}
for (int i = 0; i < maxWordLength + 1; i++)
{
maxWordCount += 1 - fields[y, x + i];
}
m.AddConstr(maxWordCount <= maxWordLength, "maxWordsX" + y + "_" + x);
}
if (y + maxWordLength < sizeY)
{
var maxWordCount = new GRBLinExpr();
var range = maxWordLength + 1;
if (y + range == sizeY)
{
range--;
}
for (int i = 0; i < maxWordLength + 1; i++)
{
maxWordCount += 1 - fields[y + i, x];
}
m.AddConstr(maxWordCount <= maxWordLength, "maxWordsY" + y + "_" + x);
}
}
}
// All non-question fields have to belong to a word
for (int y = 0; y < sizeY; y++)
{
for (int x = 0; x < sizeX; x++)
{
m.AddConstr(1 - fields[y, x] <= partOfAWord[y, x], "NonQuestionsToWords" + y + "_" + x + "_1");
m.AddConstr(1 - fields[y, x] >= partOfAWord[y, x] * 0.5, "NonQuestionsToWords" + y + "_" + x + "_2");
}
}
// after a question, no word of length 1 or 2 is allowed
for (int y = 0; y < sizeY; y++)
{
for (int x = 0; x < sizeX; x++)
{
if (x < sizeX - 3)
{
// if there's a question AND it's pointing right THEN sum(fields[y, x+1/2/3]) = 0
var minLetters = 3 - (fields[y, x + 1] + fields[y, x + 2] + fields[y, x + 3]);
m.AddConstr(fields[y, x] + (1 - questionType[y, x]) - 1 <= minLetters * (1d / 3d), "AfterRightQuestionMin2Letters" + y + "_" + x);
}
else
{
m.AddConstr(questionType[y, x] == 1, "NoRightQuestionAtRightBorder" + y + "_" + x);
}
if (y < sizeY - 3)
{
// if there's a question AND it's pointing down THEN sum(fields[y+1/2/3, x]) = 0
var minLetters = 3 - (fields[y + 1, x] + fields[y + 2, x] + fields[y + 3, x]);
m.AddConstr(fields[y, x] + questionType[y, x] - 1 <= minLetters * (1d / 3d), "AfterDownQuestionMin2Letters" + y + "_" + x);
}
else if (x < sizeX - 3)
{
m.AddConstr(questionType[y, x] == 0, "NoDownQuestionAtBottomBorder" + y + "_" + x);
}
else
{
m.AddConstr(fields[y, x] == 0, "OnlyWordsInBottomrightCorner" + y + "_" + x);
}
}
}
// Objective:
// questions should be around ~22% (allFieldsSum ~= amountQuestions)
var amountOfQuestionsRating = m.AddVar(0, sizeX * sizeY - amountQuestions, 0, GRB.INTEGER, "amountOfQuestionsRating");
var amountOfQuestionsAbsInput = m.AddVar(-amountQuestions, sizeX * sizeY - amountQuestions, 0, GRB.INTEGER, "amountOfQuestionsAbsInput");
m.AddConstr(amountOfQuestionsAbsInput == allFieldsSum - amountQuestions);
m.AddGenConstrAbs(amountOfQuestionsRating, amountOfQuestionsAbsInput, "amountOfQuestionsAbs");
/*int tolerance = (int)(amountQuestions * 0.1);
* m.AddConstr(allFieldsSum - amountQuestions >= -tolerance);
* m.AddConstr(allFieldsSum - amountQuestions <= tolerance);*/
// as many partOfAWord == 2 as possible
var manyCrossedWords = new GRBLinExpr();
for (int y = 0; y < sizeY; y++)
{
for (int x = 0; x < sizeX; x++)
{
manyCrossedWords += partOfAWord[y, x];
}
}
// ideal histogram comparison
var wordHistogramDifferences = new GRBQuadExpr();
foreach (var wl in wordLengthHistogram.Keys)
{
var diff = (wordLengthHistogram[wl] - lengths[wl]) * 2;
wordHistogramDifferences += diff * diff;
}
// question field clusters
var clusterPenalty = new GRBLinExpr();
for (int y = 0; y < sizeY - 2; y++)
{
for (int x = 0; x < sizeX - 2; x++)
{
var clusterTotal = new GRBLinExpr();
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
clusterTotal += fields[y + i, x + j];
}
}
var varClusterTotalPenalty = m.AddVar(0, 7, 0, GRB.INTEGER, "varClusterTotalPenalty" + y + "_" + x);
m.AddConstr(varClusterTotalPenalty >= clusterTotal - 2);
clusterPenalty += varClusterTotalPenalty;
}
}
//amountOfQuestionsRating * (100d / sizeX / sizeY) + manyCrossedWords + + wordHistogramDifferences
// clusterPenalty * 100
m.SetObjective(amountOfQuestionsRating * (100d / sizeX / sizeY) + clusterPenalty * 100 + wordHistogramDifferences + manyCrossedWords, GRB.MINIMIZE);
m.SetCallback(new GRBMipSolCallback(crossword, fields, questionType, null));
m.Optimize();
m.ComputeIIS();
m.Write("model.ilp");
m.Dispose();
env.Dispose();
}