SimplexTASK/simplex.cpp

#include <algorithm>
#include <iostream>
#include "tools/matrix.h"
#include "tools/math.h"
#include "tools/elimination.h"

enum solver_state {
	unbounded,
	bounded,
	unsolvable
};

struct Result {
	solver_state state;
	Vector solution;
	double objective_function_value;
};

void _printInitialInputs(Vector& C, Matrix& A, Vector& b) {

}

void _stopIterating(Matrix& generalMatrix, Vector& C, std::vector<int>& basicVars, solver_state state, Result& result) {
	DestroyMatrix destroyedGeneralMatrix = disassembleGeneralMatrix(generalMatrix);
	Matrix _A = destroyedGeneralMatrix.A;
	Vector _C = destroyedGeneralMatrix.C;
	Vector _b = destroyedGeneralMatrix.b;

	result.state = state;
	if (state == bounded) {
		result.solution = Vector(C.size());
		for (int i = 0; i < C.size(); i++) {
			result.solution[i] = 0;
		}
		for (size_t i = 1; i < basicVars.size(); i++) {		
			if (basicVars[i] < C.size()) {
				result.solution[basicVars[i]] = _b[i];
			}
		}

		result.objective_function_value = _b[0];
	} else {
		result.solution = Vector({0});
		result.objective_function_value = 0;
	}
}

/*
	Implementation of the Simplex method.
*/
Result simplex(Vector& C, Matrix& A, Vector& b, double eps = 0.01, bool maximize=true) {

	if (maximize == true) {
		for (int i = 0; i < C.size(); i++) {
		    C[i] = -C[i];
		}
	}
 	Result result{};
  	Matrix generalMatrix = createGeneralMatrix(A, C, b);
	std::cout << "Before:" << std::endl << generalMatrix;
	std::vector<int> basicVars(generalMatrix.getRows());
	basicVars[0] = -1;

	for (int i = 0; i < b.size(); ++i) {
		if (b[i] < 0) {
			_stopIterating(generalMatrix, C, basicVars, unsolvable, result);
			return result;
		}
	}

	for (size_t i = 1; i < basicVars.size(); i++) {
		basicVars[i] = static_cast<int>(basicVars.size()) + i;
	}
	int iterationCount = 0;
	while (true) {
		//3
		iterationCount++;
		int pivot_column_index = 0;
		
		pivot_column_index = min_index(generalMatrix[0]);

		if (generalMatrix[0][pivot_column_index] >= 0) {
			_stopIterating(generalMatrix, C, basicVars, bounded, result);
			if (!maximize) {
				result.objective_function_value = -result.objective_function_value;
			}
			return result;
		}

		std::cout << "Iteration: ";
		std::cout << iterationCount << std::endl;

		//4
		Vector ratio_vector(generalMatrix.getRows());
		for (int i = 1; i < generalMatrix.getRows(); i++) {
			if (generalMatrix[i][pivot_column_index] != 0) {
            	ratio_vector[i] = generalMatrix[i][generalMatrix.getColumns() - 1] / generalMatrix[i][pivot_column_index];
				if (std::abs(ratio_vector[i]) < eps) {
					ratio_vector[i] = 0;
				}
			} else {
            	ratio_vector[i] = 0;
        	}
		}
		ratio_vector[0] = 0;

		int pivot_row_index = min_index_positive(ratio_vector);

		// No leaving variable exists
		if (pivot_row_index == -1) {
			_stopIterating(generalMatrix, C, basicVars, unbounded, result);
			return result;
		}

		basicVars[pivot_row_index] = pivot_column_index;

		//5
		elimination(generalMatrix, pivot_row_index, pivot_column_index);
		std::cout << "After:" << std::endl << generalMatrix;
	}

	return result;
}

/*
Function_name(C, A, b, eps = eps_default)

Input:
- C: A vector of coefficients of the objective function
- A: A matrix of coefficients of the constraint functions
- b: A vector of right-hand side values
- eps: Approximation accuracy (optional, default = eps_default)

Steps:
1. Print the optimization problem:
   - max (or min) z = C[0] * x1 + C[1] * x2 + ... + C[n] * xn
   - subject to the constraints:
     - A[0] * x <= b[0]
     - A[1] * x <= b[1]
     - ...
     - A[m] * x <= b[m]

2. Initialize:
   - Form the initial tableau by introducing slack variables to convert inequalities into equalities.

3. Iteratively apply the Simplex method:
   - Step 1: Identify the entering variable (most negative coefficient in the objective row).
   - Step 2: Identify the leaving variable (smallest positive ratio of RHS to pivot column).
   - Step 3: Perform pivot operations to update the tableau.

4. Check for optimality or unboundedness:
   - If all coefficients in the objective function row are non-negative, the solution is optimal.
   - If no leaving variable exists, the problem is unbounded.

5. Return:
   - solver_state: {solved, unbounded}
   - x*: Optimal vector of decision variables (if solved)
   - z: Maximum (or minimum) value of the objective function (if solved)

End Function
*/