Examples with Expression org.ojalgo.optimisation.Expression used on opensource projects

Example 26 with Expression

use of org.ojalgo.optimisation.Expression in project ojAlgo by optimatika.

the class SimplexSolver method build.

static SimplexTableau build(final ExpressionsBasedModel model) {
    final List<Variable> tmpPosVariables = model.getPositiveVariables();
    final List<Variable> tmpNegVariables = model.getNegativeVariables();
    final Set<IntIndex> tmpFixVariables = model.getFixedVariables();
    final Expression tmpObjFunc = model.objective().compensate(tmpFixVariables);
    final List<Expression> tmpExprsEq = model.constraints().filter(c -> c.isEqualityConstraint() && !c.isAnyQuadraticFactorNonZero()).collect(Collectors.toList());
    final List<Expression> tmpExprsLo = model.constraints().filter(c -> c.isLowerConstraint() && !c.isAnyQuadraticFactorNonZero()).collect(Collectors.toList());
    final List<Expression> tmpExprsUp = model.constraints().filter(c -> c.isUpperConstraint() && !c.isAnyQuadraticFactorNonZero()).collect(Collectors.toList());
    final List<Variable> tmpVarsPosLo = model.bounds().filter(v -> v.isPositive() && v.isLowerConstraint() && (v.getLowerLimit().signum() > 0)).collect(Collectors.toList());
    final List<Variable> tmpVarsPosUp = model.bounds().filter(v -> v.isPositive() && v.isUpperConstraint() && (v.getUpperLimit().signum() > 0)).collect(Collectors.toList());
    final List<Variable> tmpVarsNegLo = model.bounds().filter(v -> v.isNegative() && v.isLowerConstraint() && (v.getLowerLimit().signum() < 0)).collect(Collectors.toList());
    final List<Variable> tmpVarsNegUp = model.bounds().filter(v -> v.isNegative() && v.isUpperConstraint() && (v.getUpperLimit().signum() < 0)).collect(Collectors.toList());
    final int tmpConstraiCount = tmpExprsEq.size() + tmpExprsLo.size() + tmpExprsUp.size() + tmpVarsPosLo.size() + tmpVarsPosUp.size() + tmpVarsNegLo.size() + tmpVarsNegUp.size();
    final int tmpProblVarCount = tmpPosVariables.size() + tmpNegVariables.size();
    final int tmpSlackVarCount = tmpExprsLo.size() + tmpExprsUp.size() + tmpVarsPosLo.size() + tmpVarsPosUp.size() + tmpVarsNegLo.size() + tmpVarsNegUp.size();
    final SimplexTableau retVal = SimplexTableau.make(tmpConstraiCount, tmpProblVarCount, tmpSlackVarCount);
    final int tmpPosVarsBaseIndex = 0;
    final int tmpNegVarsBaseIndex = tmpPosVarsBaseIndex + tmpPosVariables.size();
    final int tmpSlaVarsBaseIndex = tmpNegVarsBaseIndex + tmpNegVariables.size();
    for (final IntIndex tmpKey : tmpObjFunc.getLinearKeySet()) {
        final double tmpFactor = model.isMaximisation() ? -tmpObjFunc.getAdjustedLinearFactor(tmpKey) : tmpObjFunc.getAdjustedLinearFactor(tmpKey);
        final int tmpPosInd = model.indexOfPositiveVariable(tmpKey.index);
        if (tmpPosInd >= 0) {
            retVal.objective().set(tmpPosInd, tmpFactor);
        }
        final int tmpNegInd = model.indexOfNegativeVariable(tmpKey.index);
        if (tmpNegInd >= 0) {
            retVal.objective().set(tmpNegVarsBaseIndex + tmpNegInd, -tmpFactor);
        }
    }
    int tmpConstrBaseIndex = 0;
    int tmpCurrentSlackVarIndex = tmpSlaVarsBaseIndex;
    final int tmpExprsEqLength = tmpExprsEq.size();
    for (int c = 0; c < tmpExprsEqLength; c++) {
        final Expression tmpExpr = tmpExprsEq.get(c).compensate(tmpFixVariables);
        final double tmpRHS = tmpExpr.getAdjustedLowerLimit();
        if (tmpRHS < ZERO) {
            retVal.constraintsRHS().set(tmpConstrBaseIndex + c, -tmpRHS);
            for (final IntIndex tmpKey : tmpExpr.getLinearKeySet()) {
                final double tmpFactor = tmpExpr.getAdjustedLinearFactor(tmpKey);
                final int tmpPosInd = model.indexOfPositiveVariable(tmpKey.index);
                if (tmpPosInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, -tmpFactor);
                }
                final int tmpNegInd = model.indexOfNegativeVariable(tmpKey.index);
                if (tmpNegInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, tmpFactor);
                }
            }
        } else {
            retVal.constraintsRHS().set(tmpConstrBaseIndex + c, tmpRHS);
            for (final IntIndex tmpKey : tmpExpr.getLinearKeySet()) {
                final double tmpFactor = tmpExpr.getAdjustedLinearFactor(tmpKey);
                final int tmpPosInd = model.indexOfPositiveVariable(tmpKey.index);
                if (tmpPosInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, tmpFactor);
                }
                final int tmpNegInd = model.indexOfNegativeVariable(tmpKey.index);
                if (tmpNegInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, -tmpFactor);
                }
            }
        }
    }
    tmpConstrBaseIndex += tmpExprsEqLength;
    final int tmpExprsLoLength = tmpExprsLo.size();
    for (int c = 0; c < tmpExprsLoLength; c++) {
        final Expression tmpExpr = tmpExprsLo.get(c).compensate(tmpFixVariables);
        final double tmpRHS = tmpExpr.getAdjustedLowerLimit();
        if (tmpRHS < ZERO) {
            retVal.constraintsRHS().set(tmpConstrBaseIndex + c, -tmpRHS);
            for (final IntIndex tmpKey : tmpExpr.getLinearKeySet()) {
                final double tmpFactor = tmpExpr.getAdjustedLinearFactor(tmpKey);
                final int tmpPosInd = model.indexOfPositiveVariable(tmpKey.index);
                if (tmpPosInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, -tmpFactor);
                }
                final int tmpNegInd = model.indexOfNegativeVariable(tmpKey.index);
                if (tmpNegInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, tmpFactor);
                }
            }
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpCurrentSlackVarIndex++, ONE);
        } else {
            retVal.constraintsRHS().set(tmpConstrBaseIndex + c, tmpRHS);
            for (final IntIndex tmpKey : tmpExpr.getLinearKeySet()) {
                final double tmpFactor = tmpExpr.getAdjustedLinearFactor(tmpKey);
                final int tmpPosInd = model.indexOfPositiveVariable(tmpKey.index);
                if (tmpPosInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, tmpFactor);
                }
                final int tmpNegInd = model.indexOfNegativeVariable(tmpKey.index);
                if (tmpNegInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, -tmpFactor);
                }
            }
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpCurrentSlackVarIndex++, NEG);
        }
    }
    tmpConstrBaseIndex += tmpExprsLoLength;
    final int tmpExprsUpLength = tmpExprsUp.size();
    for (int c = 0; c < tmpExprsUpLength; c++) {
        final Expression tmpExpr = tmpExprsUp.get(c).compensate(tmpFixVariables);
        final double tmpRHS = tmpExpr.getAdjustedUpperLimit();
        if (tmpRHS < ZERO) {
            retVal.constraintsRHS().set(tmpConstrBaseIndex + c, -tmpRHS);
            for (final IntIndex tmpKey : tmpExpr.getLinearKeySet()) {
                final double tmpFactor = tmpExpr.getAdjustedLinearFactor(tmpKey);
                final int tmpPosInd = model.indexOfPositiveVariable(tmpKey.index);
                if (tmpPosInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, -tmpFactor);
                }
                final int tmpNegInd = model.indexOfNegativeVariable(tmpKey.index);
                if (tmpNegInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, tmpFactor);
                }
            }
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpCurrentSlackVarIndex++, NEG);
        } else {
            retVal.constraintsRHS().set(tmpConstrBaseIndex + c, tmpRHS);
            for (final IntIndex tmpKey : tmpExpr.getLinearKeySet()) {
                final double tmpFactor = tmpExpr.getAdjustedLinearFactor(tmpKey);
                final int tmpPosInd = model.indexOfPositiveVariable(tmpKey.index);
                if (tmpPosInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, tmpFactor);
                }
                final int tmpNegInd = model.indexOfNegativeVariable(tmpKey.index);
                if (tmpNegInd >= 0) {
                    retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, -tmpFactor);
                }
            }
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpCurrentSlackVarIndex++, ONE);
        }
    }
    tmpConstrBaseIndex += tmpExprsUpLength;
    final int tmpVarsPosLoLength = tmpVarsPosLo.size();
    for (int c = 0; c < tmpVarsPosLoLength; c++) {
        final Variable tmpVar = tmpVarsPosLo.get(c);
        retVal.constraintsRHS().set(tmpConstrBaseIndex + c, tmpVar.getAdjustedLowerLimit());
        final int tmpKey = model.indexOf(tmpVar);
        final double tmpFactor = tmpVar.getAdjustmentFactor();
        final int tmpPosInd = model.indexOfPositiveVariable(tmpKey);
        if (tmpPosInd >= 0) {
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, tmpFactor);
        }
        final int tmpNegInd = model.indexOfNegativeVariable(tmpKey);
        if (tmpNegInd >= 0) {
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, -tmpFactor);
        }
        retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpCurrentSlackVarIndex++, NEG);
    }
    tmpConstrBaseIndex += tmpVarsPosLoLength;
    final int tmpVarsPosUpLength = tmpVarsPosUp.size();
    for (int c = 0; c < tmpVarsPosUpLength; c++) {
        final Variable tmpVar = tmpVarsPosUp.get(c);
        retVal.constraintsRHS().set(tmpConstrBaseIndex + c, tmpVar.getAdjustedUpperLimit());
        final int tmpKey = model.indexOf(tmpVar);
        final double tmpFactor = tmpVar.getAdjustmentFactor();
        final int tmpPosInd = model.indexOfPositiveVariable(tmpKey);
        if (tmpPosInd >= 0) {
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, tmpFactor);
        }
        final int tmpNegInd = model.indexOfNegativeVariable(tmpKey);
        if (tmpNegInd >= 0) {
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, -tmpFactor);
        }
        retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpCurrentSlackVarIndex++, ONE);
    }
    tmpConstrBaseIndex += tmpVarsPosUpLength;
    final int tmpVarsNegLoLength = tmpVarsNegLo.size();
    for (int c = 0; c < tmpVarsNegLoLength; c++) {
        final Variable tmpVar = tmpVarsNegLo.get(c);
        retVal.constraintsRHS().set(tmpConstrBaseIndex + c, -tmpVar.getAdjustedLowerLimit());
        final int tmpKey = model.indexOf(tmpVar);
        final double tmpFactor = tmpVar.getAdjustmentFactor();
        final int tmpPosInd = model.indexOfPositiveVariable(tmpKey);
        if (tmpPosInd >= 0) {
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, -tmpFactor);
        }
        final int tmpNegInd = model.indexOfNegativeVariable(tmpKey);
        if (tmpNegInd >= 0) {
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, tmpFactor);
        }
        retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpCurrentSlackVarIndex++, ONE);
    }
    tmpConstrBaseIndex += tmpVarsNegLoLength;
    final int tmpVarsNegUpLength = tmpVarsNegUp.size();
    for (int c = 0; c < tmpVarsNegUpLength; c++) {
        final Variable tmpVar = tmpVarsNegUp.get(c);
        retVal.constraintsRHS().set(tmpConstrBaseIndex + c, -tmpVar.getAdjustedUpperLimit());
        final int tmpKey = model.indexOf(tmpVar);
        final double tmpFactor = tmpVar.getAdjustmentFactor();
        final int tmpPosInd = model.indexOfPositiveVariable(tmpKey);
        if (tmpPosInd >= 0) {
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpPosVarsBaseIndex + tmpPosInd, -tmpFactor);
        }
        final int tmpNegInd = model.indexOfNegativeVariable(tmpKey);
        if (tmpNegInd >= 0) {
            retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpNegVarsBaseIndex + tmpNegInd, tmpFactor);
        }
        retVal.constraintsBody().set(tmpConstrBaseIndex + c, tmpCurrentSlackVarIndex++, NEG);
    }
    tmpConstrBaseIndex += tmpVarsNegUpLength;
    if (retVal.getOvercapacity() <= OjAlgoUtils.ENVIRONMENT.getCacheElements(8L)) {
        return retVal.toDense();
    } else {
        return retVal;
    }
}

Example 27 with Expression

use of org.ojalgo.optimisation.Expression in project ojAlgo by optimatika.

the class ConvexProblems method buildModel.

static ExpressionsBasedModel buildModel(final PrimitiveDenseStore[] matrices, final PrimitiveDenseStore expectedSolution) {
    final ExpressionsBasedModel retVal = new ExpressionsBasedModel();
    final int tmpNumberOfVariables = (int) matrices[3].count();
    for (int v = 0; v < tmpNumberOfVariables; v++) {
        final Variable tmpVariable = Variable.make("X" + v);
        tmpVariable.setValue(BigDecimal.valueOf(expectedSolution.doubleValue(v)));
        retVal.addVariable(tmpVariable);
    }
    if ((matrices[0] != null) && (matrices[1] != null)) {
        for (int e = 0; e < matrices[0].countRows(); e++) {
            final Expression tmpExpression = retVal.addExpression("E" + e);
            for (int v = 0; v < tmpNumberOfVariables; v++) {
                tmpExpression.set(v, matrices[0].get(e, v));
            }
            tmpExpression.level(matrices[1].doubleValue(e));
        }
    }
    if ((matrices[4] != null) && (matrices[5] != null)) {
        for (int i = 0; i < matrices[4].countRows(); i++) {
            final Expression tmpExpression = retVal.addExpression("I" + i);
            for (int v = 0; v < tmpNumberOfVariables; v++) {
                tmpExpression.set(v, matrices[4].get(i, v));
            }
            tmpExpression.upper(matrices[5].doubleValue(i));
        }
    }
    final Expression tmpObjQ = retVal.addExpression("Q");
    for (int r = 0; r < tmpNumberOfVariables; r++) {
        for (int v = 0; v < tmpNumberOfVariables; v++) {
            tmpObjQ.set(r, v, matrices[2].doubleValue(r, v));
        }
    }
    tmpObjQ.weight(HALF);
    final Expression tmpObjC = retVal.addExpression("C");
    for (int v = 0; v < tmpNumberOfVariables; v++) {
        tmpObjC.set(v, matrices[3].doubleValue(v));
    }
    tmpObjC.weight(NEG);
    return retVal;
}

Example 28 with Expression

use of org.ojalgo.optimisation.Expression in project ojAlgo by optimatika.

the class ConvexProblems method testInfeasibleCase.

/**
 * Just make sure an obviously infeasible problem is recognised as such - this has been a problem in the
 * past
 */
@Test
public void testInfeasibleCase() {
    final Variable[] tmpVariables = new Variable[] { new Variable("X1").lower(ONE).upper(TWO).weight(ONE), new Variable("X2").lower(ONE).upper(TWO).weight(TWO), new Variable("X3").lower(ONE).upper(TWO).weight(THREE) };
    final ExpressionsBasedModel tmpModel = new ExpressionsBasedModel(tmpVariables);
    final Expression tmpExprQ = tmpModel.addExpression("Q1");
    for (int i = 0; i < tmpModel.countVariables(); i++) {
        for (int j = 0; j < tmpModel.countVariables(); j++) {
            tmpExprQ.set(i, i, Math.random());
        }
    }
    // May not be positive definite, but infeasibillity should be realised before that becomes a problem
    tmpExprQ.weight(TEN);
    // tmpModel.options.debug(ConvexSolver.class);
    final Expression tmpExprC1 = tmpModel.addExpression("C1");
    for (int i = 0; i < tmpModel.countVariables(); i++) {
        tmpExprC1.set(i, ONE);
    }
    tmpExprC1.upper(TWO);
    Optimisation.Result tmpResult = tmpModel.maximise();
    TestUtils.assertFalse(tmpResult.getState().isFeasible());
    tmpExprC1.upper(null);
    tmpExprC1.lower(SEVEN);
    tmpResult = tmpModel.maximise();
    TestUtils.assertFalse(tmpResult.getState().isFeasible());
    OptimisationConvexTests.assertDirectAndIterativeEquals(tmpModel, null);
}

Example 29 with Expression

use of org.ojalgo.optimisation.Expression in project ojAlgo by optimatika.

the class FinancePortfolioProblem method buildModel.

private static ExpressionsBasedModel buildModel(final BasicMatrix covariances, final BasicMatrix returns, final BigDecimal riskAversion) {
    ProgrammingError.throwIfNotSquare(covariances);
    ProgrammingError.throwIfNotEqualRowDimensions(covariances, returns);
    final int numberOfVariables = (int) returns.countRows();
    final Variable[] tmpVariables = new Variable[numberOfVariables];
    for (int i = 0; i < numberOfVariables; i++) {
        tmpVariables[i] = Variable.make("Asset_" + Integer.toString(i)).lower(ZERO).upper(ONE).weight(-returns.doubleValue(i));
    }
    final ExpressionsBasedModel retVal = new ExpressionsBasedModel(tmpVariables);
    final Expression tmp100P = retVal.addExpression("Balance");
    for (int i = 0; i < numberOfVariables; i++) {
        tmp100P.set(i, ONE);
    }
    tmp100P.level(ONE);
    final Expression tmpVar = retVal.addExpression("Variance");
    for (int i = 0; i < numberOfVariables; i++) {
        for (int j = 0; j < numberOfVariables; j++) {
            tmpVar.set(i, j, covariances.doubleValue(i, j));
        }
    }
    tmpVar.weight(BigFunction.DIVIDE.invoke(riskAversion, TWO));
    return retVal;
}

Example 30 with Expression

use of org.ojalgo.optimisation.Expression in project ojAlgo by optimatika.

the class OJAlgoTest3 method main.

/**
 * @param args the command line arguments Objective: allocate the maximum qty, and try to keep
 *        proportionality between customer.
 */
public static void main(final String[] args) {
    /*
         * 5 Products with associated Qty.
         */
    final Map<String, Integer> constraintsProduct = new HashMap<>();
    constraintsProduct.put("PRODUCT_1", 296_000);
    constraintsProduct.put("PRODUCT_2", 888_000);
    constraintsProduct.put("PRODUCT_3", 636_000);
    constraintsProduct.put("PRODUCT_4", 220_000);
    constraintsProduct.put("PRODUCT_5", 0);
    final double stockTotal = constraintsProduct.values().stream().mapToDouble(e -> e.doubleValue()).sum();
    BasicLogger.debug("STOCK_TOTAL " + stockTotal);
    /*
         * Demand of each Customers
         */
    final Map<String, Integer> constraintsCustomer = new LinkedHashMap<>();
    constraintsCustomer.put("CUSTOMER_A_1", 72_000);
    constraintsCustomer.put("CUSTOMER_A_2", 44_000);
    constraintsCustomer.put("CUSTOMER_A_3", 12_000);
    constraintsCustomer.put("CUSTOMER_A_4", 36_000);
    constraintsCustomer.put("CUSTOMER_A_5", 0);
    constraintsCustomer.put("CUSTOMER_A_6", 36_000);
    constraintsCustomer.put("CUSTOMER_A_7", 12_000);
    constraintsCustomer.put("CUSTOMER_A_8", 0);
    constraintsCustomer.put("CUSTOMER_A_9", 0);
    constraintsCustomer.put("CUSTOMER_A_10", 12_000);
    constraintsCustomer.put("CUSTOMER_A_11", 12_000);
    constraintsCustomer.put("CUSTOMER_A_12", 0);
    constraintsCustomer.put("CUSTOMER_A_13", 0);
    constraintsCustomer.put("CUSTOMER_A_14", 0);
    constraintsCustomer.put("CUSTOMER_B_1", 24_000);
    constraintsCustomer.put("CUSTOMER_B_2", 12_000);
    constraintsCustomer.put("CUSTOMER_B_3", 300);
    constraintsCustomer.put("CUSTOMER_C_1", 24_000);
    constraintsCustomer.put("CUSTOMER_D_1", 20_000);
    constraintsCustomer.put("CUSTOMER_E_1", 12_000);
    constraintsCustomer.put("CUSTOMER_F_1", 12_000);
    constraintsCustomer.put("CUSTOMER_G_1", 72_000);
    constraintsCustomer.put("CUSTOMER_H_1", 28_000);
    constraintsCustomer.put("CUSTOMER_I_1", 24_000);
    constraintsCustomer.put("CUSTOMER_J_1", 16_000);
    constraintsCustomer.put("CUSTOMER_K_1", 24_000);
    constraintsCustomer.put("CUSTOMER_L_1", 56_000);
    final double demandTotal = constraintsCustomer.values().stream().mapToDouble(e -> e.doubleValue()).sum();
    BasicLogger.debug("DEMAND_TOTAL " + demandTotal);
    /*
         * User constraint. In this case, user want to allocate 236_000 Qty on Customer_A_*
         */
    final double userConstraintQty = 236_000;
    final List<String> userConstraint = new ArrayList<>();
    userConstraint.add("CUSTOMER_A_1|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_2|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_3|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_4|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_5|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_6|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_7|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_8|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_9|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_10|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_11|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_12|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_13|PRODUCT_2");
    userConstraint.add("CUSTOMER_A_14|PRODUCT_2");
    // List of Variable Names
    final List<String> variablesName = new ArrayList<>();
    variablesName.add("CUSTOMER_A_1|PRODUCT_2");
    variablesName.add("CUSTOMER_A_2|PRODUCT_2");
    variablesName.add("CUSTOMER_A_3|PRODUCT_2");
    variablesName.add("CUSTOMER_A_4|PRODUCT_2");
    variablesName.add("CUSTOMER_A_5|PRODUCT_2");
    variablesName.add("CUSTOMER_A_6|PRODUCT_2");
    variablesName.add("CUSTOMER_A_7|PRODUCT_2");
    variablesName.add("CUSTOMER_A_8|PRODUCT_2");
    variablesName.add("CUSTOMER_A_9|PRODUCT_2");
    variablesName.add("CUSTOMER_A_10|PRODUCT_2");
    variablesName.add("CUSTOMER_A_11|PRODUCT_2");
    variablesName.add("CUSTOMER_A_12|PRODUCT_2");
    variablesName.add("CUSTOMER_A_13|PRODUCT_2");
    variablesName.add("CUSTOMER_A_14|PRODUCT_2");
    variablesName.add("CUSTOMER_B_1|PRODUCT_2");
    variablesName.add("CUSTOMER_B_1|PRODUCT_3");
    variablesName.add("CUSTOMER_B_2|PRODUCT_2");
    variablesName.add("CUSTOMER_B_2|PRODUCT_3");
    variablesName.add("CUSTOMER_B_3|PRODUCT_2");
    variablesName.add("CUSTOMER_B_3|PRODUCT_3");
    variablesName.add("CUSTOMER_C_1|PRODUCT_2");
    variablesName.add("CUSTOMER_C_1|PRODUCT_3");
    variablesName.add("CUSTOMER_D_1|PRODUCT_4");
    variablesName.add("CUSTOMER_D_1|PRODUCT_5");
    variablesName.add("CUSTOMER_D_1|PRODUCT_2");
    variablesName.add("CUSTOMER_D_1|PRODUCT_3");
    variablesName.add("CUSTOMER_E_1|PRODUCT_1");
    variablesName.add("CUSTOMER_F_1|PRODUCT_4");
    variablesName.add("CUSTOMER_F_1|PRODUCT_5");
    variablesName.add("CUSTOMER_F_1|PRODUCT_2");
    variablesName.add("CUSTOMER_F_1|PRODUCT_3");
    variablesName.add("CUSTOMER_G_1|PRODUCT_4");
    variablesName.add("CUSTOMER_G_1|PRODUCT_5");
    variablesName.add("CUSTOMER_G_1|PRODUCT_2");
    variablesName.add("CUSTOMER_G_1|PRODUCT_3");
    variablesName.add("CUSTOMER_H_1|PRODUCT_4");
    variablesName.add("CUSTOMER_H_1|PRODUCT_5");
    variablesName.add("CUSTOMER_H_1|PRODUCT_2");
    variablesName.add("CUSTOMER_H_1|PRODUCT_3");
    variablesName.add("CUSTOMER_I_1|PRODUCT_4");
    variablesName.add("CUSTOMER_I_1|PRODUCT_5");
    variablesName.add("CUSTOMER_I_1|PRODUCT_2");
    variablesName.add("CUSTOMER_I_1|PRODUCT_3");
    variablesName.add("CUSTOMER_J_1|PRODUCT_4");
    variablesName.add("CUSTOMER_J_1|PRODUCT_5");
    variablesName.add("CUSTOMER_J_1|PRODUCT_2");
    variablesName.add("CUSTOMER_J_1|PRODUCT_3");
    variablesName.add("CUSTOMER_K_1|PRODUCT_4");
    variablesName.add("CUSTOMER_K_1|PRODUCT_5");
    variablesName.add("CUSTOMER_K_1|PRODUCT_2");
    variablesName.add("CUSTOMER_K_1|PRODUCT_3");
    variablesName.add("CUSTOMER_L_1|PRODUCT_1");
    /*
         *
         */
    final ExpressionsBasedModel model = new ExpressionsBasedModel();
    final List<Variable> variables = new ArrayList<>();
    /*
         * Create All Variables:
         */
    BasicLogger.debug("---- Variable creation ------");
    variablesName.forEach(name -> {
        final Variable var = Variable.make(name).lower(0.0).weight(1.0);
        model.addVariable(var);
        variables.add(var);
        BasicLogger.debug(var);
    });
    BasicLogger.debug("---- Constraints customers ------");
    // Apply Customers constraints.
    // CUSTOMER_A of Demand constraint because managed by user constraints.
    constraintsCustomer.entrySet().stream().filter(e -> !e.getKey().startsWith("CUSTOMER_A")).forEach(entry -> {
        final List<Variable> linked = variables.stream().filter(v -> v.getName().startsWith(entry.getKey())).collect(Collectors.toList());
        final Expression constraint = model.addExpression("CONSTRAINTS_" + entry.getKey());
        constraint.upper(entry.getValue().doubleValue());
        constraint.setLinearFactorsSimple(linked);
        BasicLogger.debug(constraint);
    });
    BasicLogger.debug("---- User Constraints Customers ------");
    // Apply Product Type constraints.
    final List<Variable> userLinked = variables.stream().filter(v -> userConstraint.contains(v.getName())).collect(Collectors.toList());
    final Expression constraintUser = model.addExpression("CONSTRAINTS_USER_CUSTOMER_A");
    constraintUser.level(userConstraintQty);
    constraintUser.setLinearFactorsSimple(userLinked);
    BasicLogger.debug(constraintUser);
    BasicLogger.debug("---- Constraints Product ------");
    // Apply Product Type constraints.
    constraintsProduct.entrySet().forEach(entry -> {
        final List<Variable> linked = variables.stream().filter(v -> v.getName().endsWith(entry.getKey())).collect(Collectors.toList());
        final Expression constraint = model.addExpression("CONSTRAINTS_" + entry.getKey());
        constraint.upper(entry.getValue().doubleValue());
        constraint.setLinearFactorsSimple(linked);
        BasicLogger.debug(constraint);
    });
    /*
         * Objective expression. - Maximize the Sum of all variables - Minimize the Sum of square error vs
         * proportionality.
         */
    BasicLogger.debug("---- Objective  ------");
    final Expression objective = model.addExpression("OBJECTIVE").weight(-1.0);
    // - Maximize the Sum of all variables
    // objective.setLinearFactorsSimple(variables);
    BasicLogger.debug("---- Error formula ------");
    /*
         * Example: x1, x2, x3 linked variables for Customer X Error = ( (x1+x2+x3) / Target - 1 )^2 * ratio
         */
    constraintsCustomer.entrySet().forEach(entry -> {
        final List<Variable> linked = variables.stream().filter(v -> v.getName().startsWith(entry.getKey())).collect(Collectors.toList());
        if (!linked.isEmpty() && (entry.getValue().doubleValue() > 0)) {
            final double demand = entry.getValue();
            final double ratio = demand / demandTotal;
            final double target = stockTotal * ratio;
            linked.forEach(v1 -> {
                linked.forEach(v2 -> {
                    objective.set(v1, v2, ratio / (target * target));
                });
                objective.set(v1, (-2.0 * ratio) / target);
            });
        }
    });
    // - Maximise
    // model.options.validate = true;
    final Result result = model.maximise();
    BasicLogger.debug(result);
    // GOOD  OPTIMAL 560300.4702803734
    // WRONG OPTIMAL 560300.4015031556
    BasicLogger.debug("");
    BasicLogger.debug("");
    variables.forEach(v -> BasicLogger.debug(v.getName() + " = " + v.getValue().doubleValue()));
/*
         * WRONG ALLOCATION CUSTOMER_A_1|PRODUCT_2 = 236000.0 CUSTOMER_A_2|PRODUCT_2 = 0.0
         * CUSTOMER_A_3|PRODUCT_2 = 0.0 CUSTOMER_A_4|PRODUCT_2 = 0.0 CUSTOMER_A_5|PRODUCT_2 = 0.0
         * CUSTOMER_A_6|PRODUCT_2 = 0.0 CUSTOMER_A_7|PRODUCT_2 = 0.0 CUSTOMER_A_8|PRODUCT_2 = 0.0
         * CUSTOMER_A_9|PRODUCT_2 = 0.0 CUSTOMER_A_10|PRODUCT_2 = 0.0 CUSTOMER_A_11|PRODUCT_2 = 0.0
         * CUSTOMER_A_12|PRODUCT_2 = 0.0 CUSTOMER_A_13|PRODUCT_2 = 0.0 CUSTOMER_A_14|PRODUCT_2 = 0.0
         * CUSTOMER_B_1|PRODUCT_2 = 24000.0 CUSTOMER_B_1|PRODUCT_3 = 0.0 CUSTOMER_B_2|PRODUCT_2 = 12000.0
         * CUSTOMER_B_2|PRODUCT_3 = 0.0 CUSTOMER_B_3|PRODUCT_2 = 0.0 CUSTOMER_B_3|PRODUCT_3 = 300.0
         * CUSTOMER_C_1|PRODUCT_2 = 24000.0 CUSTOMER_C_1|PRODUCT_3 = 0.0 CUSTOMER_D_1|PRODUCT_4 = 20000.0
         * CUSTOMER_D_1|PRODUCT_5 = 0.0 CUSTOMER_D_1|PRODUCT_2 = 0.0 CUSTOMER_D_1|PRODUCT_3 = 0.0
         * CUSTOMER_E_1|PRODUCT_1 = 12000.0 CUSTOMER_F_1|PRODUCT_4 = 12000.0 CUSTOMER_F_1|PRODUCT_5 = 0.0
         * CUSTOMER_F_1|PRODUCT_2 = 0.0 CUSTOMER_F_1|PRODUCT_3 = 0.0 CUSTOMER_G_1|PRODUCT_4 = 72000.0
         * CUSTOMER_G_1|PRODUCT_5 = 0.0 CUSTOMER_G_1|PRODUCT_2 = 0.0 CUSTOMER_G_1|PRODUCT_3 = 0.0
         * CUSTOMER_H_1|PRODUCT_4 = 28000.0 CUSTOMER_H_1|PRODUCT_5 = 0.0 CUSTOMER_H_1|PRODUCT_2 = 0.0
         * CUSTOMER_H_1|PRODUCT_3 = 0.0 CUSTOMER_I_1|PRODUCT_4 = 24000.0 CUSTOMER_I_1|PRODUCT_5 = 0.0
         * CUSTOMER_I_1|PRODUCT_2 = 0.0 CUSTOMER_I_1|PRODUCT_3 = 0.0 CUSTOMER_J_1|PRODUCT_4 = 16000.0
         * CUSTOMER_J_1|PRODUCT_5 = 0.0 CUSTOMER_J_1|PRODUCT_2 = 0.0 CUSTOMER_J_1|PRODUCT_3 = 0.0
         * CUSTOMER_K_1|PRODUCT_4 = 24000.0 CUSTOMER_K_1|PRODUCT_5 = 0.0 CUSTOMER_K_1|PRODUCT_2 = 0.0
         * CUSTOMER_K_1|PRODUCT_3 = 0.0 CUSTOMER_L_1|PRODUCT_1 = 56000.0
         */
/*
         * GOOD ALLOCATION CUSTOMER_A_1|PRODUCT_2 = 80150.9434796 CUSTOMER_A_2|PRODUCT_2 = 48981.1320493
         * CUSTOMER_A_3|PRODUCT_2 = 13358.4905589 CUSTOMER_A_4|PRODUCT_2 = 40075.4716767
         * CUSTOMER_A_5|PRODUCT_2 = 0.0 CUSTOMER_A_6|PRODUCT_2 = 40075.4716767 CUSTOMER_A_7|PRODUCT_2 =
         * 13358.4905589 CUSTOMER_A_8|PRODUCT_2 = 0.0 CUSTOMER_A_9|PRODUCT_2 = 0.0 CUSTOMER_A_10|PRODUCT_2 =
         * 0.0 CUSTOMER_A_11|PRODUCT_2 = 0.0 CUSTOMER_A_12|PRODUCT_2 = 0.0 CUSTOMER_A_13|PRODUCT_2 = 0.0
         * CUSTOMER_A_14|PRODUCT_2 = 0.0 CUSTOMER_B_1|PRODUCT_2 = 24000.0 CUSTOMER_B_1|PRODUCT_3 = 0.0
         * CUSTOMER_B_2|PRODUCT_2 = 12000.0 CUSTOMER_B_2|PRODUCT_3 = 0.0 CUSTOMER_B_3|PRODUCT_2 = 0.0
         * CUSTOMER_B_3|PRODUCT_3 = 300.0 CUSTOMER_C_1|PRODUCT_2 = 24000.0 CUSTOMER_C_1|PRODUCT_3 = 0.0
         * CUSTOMER_D_1|PRODUCT_4 = 20000.0 CUSTOMER_D_1|PRODUCT_5 = 0.0 CUSTOMER_D_1|PRODUCT_2 = 0.0
         * CUSTOMER_D_1|PRODUCT_3 = 0.0 CUSTOMER_E_1|PRODUCT_1 = 12000.0 CUSTOMER_F_1|PRODUCT_4 = 12000.0
         * CUSTOMER_F_1|PRODUCT_5 = 0.0 CUSTOMER_F_1|PRODUCT_2 = 0.0 CUSTOMER_F_1|PRODUCT_3 = 0.0
         * CUSTOMER_G_1|PRODUCT_4 = 72000.0 CUSTOMER_G_1|PRODUCT_5 = 0.0 CUSTOMER_G_1|PRODUCT_2 = 0.0
         * CUSTOMER_G_1|PRODUCT_3 = 0.0 CUSTOMER_H_1|PRODUCT_4 = 28000.0 CUSTOMER_H_1|PRODUCT_5 = 0.0
         * CUSTOMER_H_1|PRODUCT_2 = 0.0 CUSTOMER_H_1|PRODUCT_3 = 0.0 CUSTOMER_I_1|PRODUCT_4 = 24000.0
         * CUSTOMER_I_1|PRODUCT_5 = 0.0 CUSTOMER_I_1|PRODUCT_2 = 0.0 CUSTOMER_I_1|PRODUCT_3 = 0.0
         * CUSTOMER_J_1|PRODUCT_4 = 16000.0 CUSTOMER_J_1|PRODUCT_5 = 0.0 CUSTOMER_J_1|PRODUCT_2 = 0.0
         * CUSTOMER_J_1|PRODUCT_3 = 0.0 CUSTOMER_K_1|PRODUCT_4 = 24000.0 CUSTOMER_K_1|PRODUCT_5 = 0.0
         * CUSTOMER_K_1|PRODUCT_2 = 0.0 CUSTOMER_K_1|PRODUCT_3 = 0.0 CUSTOMER_L_1|PRODUCT_1 = 56000.0
         */
}