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

Example 11 with Variable

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

the class ConvexProblems method testP20080118.

/**
 * Ended up with a singular matrix (the equation system body generated by the LagrangeSolver) that
 * resulted in a solution with NaN and Inf elements. This was not recognised and handled.
 */
@Test
public void testP20080118() {
    // create expected returns matrix
    final PrimitiveMatrix expectedReturnsMatrix = PrimitiveMatrix.FACTORY.rows(new double[][] { { 10.003264 }, { 9.989771 }, { 9.987513 }, { 9.988449 }, { 9.996579 }, { 9.990690 }, { 9.994904 }, { 9.994514 }, { 9.984064 }, { 9.987534 } });
    // create covariance matrix
    final PrimitiveMatrix covarianceMatrix = PrimitiveMatrix.FACTORY.rows(new double[][] { { 6.483565230120298E-4, -1.3344603795915894E-4, -4.610345510893708E-4, -7.334405624030001E-4, 1.1551383115707195E-5, -0.00104145662863434, -1.0725896685568462E-4, -1.221384153392056E-4, -4.173413644389791E-4, -2.4861043894946935E-4 }, { -1.3344603795915894E-4, 0.0026045957224784455, 0.0012394355327235707, 9.243919166568456E-4, -8.653805945112411E-5, 8.100239312410631E-4, 4.215960274481846E-4, 5.243272007211247E-4, 0.0013062718630332956, 1.4766450293395405E-4 }, { -4.610345510893708E-4, 0.0012394355327235707, 0.002361436913752224, 0.0020101714731002238, -1.4236763916609785E-5, 0.002120395905829043, 5.399158658928662E-4, 5.048790842067473E-4, 0.0014855261720730444, 4.841458106181396E-4 }, { -7.334405624030001E-4, 9.243919166568456E-4, 0.0020101714731002238, 0.0028542819089926895, -4.311102526746861E-6, 0.0028465650900869476, 6.242643883624462E-4, 4.086484048798765E-4, 0.001647437646316569, 7.58419663970477E-4 }, { 1.1551383115707195E-5, -8.653805945112411E-5, -1.4236763916609785E-5, -4.311102526746861E-6, 1.213366124417227E-4, -9.027529241741836E-5, 7.241389994693716E-6, -3.166855950737129E-5, -1.2445276374560802E-5, -5.3976919759028745E-5 }, { -0.00104145662863434, 8.100239312410631E-4, 0.002120395905829043, 0.0028465650900869476, -9.027529241741836E-5, 0.0064756879298965295, 2.8076277564885113E-4, 3.6082073553997553E-4, 0.001945238279500792, 0.0012421132342988626 }, { -1.0725896685568462E-4, 4.215960274481846E-4, 5.399158658928662E-4, 6.242643883624462E-4, 7.241389994693716E-6, 2.8076277564885113E-4, 0.0010121500024739688, 8.206099676659543E-5, 1.6129237403855146E-4, 7.550465994733837E-4 }, { -1.221384153392056E-4, 5.243272007211247E-4, 5.048790842067473E-4, 4.086484048798765E-4, -3.166855950737129E-5, 3.6082073553997553E-4, 8.206099676659543E-5, 4.504461842318998E-4, 4.7980942831718363E-4, -4.763223568683059E-5 }, { -4.173413644389791E-4, 0.0013062718630332956, 0.0014855261720730444, 0.001647437646316569, -1.2445276374560802E-5, 0.001945238279500792, 1.6129237403855146E-4, 4.7980942831718363E-4, 0.002228245076175045, 3.2083564921169634E-4 }, { -2.4861043894946935E-4, 1.4766450293395405E-4, 4.841458106181396E-4, 7.58419663970477E-4, -5.3976919759028745E-5, 0.0012421132342988626, 7.550465994733837E-4, -4.763223568683059E-5, 3.2083564921169634E-4, 0.0017093327832123186 } });
    // create asset variables - cost and weighting constraints
    final Variable[] tmpVariables = new Variable[(int) expectedReturnsMatrix.countRows()];
    for (int i = 0; i < tmpVariables.length; i++) {
        tmpVariables[i] = new Variable("VAR" + i);
        final int row = i;
        tmpVariables[i].weight(TypeUtils.toBigDecimal(expectedReturnsMatrix.get(row, 0)).negate());
        // set the constraints on the asset weights
        // require at least a 2% allocation to each asset
        tmpVariables[i].lower(new BigDecimal("0.05"));
        // require no more than 80% allocation to each asset
        tmpVariables[i].upper(new BigDecimal("0.35"));
    }
    final RationalMatrix tmpExpected = RationalMatrix.FACTORY.rows(new double[][] { { 0.35 }, { 0.05 }, { 0.05 }, { 0.05 }, { 0.25 }, { 0.05 }, { 0.05 }, { 0.05 }, { 0.05 }, { 0.05 } });
    ConvexProblems.doEarly2008(tmpVariables, covarianceMatrix, tmpExpected);
}

Example 12 with Variable

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

the class ConvexProblems method builAndTestModel.

static void builAndTestModel(final PrimitiveDenseStore[] matrices, final PrimitiveDenseStore expectedSolution, final NumberContext modelValidationContext, final boolean testSolverDirectly) {
    final MatrixStore<Double> tmpPartQ = expectedSolution.transpose().multiply(matrices[2].multiply(expectedSolution));
    final MatrixStore<Double> tmpPartC = matrices[3].transpose().multiply(expectedSolution);
    final double tmpExpectedValue = tmpPartQ.multiply(HALF.doubleValue()).subtract(tmpPartC).doubleValue(0);
    final Optimisation.Result tmpExpectedResult = new Optimisation.Result(Optimisation.State.OPTIMAL, tmpExpectedValue, expectedSolution);
    final ExpressionsBasedModel tmpModel = ConvexProblems.buildModel(matrices, expectedSolution);
    OptimisationConvexTests.assertDirectAndIterativeEquals(tmpModel, modelValidationContext);
    if (DEBUG) {
        tmpModel.options.debug(ConvexSolver.class);
        tmpModel.options.validate = false;
    }
    TestUtils.assertTrue("Expected solution not ok!", tmpModel.validate(tmpExpectedResult, modelValidationContext));
    // The expected solution is written to the variables
    TestUtils.assertTrue("Expected solution not ok!", tmpModel.validate(modelValidationContext));
    // When/if the correct/optimal solution is used to kickStart ojAlgo should return that solution
    final Result tmpInitialisedModelResult = tmpModel.minimise();
    TestUtils.assertStateNotLessThanOptimal(tmpInitialisedModelResult);
    TestUtils.assertEquals(tmpExpectedResult, tmpInitialisedModelResult, modelValidationContext);
    TestUtils.assertEquals(tmpExpectedValue, tmpInitialisedModelResult.getValue(), modelValidationContext);
    TestUtils.assertEquals(tmpExpectedValue, tmpModel.objective().evaluate(tmpInitialisedModelResult).doubleValue(), modelValidationContext);
    TestUtils.assertEquals(tmpExpectedValue, tmpModel.objective().toFunction().invoke(expectedSolution).doubleValue(), modelValidationContext);
    for (final Variable tmpVariable : tmpModel.getVariables()) {
        tmpVariable.setValue(null);
    }
    // Initial variable values have been cleared
    final Result tmpUninitialisedModelResult = tmpModel.minimise();
    TestUtils.assertStateNotLessThanOptimal(tmpUninitialisedModelResult);
    TestUtils.assertEquals(tmpExpectedResult, tmpUninitialisedModelResult, modelValidationContext);
    TestUtils.assertEquals(tmpExpectedValue, tmpUninitialisedModelResult.getValue(), modelValidationContext);
    TestUtils.assertEquals(tmpExpectedValue, tmpModel.objective().evaluate(tmpUninitialisedModelResult).doubleValue(), modelValidationContext);
    TestUtils.assertEquals(tmpExpectedValue, tmpModel.objective().toFunction().invoke(expectedSolution).doubleValue(), modelValidationContext);
    if (testSolverDirectly) {
        final ConvexSolver.Builder tmpBuilder = new ConvexSolver.Builder(matrices);
        final ConvexSolver tmpSolver = tmpBuilder.build();
        // tmpSolver.options.debug(ConvexSolver.class);
        // tmpSolver.options.validate = false;
        final Optimisation.Result tmpResult = tmpSolver.solve();
        TestUtils.assertStateNotLessThanOptimal(tmpResult);
        TestUtils.assertEquals(tmpExpectedResult, tmpResult, NumberContext.getGeneral(2, 4));
        TestUtils.assertEquals(tmpExpectedValue, tmpModel.objective().evaluate(tmpResult).doubleValue(), NumberContext.getGeneral(4, 8));
    }
}

Example 13 with Variable

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

the class ConvexProblems method testP20111129.

/**
 * ojAlgo could not solve this, but LOQO (and others) could. I re-implemented the problem code just to
 * verify there was no problem there. http://bugzilla.optimatika.se/show_bug.cgi?id=11
 */
@Test
public void testP20111129() {
    final Variable x1 = new Variable("X1");
    final Variable x2 = new Variable("X2").lower(BigMath.HUNDRED.negate()).upper(BigMath.HUNDRED);
    final Variable x3 = new Variable("X3").lower(BigMath.ZERO);
    final Variable x4 = new Variable("X4").lower(BigMath.ZERO);
    final Variable[] tmpVariables = new Variable[] { x1, x2, x3, x4 };
    final ExpressionsBasedModel tmpModel = new ExpressionsBasedModel(tmpVariables);
    final Expression tmpObjExpr = tmpModel.addExpression("Objective");
    tmpModel.setMinimisation();
    tmpObjExpr.set(2, 2, BigMath.HALF);
    tmpObjExpr.set(3, 3, BigMath.TWO);
    tmpObjExpr.set(2, 3, BigMath.TWO.negate());
    tmpObjExpr.set(0, BigMath.THREE);
    tmpObjExpr.set(1, BigMath.TWO.negate());
    tmpObjExpr.set(2, BigMath.ONE);
    tmpObjExpr.set(3, BigMath.FOUR.negate());
    tmpObjExpr.weight(BigMath.ONE);
    Expression tmpConstrExpr;
    tmpConstrExpr = tmpModel.addExpression("C1").lower(BigMath.FOUR);
    tmpConstrExpr.set(0, BigMath.ONE);
    tmpConstrExpr.set(1, BigMath.ONE);
    tmpConstrExpr.set(2, BigMath.FOUR.negate());
    tmpConstrExpr.set(3, BigMath.TWO);
    tmpConstrExpr = tmpModel.addExpression("C2").upper(BigMath.SIX);
    tmpConstrExpr.set(0, BigMath.THREE.negate());
    tmpConstrExpr.set(1, BigMath.ONE);
    tmpConstrExpr.set(2, BigMath.TWO.negate());
    tmpConstrExpr = tmpModel.addExpression("C3").level(BigMath.NEG);
    tmpConstrExpr.set(1, BigMath.ONE);
    tmpConstrExpr.set(3, BigMath.NEG);
    tmpConstrExpr = tmpModel.addExpression("C4").level(BigMath.ZERO);
    tmpConstrExpr.set(0, BigMath.ONE);
    tmpConstrExpr.set(1, BigMath.ONE);
    tmpConstrExpr.set(2, BigMath.NEG);
    // tmpModel.options.debug(ConvexSolver.class);
    final Result tmpResult = tmpModel.minimise();
    final double tmpObjFuncVal = tmpResult.getValue();
    TestUtils.assertEquals(-5.281249989, tmpObjFuncVal, new NumberContext(7, 6));
    final double[] tmpExpected = new double[] { -1.1875, 1.5625, 0.375, 2.5625 };
    for (int i = 0; i < tmpExpected.length; i++) {
        TestUtils.assertEquals(tmpExpected[i], tmpVariables[i].getValue().doubleValue(), new NumberContext(5, 4));
    }
    OptimisationConvexTests.assertDirectAndIterativeEquals(tmpModel, null);
}

Example 14 with Variable

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

the class P20150720 method buildModel3.

/**
 * Sent in 2015-09-03
 */
public static ExpressionsBasedModel buildModel3() {
    /*
         * 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);
            });
        }
    });
    return model;
}

Example 15 with Variable

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

the class P20150720 method buildModel1.

public static ExpressionsBasedModel buildModel1() {
    // List of Variable Names
    final List<String> variablesName = new ArrayList<>();
    variablesName.add("CUSTOMER_1|PRODUCT_TYPE_1");
    variablesName.add("CUSTOMER_2|PRODUCT_TYPE_1");
    variablesName.add("CUSTOMER_3|PRODUCT_TYPE_1");
    variablesName.add("CUSTOMER_3|PRODUCT_TYPE_2");
    variablesName.add("CUSTOMER_3|PRODUCT_TYPE_3");
    variablesName.add("CUSTOMER_3|PRODUCT_TYPE_4");
    variablesName.add("CUSTOMER_3|PRODUCT_TYPE_5");
    variablesName.add("CUSTOMER_4|PRODUCT_TYPE_1");
    variablesName.add("CUSTOMER_4|PRODUCT_TYPE_2");
    variablesName.add("CUSTOMER_5|PRODUCT_TYPE_2");
    variablesName.add("CUSTOMER_5|PRODUCT_TYPE_3");
    variablesName.add("CUSTOMER_5|PRODUCT_TYPE_4");
    variablesName.add("CUSTOMER_6|PRODUCT_TYPE_2");
    variablesName.add("CUSTOMER_6|PRODUCT_TYPE_3");
    variablesName.add("CUSTOMER_6|PRODUCT_TYPE_4");
    variablesName.add("CUSTOMER_6|PRODUCT_TYPE_5");
    /*
         * Constraints for each Customer = Demand of each Customer Sum of all variable linked to the customer
         * <= Demand.
         */
    final Map<String, Integer> constraintsCustomer = new LinkedHashMap<>();
    constraintsCustomer.put("CUSTOMER_1", 40_000);
    constraintsCustomer.put("CUSTOMER_2", 25_000);
    constraintsCustomer.put("CUSTOMER_3", 15_000);
    constraintsCustomer.put("CUSTOMER_4", 5_000);
    constraintsCustomer.put("CUSTOMER_5", 2_000);
    final double demandTotal = constraintsCustomer.values().stream().mapToDouble(e -> e.doubleValue()).sum();
    /*
         * Constraits for each product type = Stock per product type. Sum of all variable linked to this
         * product type <=
         */
    final Map<String, Integer> constraintsProduct = new HashMap<>();
    constraintsProduct.put("PRODUCT_TYPE_1", 50_000);
    constraintsProduct.put("PRODUCT_TYPE_2", 0);
    constraintsProduct.put("PRODUCT_TYPE_3", 0);
    constraintsProduct.put("PRODUCT_TYPE_4", 0);
    constraintsProduct.put("PRODUCT_TYPE_5", 0);
    final double stockTotal = constraintsProduct.values().stream().mapToDouble(e -> e.doubleValue()).sum();
    /*
         *
         */
    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).integer(true).lower(0.0);
        model.addVariable(var);
        variables.add(var);
    // BasicLogger.debug(var);
    });
    // BasicLogger.debug("---- Constraints customers ------");
    // Apply Customers constraints.
    constraintsCustomer.entrySet().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.lower(0.0).upper(entry.getValue().doubleValue());
        constraint.setLinearFactorsSimple(linked);
        linked.forEach(v -> v.upper(entry.getValue().doubleValue()));
    // BasicLogger.debug(constraint);
    });
    // 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.lower(0.0).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);
    final List<Variable> errors = new ArrayList<>();
    // BasicLogger.debug("---- Error formula ------");
    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 Variable error = Variable.make("ERROR:" + entry.getKey());
            model.addVariable(error);
            errors.add(error);
            final Expression errorExp = model.addExpression("ERROR_EXP:" + entry.getKey()).level(stockTotal / demandTotal);
            linked.forEach(v -> errorExp.set(v, 1.0 / entry.getValue().doubleValue()));
            errorExp.set(error, -1.0);
            // - Squared of error.
            objective.set(error, error, -1.0);
        }
    });
    return model;
}