使用 Commons Math、Hipparchus、OptaPlanner 和 Timefold 的 Groovy 解决简单的优化问题

static scalar(coeffs, rel, double val) {
    new LinearConstraint(coeffs as double[], rel, val)
}

var milk_max   = scalar([0, 1, 0, 0, 0, 0], LEQ, 1)
var fish_min   = scalar([0, 0, 0, 0, 1, 0], GEQ, 0.5)
var protein    = scalar([4.0, 8.0, 7.0, 1.3, 8.0, 9.2],     LEQ, 10)
var fat        = scalar([1.0, 5.0, 9.0, 0.1, 7.0, 1.0],     GEQ, 8)
var carbs      = scalar([15.0, 11.7, 0.4, 22.6, 0.0, 17.0], GEQ, 10)
var calories   = scalar([90, 120, 106, 97, 130, 180],       GEQ, 300)

LinearConstraintSet constraints = [milk_max, fish_min, protein, fat, carbs, calories]

var cost = new LinearObjectiveFunction([2.0, 3.5, 8.0, 1.5, 11.0, 1.0] as double[], 0)

var zeroOrMore = new NonNegativeConstraint(true)

var solution = new SimplexSolver().optimize(cost, constraints, zeroOrMore)

static pretty(int idx, double d) {
    d ? [sprintf('%s %.2f', ['🍞', '🥛', '🧀', '🥔', '🐟', '🍶'][idx], d)] : []
}

if (solution != null) {
    printf "Cost: %.2f%n", solution.value
    println solution.point.indexed().collectMany(this::pretty).join(', ')
}

Cost: 12.08
🥛 0.05, 🧀 0.45, 🥔 1.87, 🐟 0.50

@PlanningEntity
@TupleConstructor(includeFields = true)
class Food {
    final String name, emoji
    final double cost, protein, fat, carbs, calories
    @PlanningVariable(valueRangeProviderRefs = "amount")
    Integer amount // times 100
}

@PlanningSolution
class DietSolution {
    @PlanningEntityCollectionProperty
    List<Food> foods

    @ValueRangeProvider(id = "amount")
    CountableValueRange<Integer> getAmount() {
        ValueRangeFactory.createIntValueRange(0, 200, 5)
    }

    @PlanningScore
    HardSoftScore score

    String toString() {
        var sb = new StringBuilder()
        foods.eachWithIndex { f, idx ->
            sb << "$f.emoji $f.name: ${f.amount / 100}\n"
        }
        for (name in ['fat', 'carbs', 'protein', 'calories', 'cost']) {
            var total = foods.sum{ f -> f."$name" * f.amount / 100 }
            sb << sprintf("Total %s: %.2f%n", name, total)
        }
        sb << "Score: $score"
        sb
    }
}

class DietConstraintProvider implements ConstraintProvider {
    @Override
    Constraint[] defineConstraints(ConstraintFactory factory) {
        new Constraint[]{
                maxField(factory, 'protein', 10),
                minField(factory, 'fat', 8),
                minField(factory, 'carbs', 10),
                minField(factory, 'calories', 300),
                minFood(factory, 'Fish', 50),
                maxFood(factory, 'Milk', 100),
                minCost(factory),
        }
    }

    private static int amountOf(Food f, String name) {
        (f."$name" * f.amount).toInteger()
    }

    private static Constraint minField(ConstraintFactory factory, String fieldName, double minAmount) {
        ToIntFunction<Food> amount = f -> amountOf(f, fieldName)
        factory.forEach(Food)
                .groupBy(sum(amount))
                .filter(fs -> fs < minAmount * 100)
                .penalize(ONE_HARD)
                .asConstraint("Min $fieldName")
    }

    private static Constraint maxField(ConstraintFactory factory, String fieldName, double maxAmount) {
        ToIntFunction<Food> amount = f -> amountOf(f, fieldName)
        factory.forEach(Food)
                .groupBy(sum(amount))
                .filter(fs -> fs > maxAmount * 100)
                .penalize(ONE_HARD)
                .asConstraint("Max $fieldName")
    }

    private static Constraint minFood(ConstraintFactory factory, String foodName, double minAmount) {
        factory.forEach(Food)
                .filter(f -> f.name == foodName && f.amount < minAmount)
                .penalize(ONE_HARD)
                .asConstraint("Min $foodName")
    }

    private static Constraint maxFood(ConstraintFactory factory, String foodName, double maxAmount) {
        factory.forEach(Food)
                .filter(f -> f.name == foodName && f.amount > maxAmount)
                .penalize(ONE_HARD)
                .asConstraint("Max $foodName")
    }

    private static ToIntFunction<Food> totalCost = f -> (f.cost * f.amount).toInteger()

    private static Constraint minCost(ConstraintFactory factory) {
        factory.forEach(Food)
                .filter(f -> f.amount > 0)
                .groupBy(sum(totalCost))
                .penalize(ONE_SOFT, fs -> fs >> 2)
                .asConstraint('Min cost')
    }
}

def unsolved = new DietSolution(foods: [
        new Food('Bread' , '🍞',  2.0, 4.0, 1.0, 15.0,  90),
        new Food('Milk'  , '🥛',  3.5, 8.0, 5.0, 11.7, 120),
        new Food('Cheese', '🧀',  8.0, 7.0, 9.0,  0.4, 106),
        new Food('Potato', '🥔',  1.5, 1.3, 0.1, 22.6,  97),
        new Food('Fish'  , '🐟', 11.0, 8.0, 7.0,  0.0, 130),
        new Food('Yogurt', '🍶',  1.0, 9.2, 1.0, 17.0, 180)
])

def config = new SolverConfig()
        .withSolutionClass(DietSolution)
        .withEntityClasses(Food)
        .withConstraintProviderClass(DietConstraintProvider)
        .withTerminationSpentLimit(Duration.ofSeconds(10))

def factory = SolverFactory.create(config)
def solver = factory.buildSolver()
println solver.solve(unsolved)

08:17:05.202 [main] INFO  a.t.s.core.impl.solver.DefaultSolver - Solving started: time spent (25), best score (-6init/0hard/0soft), environment mode (REPRODUCIBLE), move thread count (NONE), random (JDK with seed 0).
08:17:05.385 [main] INFO  a.t.s.c.i.c.DefaultConstructionHeuristicPhase - Construction Heuristic phase (0) ended: time spent (210), best score (-1hard/-521soft), score calculation speed (1355/sec), step total (6).
08:17:15.175 [main] INFO  a.t.s.c.i.l.DefaultLocalSearchPhase - Local Search phase (1) ended: time spent (10000), best score (-1hard/-261soft), score calculation speed (155967/sec), step total (1030).
08:17:15.176 [main] INFO  a.t.s.core.impl.solver.DefaultSolver - Solving ended: time spent (10000), best score (-1hard/-261soft), score calculation speed (152685/sec), phase total (2), environment mode (REPRODUCIBLE), move thread count (NONE).
🍞 Bread: 0.6
🥛 Milk: 0.6
🧀 Cheese: 0
🥔 Potato: 0.4
🐟 Fish: 0.5
🍶 Yogurt: 1.05
Total fat: 8.19
Total carbs: 42.91
Total protein: 21.38
Total calories: 418.80
Total cost: 10.45
Score: -1hard/-261soft

def construction = new ConstructionHeuristicPhaseConfig(constructionHeuristicType: FIRST_FIT)
def moveSelector = new UnionMoveSelectorConfig([
        new ChangeMoveSelectorConfig(),
        new SwapMoveSelectorConfig()
])
def localSearch = new LocalSearchPhaseConfig(localSearchType: VARIABLE_NEIGHBORHOOD_DESCENT,
        moveSelectorConfig: moveSelector)
def config = new SolverConfig()
        .withSolutionClass(DietSolution)
        .withEntityClasses(Food)
        .withConstraintProviderClass(DietConstraintProvider)
        .withPhases(construction, localSearch) // additional solution guidance
        .withTerminationSpentLimit(Duration.ofSeconds(10))

🍞 Bread: 0
🥛 Milk: 0
🧀 Cheese: 0.5
🥔 Potato: 1.9
🐟 Fish: 0.5
🍶 Yogurt: 0
Total fat: 8.19
Total carbs: 43.14
Total protein: 9.97
Total calories: 302.30
Total cost: 12.35
Score: 0hard/-308soft