optirustic 1.2.3

use std::cmp::Ordering;

use crate::core::{Individual, OError};

/// The preferred solution with the `BinaryComparisonOperator`.
#[derive(Debug, PartialOrd, PartialEq)]
pub enum PreferredSolution {
    /// The first solution is preferred.
    First,
    /// The second solution is preferred.
    Second,
    /// The two solutions are mutually preferred.
    MutuallyPreferred,
}

/// A trait to implement a comparison operator between two solutions.
pub trait BinaryComparisonOperator {
    /// Compare two solution and select the best one.
    ///
    /// # Arguments
    ///
    /// * `first_solution`: The first solution to compare.
    /// * `second_solution`: The second solution to compare.
    ///
    /// returns: `Result<PreferredSolution, OError>` The preferred solution.
    fn compare(
        first_solution: &Individual,
        second_solution: &Individual,
    ) -> Result<PreferredSolution, OError>
    where
        Self: Sized;
}

/// This assesses the Pareto dominance between two solutions $S_1$ and $S_2$ and their constraint
/// violations in constrained multi-objective optimization problems. A solution $S_1$ is
/// constraint-dominated if:
/// 1) $S_1$ is feasible but $S_2$ is not.
/// 2) Both $S_1$ and $S_2$ are infeasible and $CV(S_1) < CV(S_2)$ (where $CV$ is the constraint
///    violation function); or
/// 3) both are feasible and $S_1$ Pareto-dominate $S_2$ ($ S_1 \prec S_2 $).
///
///
/// See:
///  - Kalyanmoy Deb & Samir Agrawal. (2002). <https://doi.org/10.1007/978-3-7091-6384-9_40>.
///  - Shuang Li, Ke Li, Wei Li. (2022). <https://doi.org/10.48550/arXiv.2205.14349>.
///
pub struct ParetoConstrainedDominance;

impl BinaryComparisonOperator for ParetoConstrainedDominance {
    /// Get the dominance relation between two solutions with constraints.
    ///
    /// # Arguments
    ///
    /// * `first_solution`: The first solution to compare.
    /// * `second_solution`: The second solution to compare.
    ///
    /// returns: `Result<PreferredSolution, OError>` The dominance relation between solution 1
    /// and 2.
    fn compare(
        first_solution: &Individual,
        second_solution: &Individual,
    ) -> Result<PreferredSolution, OError> {
        let problem = first_solution.problem();
        let cv1 = first_solution.constraint_violation();
        let cv2 = second_solution.constraint_violation();

        // at least one solution is not feasible (step 1-2)
        if problem.number_of_constraints() > 0 && cv1 != cv2 {
            if first_solution.is_feasible() {
                // solution 1 dominates
                return Ok(PreferredSolution::First);
            } else if second_solution.is_feasible() {
                // solution 2 dominates
                return Ok(PreferredSolution::Second);
            } else if cv1 < cv2 {
                // solution 1 dominates
                return Ok(PreferredSolution::First);
            } else if cv1 > cv2 {
                // solution 2 dominates
                return Ok(PreferredSolution::Second);
            }
        }

        // check pareto dominance using all the objectives (step 2)
        let mut relation = PreferredSolution::MutuallyPreferred;
        for objective_name in problem.objective_names() {
            let obj_sol1 = first_solution.get_objective_value(objective_name.as_str())?;
            let obj_sol2 = second_solution.get_objective_value(objective_name.as_str())?;

            if obj_sol1 < obj_sol2 {
                // previous objective favours 2nd solution
                if relation == PreferredSolution::Second {
                    // mutually dominated
                    return Ok(PreferredSolution::MutuallyPreferred);
                }
                relation = PreferredSolution::First;
            } else if obj_sol1 > obj_sol2 {
                // previous objective favours 1st solution
                if relation == PreferredSolution::First {
                    // mutually dominated
                    return Ok(PreferredSolution::MutuallyPreferred);
                }
                relation = PreferredSolution::Second;
            }
        }

        Ok(relation)
    }
}

/// This implements the crowded-comparison operator from Deb et al. (2002) for the NSGAII algorithm.
/// A solution $S_i$ dominates a solution $S_j$ if:
///
///    - $rank_i < rank_j$
///
/// or when $rank_i =rank_j$
///
///    - ${distance}_i > {distance}_j$
///
/// where $rank_x$ is the rank from the fast non-dominated sort algorithm (see
/// [`crate::utils::fast_non_dominated_sort()`]) and $distance_x$ is the crowding distance using
/// neighboring solutions.
///
/// Implemented based on:
/// > K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, "A fast and elitist multi-objective genetic
/// > algorithm: NSGA-II," in IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp.
/// > 182-197, April 2002, doi: 10.1109/4235.996017.
///
pub struct CrowdedComparison;

impl BinaryComparisonOperator for CrowdedComparison {
    /// Get the crowded comparison relation between two solutions with rank and crowding distance
    /// data. This returns an error if the data does not exist on either solutions.
    ///
    /// # Arguments
    ///
    /// * `first_solution`: The first solution to compare.
    /// * `second_solution`: The second solution to compare.
    ///
    /// returns: `Result<PreferredSolution, OError>` The dominance relation between solution 1
    /// and 2.
    fn compare(
        first_solution: &Individual,
        second_solution: &Individual,
    ) -> Result<PreferredSolution, OError> {
        let name = "CrowdedComparison".to_string();
        let rank1 = match first_solution.get_data("rank") {
            Err(_) => {
                return Err(OError::ComparisonOperator(
                    name,
                    "The rank on the first individual does not exist".to_string(),
                ))
            }
            Ok(r) => r.as_integer()?,
        };
        let rank2 = match second_solution.get_data("rank") {
            Err(_) => {
                return Err(OError::ComparisonOperator(
                    name,
                    "The rank on the second individual does not exist".to_string(),
                ))
            }
            Ok(r) => r.as_integer()?,
        };

        match rank1.cmp(&rank2) {
            Ordering::Less => Ok(PreferredSolution::First),
            Ordering::Equal => {
                let d1 = match first_solution.get_data("crowding_distance") {
                    Err(_) => {
                        return Err(OError::ComparisonOperator(
                            name,
                            format!(
                                "The crowding distance on the first individual {:?} does not exist",
                                first_solution.variables()
                            ),
                        ))
                    }
                    Ok(r) => r.as_real()?,
                };
                let d2 = match second_solution.get_data("crowding_distance") {
                    Err(_) => {
                        return Err(OError::ComparisonOperator(
                            name,
                            format!(
                            "The crowding distance on the second individual {:?} does not exist",
                            second_solution.variables()
                        ),
                        ))
                    }
                    Ok(r) => r.as_real()?,
                };

                if d1 > d2 {
                    Ok(PreferredSolution::First)
                } else {
                    Ok(PreferredSolution::Second)
                }
            }
            Ordering::Greater => Ok(PreferredSolution::Second),
        }
    }
}

#[cfg(test)]
mod test_pareto_constrained_dominance {
    use std::sync::Arc;

    use crate::core::utils::dummy_evaluator;
    use crate::core::{
        BoundedNumber, Constraint, Individual, Objective, ObjectiveDirection, Problem,
        RelationalOperator, VariableType,
    };
    use crate::operators::{
        BinaryComparisonOperator, ParetoConstrainedDominance, PreferredSolution,
    };

    #[test]
    /// Test unconstrained problem with one objective
    fn test_unconstrained_solutions_1_objective() {
        let objectives = vec![Objective::new("obj1", ObjectiveDirection::Minimise)];
        let variables = vec![VariableType::Real(
            BoundedNumber::new("X1", 0.0, 2.0).unwrap(),
        )];
        let e = dummy_evaluator();
        let problem = Arc::new(Problem::new(objectives, variables, None, e).unwrap());

        let mut solution1 = Individual::new(problem.clone());
        let mut solution2 = Individual::new(problem.clone());

        // Sol 1 dominates
        solution1.update_objective("obj1", 5.0).unwrap();
        solution2.update_objective("obj1", 15.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::First
        );

        // Sol 2 dominates
        solution1.update_objective("obj1", 5.0).unwrap();
        solution2.update_objective("obj1", 1.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::Second
        );

        // Both are non dominated
        solution1.update_objective("obj1", 5.0).unwrap();
        solution2.update_objective("obj1", 5.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::MutuallyPreferred
        );

        // Maximisation problem
        let objectives = vec![Objective::new("obj1", ObjectiveDirection::Maximise)];
        let variables = vec![VariableType::Real(
            BoundedNumber::new("X1", 0.0, 2.0).unwrap(),
        )];
        let e = dummy_evaluator();
        let problem = Arc::new(Problem::new(objectives, variables, None, e).unwrap());

        let mut solution1 = Individual::new(problem.clone());
        let mut solution2 = Individual::new(problem.clone());

        // Sol 2 dominates with larger objective
        solution1.update_objective("obj1", 5.0).unwrap();
        solution2.update_objective("obj1", 15.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::Second
        );
    }

    #[test]
    /// Test unconstrained problem with two objectives
    fn test_unconstrained_solutions_2_objectives() {
        let objectives = vec![
            Objective::new("obj1", ObjectiveDirection::Minimise),
            Objective::new("obj2", ObjectiveDirection::Minimise),
        ];
        let variables = vec![VariableType::Real(
            BoundedNumber::new("X1", 0.0, 2.0).unwrap(),
        )];
        let e = dummy_evaluator();
        let problem = Arc::new(Problem::new(objectives, variables, None, e).unwrap());

        let mut solution1 = Individual::new(problem.clone());
        let mut solution2 = Individual::new(problem.clone());

        // Sol 1 dominates
        solution1.update_objective("obj1", 5.0).unwrap();
        solution1.update_objective("obj2", 1.0).unwrap();
        solution2.update_objective("obj1", 15.0).unwrap();
        solution2.update_objective("obj2", 25.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::First
        );

        // Sol 2 dominates
        solution1.update_objective("obj1", 5.0).unwrap();
        solution1.update_objective("obj2", 1.0).unwrap();
        solution2.update_objective("obj1", -15.0).unwrap();
        solution2.update_objective("obj2", -25.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::Second
        );

        // Obj1 of Sol 1 dominates and Obj2 of Sol 2 dominates
        solution1.update_objective("obj1", 5.0).unwrap();
        solution1.update_objective("obj2", 100.0).unwrap();
        solution2.update_objective("obj1", 15.0).unwrap();
        solution2.update_objective("obj2", 25.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::MutuallyPreferred
        );

        // compare three solutions
        let mut solution3 = Individual::new(problem.clone());
        solution1.update_objective("obj1", 0.0).unwrap();
        solution1.update_objective("obj2", 0.0).unwrap();
        solution2.update_objective("obj1", 1.0).unwrap();
        solution2.update_objective("obj2", 1.0).unwrap();
        solution3.update_objective("obj1", 0.0).unwrap();
        solution3.update_objective("obj2", 1.0).unwrap();

        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::First
        );
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution2, &solution1).unwrap(),
            PreferredSolution::Second
        );
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution3).unwrap(),
            PreferredSolution::First
        );
        // mutually dominated for obj1, but obj2 of sol1 dominates
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution3, &solution1).unwrap(),
            PreferredSolution::Second
        );

        // non-dominance
        solution1.update_objective("obj1", 0.0).unwrap();
        solution1.update_objective("obj2", 1.0).unwrap();
        solution2.update_objective("obj1", 0.5).unwrap();
        solution2.update_objective("obj2", 0.5).unwrap();
        solution3.update_objective("obj1", 1.0).unwrap();
        solution3.update_objective("obj2", 0.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::MutuallyPreferred
        );
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution2, &solution1).unwrap(),
            PreferredSolution::MutuallyPreferred
        );
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution2, &solution3).unwrap(),
            PreferredSolution::MutuallyPreferred
        );
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution3, &solution2).unwrap(),
            PreferredSolution::MutuallyPreferred
        );
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution3).unwrap(),
            PreferredSolution::MutuallyPreferred
        );
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution3, &solution1).unwrap(),
            PreferredSolution::MutuallyPreferred
        );

        // Maximisation problem
        let objectives = vec![
            Objective::new("obj1", ObjectiveDirection::Minimise),
            Objective::new("obj2", ObjectiveDirection::Maximise),
        ];
        let variables = vec![VariableType::Real(
            BoundedNumber::new("X1", 0.0, 2.0).unwrap(),
        )];
        let e = dummy_evaluator();
        let problem = Arc::new(Problem::new(objectives, variables, None, e).unwrap());

        let mut solution1 = Individual::new(problem.clone());
        let mut solution2 = Individual::new(problem.clone());

        // Neither dominates
        solution1.update_objective("obj1", 5.0).unwrap();
        solution2.update_objective("obj1", 15.0).unwrap();
        solution1.update_objective("obj2", 5.0).unwrap();
        solution2.update_objective("obj2", 15.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::MutuallyPreferred
        );

        // Sol 2 dominates
        solution1.update_objective("obj1", 5.0).unwrap();
        solution1.update_objective("obj2", -5.0).unwrap();
        solution2.update_objective("obj1", 1.0).unwrap();
        solution2.update_objective("obj2", 15.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::Second
        );
    }

    #[test]
    /// Test constrained problem with. The constraint violation determines the dominance relation.
    fn test_constrained_solutions() {
        let objectives = vec![Objective::new("obj1", ObjectiveDirection::Minimise)];
        let variables = vec![VariableType::Real(
            BoundedNumber::new("X1", 0.0, 2.0).unwrap(),
        )];
        let constraints = vec![Constraint::new("c1", RelationalOperator::EqualTo, 1.0)];

        let e = dummy_evaluator();
        let problem = Arc::new(Problem::new(objectives, variables, Some(constraints), e).unwrap());

        let mut solution1 = Individual::new(problem.clone());
        let mut solution2 = Individual::new(problem.clone());
        solution1.update_objective("obj1", 5.0).unwrap();
        solution2.update_objective("obj1", 15.0).unwrap();

        // Sol 2 dominates because is feasible
        solution1.update_constraint("c1", 0.0).unwrap();
        solution2.update_constraint("c1", 1.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::Second
        );

        // Solution 1 dominates due to the smaller violation
        solution1.update_constraint("c1", 0.5).unwrap();
        solution2.update_constraint("c1", 3.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::First
        );

        // Solution 1 is returned when violation magnitude is the same
        solution1.update_constraint("c1", 0.5).unwrap();
        solution2.update_constraint("c1", 0.5).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::First
        );

        // Two objectives
        let objectives = vec![
            Objective::new("obj1", ObjectiveDirection::Minimise),
            Objective::new("obj2", ObjectiveDirection::Minimise),
        ];
        let variables = vec![VariableType::Real(
            BoundedNumber::new("X1", 0.0, 2.0).unwrap(),
        )];
        let constraints = vec![Constraint::new("c1", RelationalOperator::EqualTo, 5.0)];

        let e = dummy_evaluator();
        let problem2 = Arc::new(Problem::new(objectives, variables, Some(constraints), e).unwrap());

        let mut solution1 = Individual::new(problem2.clone());
        let mut solution2 = Individual::new(problem2);
        solution1.update_objective("obj2", 100.0).unwrap();
        solution2.update_objective("obj2", 15.0).unwrap();
        solution1.update_constraint("c1", 0.5).unwrap();
        solution2.update_constraint("c1", 3.0).unwrap();
        assert_eq!(
            ParetoConstrainedDominance::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::Second
        );
    }
}

#[cfg(test)]
mod test_crowded_comparison {
    use std::sync::Arc;

    use crate::core::utils::dummy_evaluator;
    use crate::core::{
        BoundedNumber, DataValue, Individual, Objective, ObjectiveDirection, Problem, VariableType,
    };
    use crate::operators::comparison::CrowdedComparison;
    use crate::operators::{BinaryComparisonOperator, PreferredSolution};

    #[test]
    fn test_different_rank() {
        let objectives = vec![Objective::new("obj1", ObjectiveDirection::Minimise)];
        let variables = vec![VariableType::Real(
            BoundedNumber::new("X1", 0.0, 2.0).unwrap(),
        )];
        let e = dummy_evaluator();
        let problem = Arc::new(Problem::new(objectives, variables, None, e).unwrap());

        let mut solution1 = Individual::new(problem.clone());
        let mut solution2 = Individual::new(problem.clone());
        solution1.set_data("rank", DataValue::Integer(1));
        solution2.set_data("rank", DataValue::Integer(4));

        // Sol 1 dominates
        assert_eq!(
            CrowdedComparison::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::First
        );

        // Sol 2 dominates
        solution1.set_data("rank", DataValue::Integer(5));
        assert_eq!(
            CrowdedComparison::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::Second
        );
    }

    #[test]
    fn test_same_rank() {
        let objectives = vec![Objective::new("obj1", ObjectiveDirection::Minimise)];
        let variables = vec![VariableType::Real(
            BoundedNumber::new("X1", 0.0, 2.0).unwrap(),
        )];
        let e = dummy_evaluator();
        let problem = Arc::new(Problem::new(objectives, variables, None, e).unwrap());

        let mut solution1 = Individual::new(problem.clone());
        let mut solution2 = Individual::new(problem.clone());
        solution1.set_data("rank", DataValue::Integer(1));
        solution2.set_data("rank", DataValue::Integer(1));

        solution1.set_data("crowding_distance", DataValue::Real(10.5));
        solution2.set_data("crowding_distance", DataValue::Real(0.32));
        // Sol 1 dominates
        assert_eq!(
            CrowdedComparison::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::First
        );

        // Sol 2 dominates
        solution2.set_data("crowding_distance", DataValue::Real(100.32));
        assert_eq!(
            CrowdedComparison::compare(&solution1, &solution2).unwrap(),
            PreferredSolution::Second
        );
    }
}