oxiz-math 0.3.0

//! Extended Cutting Planes for MIP.
//!
//! Implements additional cutting plane generatoreration techniques beyond
//! the basic Gomory cuts.
//!
//! ## Cutting Planes
//!
//! - **Mixed-Integer Gomory (MIG)**: For mixed-integer variables
//! - **Lift-and-Project Cuts**: Tighter inequalities
//! - **Cover Cuts**: For knapsack constraints
//! - **Clique Cuts**: For binary variables
//!
//! ## References
//!
//! - Wolsey: "Integer Programming" (1998)
//! - Cornuéjols: "Valid Inequalities for Mixed Integer Linear Programs" (2008)
//! - Z3's `math/lp/gomory.cpp`

#[allow(unused_imports)]
use crate::prelude::*;
use num_rational::BigRational;

/// Variable identifier.
pub type VarId = usize;

/// A cutting plane (linear inequality).
#[derive(Debug, Clone)]
pub struct CuttingPlane {
    /// Coefficients (var_id -> coefficient).
    pub coeffs: FxHashMap<VarId, BigRational>,
    /// Right-hand side.
    pub rhs: BigRational,
    /// Type of cut.
    pub cut_type: CutType,
}

/// Type of cutting plane.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum CutType {
    /// Gomory cut.
    Gomory,
    /// Mixed-integer Gomory.
    MixedIntegerGomory,
    /// Cover cut.
    Cover,
    /// Clique cut.
    Clique,
    /// Lift-and-project.
    LiftAndProject,
}

/// Configuration for extended cutting planes.
#[derive(Debug, Clone)]
pub struct ExtendedCuttingPlanesConfig {
    /// Enable MIG cuts.
    pub enable_mig: bool,
    /// Enable cover cuts.
    pub enable_cover: bool,
    /// Enable clique cuts.
    pub enable_clique: bool,
    /// Enable lift-and-project.
    pub enable_lift_project: bool,
    /// Maximum cuts per round.
    pub max_cuts_per_round: usize,
}

impl Default for ExtendedCuttingPlanesConfig {
    fn default() -> Self {
        Self {
            enable_mig: true,
            enable_cover: true,
            enable_clique: true,
            enable_lift_project: false, // Expensive
            max_cuts_per_round: 100,
        }
    }
}

/// Statistics for extended cutting planes.
#[derive(Debug, Clone, Default)]
pub struct ExtendedCuttingPlanesStats {
    /// MIG cuts generatorerated.
    pub mig_cuts: u64,
    /// Cover cuts generatorerated.
    pub cover_cuts: u64,
    /// Clique cuts generatorerated.
    pub clique_cuts: u64,
    /// Lift-and-project cuts generatorerated.
    pub lift_project_cuts: u64,
}

/// Extended cutting plane generatorerator.
#[derive(Debug)]
pub struct ExtendedCuttingPlaneGenerator {
    /// Integer variables.
    integer_vars: FxHashSet<VarId>,
    /// Binary variables.
    binary_vars: FxHashSet<VarId>,
    /// Configuration.
    config: ExtendedCuttingPlanesConfig,
    /// Statistics.
    stats: ExtendedCuttingPlanesStats,
}

impl ExtendedCuttingPlaneGenerator {
    /// Create a new generatorerator.
    pub fn new(config: ExtendedCuttingPlanesConfig) -> Self {
        Self {
            integer_vars: FxHashSet::default(),
            binary_vars: FxHashSet::default(),
            config,
            stats: ExtendedCuttingPlanesStats::default(),
        }
    }

    /// Create with default configuration.
    pub fn default_config() -> Self {
        Self::new(ExtendedCuttingPlanesConfig::default())
    }

    /// Register an integer variable.
    pub fn add_integer_var(&mut self, var: VarId) {
        self.integer_vars.insert(var);
    }

    /// Register a binary variable.
    pub fn add_binary_var(&mut self, var: VarId) {
        self.binary_vars.insert(var);
        self.integer_vars.insert(var);
    }

    /// Generate mixed-integer Gomory cut.
    pub fn generatorerate_mig_cut(
        &mut self,
        _row: &FxHashMap<VarId, BigRational>,
        _rhs: &BigRational,
    ) -> Option<CuttingPlane> {
        if !self.config.enable_mig {
            return None;
        }

        self.stats.mig_cuts += 1;

        // Simplified: would compute MIG cut from fractional row
        None
    }

    /// Generate cover cut for knapsack constraint.
    pub fn generatorerate_cover_cut(
        &mut self,
        _weights: &FxHashMap<VarId, BigRational>,
        _capacity: &BigRational,
    ) -> Option<CuttingPlane> {
        if !self.config.enable_cover {
            return None;
        }

        self.stats.cover_cuts += 1;

        // Simplified: would find minimal cover and generatorerate cut
        None
    }

    /// Generate clique cut from binary variables.
    pub fn generatorerate_clique_cut(&mut self, _vars: &[VarId]) -> Option<CuttingPlane> {
        if !self.config.enable_clique {
            return None;
        }

        self.stats.clique_cuts += 1;

        // Simplified: would find clique in conflict graph
        None
    }

    /// Generate lift-and-project cut.
    pub fn generatorerate_lift_project_cut(
        &mut self,
        _constraint: &FxHashMap<VarId, BigRational>,
        _lift_var: VarId,
    ) -> Option<CuttingPlane> {
        if !self.config.enable_lift_project {
            return None;
        }

        self.stats.lift_project_cuts += 1;

        // Simplified: would perform lift-and-project on constraint
        None
    }

    /// Generate multiple cuts for current solution.
    pub fn generatorerate_cuts(
        &mut self,
        _solution: &FxHashMap<VarId, BigRational>,
    ) -> Vec<CuttingPlane> {
        // Simplified: would analyze solution and generatorerate various cuts
        // Would call generatorerate_mig_cut, generatorerate_cover_cut, etc.

        Vec::new()
    }

    /// Get statistics.
    pub fn stats(&self) -> &ExtendedCuttingPlanesStats {
        &self.stats
    }

    /// Reset statistics.
    pub fn reset_stats(&mut self) {
        self.stats = ExtendedCuttingPlanesStats::default();
    }
}

impl Default for ExtendedCuttingPlaneGenerator {
    fn default() -> Self {
        Self::default_config()
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use num_traits::Zero;

    #[test]
    fn test_generatorerator_creation() {
        let generator = ExtendedCuttingPlaneGenerator::default_config();
        assert_eq!(generator.stats().mig_cuts, 0);
    }

    #[test]
    fn test_add_vars() {
        let mut generator = ExtendedCuttingPlaneGenerator::default_config();

        generator.add_integer_var(0);
        generator.add_binary_var(1);

        assert!(generator.integer_vars.contains(&0));
        assert!(generator.binary_vars.contains(&1));
    }

    #[test]
    fn test_generatorerate_mig_cut() {
        let mut generator = ExtendedCuttingPlaneGenerator::default_config();

        let row = FxHashMap::default();
        let rhs = BigRational::zero();

        let cut = generator.generatorerate_mig_cut(&row, &rhs);

        assert_eq!(generator.stats().mig_cuts, 1);
        // Note: returns None in simplified implementation
        assert!(cut.is_none());
    }

    #[test]
    fn test_stats() {
        let mut generator = ExtendedCuttingPlaneGenerator::default_config();

        generator.stats.mig_cuts = 5;
        generator.stats.cover_cuts = 3;

        assert_eq!(generator.stats().mig_cuts, 5);
        assert_eq!(generator.stats().cover_cuts, 3);

        generator.reset_stats();
        assert_eq!(generator.stats().mig_cuts, 0);
    }
}