tsp.cpp

/*****************************************************************************
 *   Copyright (C) 2004-2014 The PaGMO development team,                     *
 *   Advanced Concepts Team (ACT), European Space Agency (ESA)               *
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 *   https://github.com/esa/pagmo                                            *
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 *   act@esa.int                                                             *
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#include "tsp.h"
#include "../population.h"

namespace pagmo { namespace problem {


    tsp::tsp() : base_tsp(3, 0, 0 , base_tsp::RANDOMKEYS), m_weights()
    {
        std::vector<double> dumb(3,0);
        m_weights = std::vector<std::vector<double> > (3,dumb);
        m_weights[0][1] = 1;
        m_weights[0][2] = 1;
        m_weights[2][1] = 1;
        m_weights[1][0] = 1;
        m_weights[2][0] = 1;
        m_weights[1][2] = 1;
    }


    tsp::tsp(const std::vector<std::vector<double> >& weights, const base_tsp::encoding_type& encoding): 
        base_tsp(weights.size(), 
            compute_dimensions(weights.size(), encoding)[0],
            compute_dimensions(weights.size(), encoding)[1],
            encoding
        ),  m_weights(weights)
    {
        check_weights(m_weights);
    }

    base_ptr tsp::clone() const
    {
        return base_ptr(new tsp(*this));
    }


    void tsp::check_weights(const std::vector<std::vector<double> > &matrix) const 
    {   
        decision_vector::size_type n_cols = matrix.size();
        
        for (decision_vector::size_type i = 0; i < n_cols; ++i) {
            decision_vector::size_type n_rows = matrix[i].size();
            // check if the matrix is square
            if (n_rows != n_cols)
                pagmo_throw(value_error, "adjacency matrix is not square");
            
            for (size_t j = 0; j < n_rows; ++j) {
                if (i == j && matrix.at(i).at(j) != 0)
                    pagmo_throw(value_error, "main diagonal elements must all be zeros.");
                if (i != j && !matrix.at(i).at(j)) // fully connected
                    pagmo_throw(value_error, "adjacency matrix contains zero values.");
                if (i != j && (!matrix.at(i).at(j)) == matrix[i][j]) // fully connected
                    pagmo_throw(value_error, "adjacency matrix contains NaN values.");                    
            }
        }
    }

    boost::array<int, 2> tsp::compute_dimensions(decision_vector::size_type n_cities, base_tsp::encoding_type encoding)
    {
        boost::array<int,2> retval;
        switch( encoding ) {
            case FULL:
                retval[0] = n_cities*(n_cities-1)+2;
                retval[1] = (n_cities-1)*(n_cities-2);
                break;
            case RANDOMKEYS:
                retval[0] = 0;
                retval[1] = 0;
                break;
            case CITIES:
                retval[0] = 1;
                retval[1] = 0;
                break;
        }
        return retval;
    }

    void tsp::objfun_impl(fitness_vector &f, const decision_vector& x) const 
    {
        f[0]=0;
        decision_vector tour;
        decision_vector::size_type n_cities = get_n_cities();
        switch( get_encoding() ) {
            case FULL:
            {
                tour = full2cities(x);
                for (decision_vector::size_type i=0; i<n_cities-1; ++i) {
                    f[0] += m_weights[tour[i]][tour[i+1]];
                }
                f[0]+= m_weights[tour[n_cities-1]][tour[0]];
                break;
            }
            case RANDOMKEYS:
            {
                tour = randomkeys2cities(x);
                for (decision_vector::size_type i=0; i<n_cities-1; ++i) {
                        f[0] += m_weights[tour[i]][tour[i+1]];
                }
                   f[0]+= m_weights[tour[n_cities-1]][tour[0]];
                break;
               }
            case CITIES:
               {
                for (decision_vector::size_type i=0; i<n_cities-1; ++i) {
                                f[0] += m_weights[x[i]][x[i+1]];
                }
                f[0]+= m_weights[x[n_cities-1]][x[0]];
                break;
               }
        }
        return;
    }

    size_t tsp::compute_idx(const size_t i, const size_t j, const size_t n) const
    {
        pagmo_assert( i!=j && i<n && j<n );
        return i*(n-1) + j - (j>i? 1:0);
    }

    void tsp::compute_constraints_impl(constraint_vector &c, const decision_vector& x) const 
    {
        decision_vector::size_type n_cities = get_n_cities();

        switch( get_encoding() ) 
        {
            case FULL:
            {
                // 1 - We set the equality constraints
                for (size_t i = 0; i < n_cities; i++) {
                    c[i] = 0;
                    c[i+n_cities] = 0;
                    for (size_t j = 0; j < n_cities; j++) {
                        if(i==j) continue; // ignoring main diagonal
                        decision_vector::size_type rows = compute_idx(i, j, n_cities);
                        decision_vector::size_type cols = compute_idx(j, i, n_cities);
                        c[i] += x[rows];
                        c[i+n_cities] += x[cols];
                    }
                    c[i] = c[i]-1;
                    c[i+n_cities] = c[i+n_cities]-1;
                }

                //2 - We set the inequality constraints
                //2.1 - First we compute the uj (see http://en.wikipedia.org/wiki/Travelling_salesman_problem#Integer_linear_programming_formulation)
                //      we start always out tour from the first city, without loosing generality
                size_t next_city = 0,current_city = 0;
                std::vector<int> u(n_cities);
                for (size_t i = 0; i < n_cities; i++) {
                    u[current_city] = i+1;
                    for (size_t j = 0; j < n_cities; j++) 
                    {
                        if (current_city==j) continue;
                        if (x[compute_idx(current_city, j, n_cities)] == 1) 
                        {
                            next_city = j;
                            break;
                        }
                    }
                    current_city = next_city;
                }
                int count=0;
                for (size_t i = 1; i < n_cities; i++) {
                    for (size_t j = 1; j < n_cities; j++) 
                    {
                        if (i==j) continue;
                        c[2*n_cities+count] = u[i]-u[j] + (n_cities+1) * x[compute_idx(i, j, n_cities)] - n_cities;
                        count++;
                    }
                }
                break;
            }
            case RANDOMKEYS:
                break;
            case CITIES:
            {
                std::vector<population::size_type> range(n_cities);
                for (std::vector<population::size_type>::size_type i=0; i<range.size(); ++i) 
                {
                    range[i]=i;
                }
                c[0] = !std::is_permutation(x.begin(),x.end(),range.begin());
                break;
            }
        }
        return;
    }

    double tsp::distance(decision_vector::size_type i, decision_vector::size_type j) const
    {
        return m_weights[i][j];
    }


    const std::vector<std::vector<double> >&  tsp::get_weights() const
    { 
        return m_weights; 
    }

    std::string tsp::get_name() const
    {
        return "Travelling Salesman Problem (TSP-ATSP)";
    }


    std::string tsp::human_readable_extra() const 
    {
        std::ostringstream oss;
        oss << "\n\tNumber of cities: " << get_n_cities() << '\n';
        oss << "\tEncoding: ";
        switch( get_encoding()  ) {
            case FULL:
                oss << "FULL" << '\n';
                break;
            case RANDOMKEYS:
                oss << "RANDOMKEYS" << '\n';
                break;
            case CITIES:
                oss << "CITIES" << '\n';
                break;
        }
        oss << "\tWeight Matrix: \n";
        for (decision_vector::size_type i=0; i<get_n_cities() ; ++i)
        {
            oss << "\t\t" << m_weights[i] << '\n';
            if (i>5)
            {
                oss << "\t\t..." << '\n';
                break;
            }
        }
        return oss.str();
    }

    
}} //namespaces

BOOST_CLASS_EXPORT_IMPLEMENT(pagmo::problem::tsp)