Source code for skcriteria.madm.moora

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# License: BSD-3 (https://tldrlegal.com/license/bsd-3-clause-license-(revised))
# Copyright (c) 2016-2021, Cabral, Juan; Luczywo, Nadia
# Copyright (c) 2022, QuatroPe
# All rights reserved.

# =============================================================================
# DOCS
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"""Implementation of a family of Multi-objective optimization on the basis of \
ratio analysis (MOORA) methods."""


# =============================================================================
# IMPORTS
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import itertools as it

import numpy as np

from ._base import RankResult, SKCDecisionMakerABC
from ..core import Objective
from ..utils import doc_inherit, rank


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# Ratio MOORA
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[docs]def ratio(matrix, objectives, weights): """Execute ratio MOORA without any validation.""" # change the sign the minimization criteria # If we multiply by -1 (min) the weights, # when we multipliying this weights by the matrix we emulate # the -+ ratio mora strategy objective_x_weights = weights * objectives # calculate ranking by inner prodcut rank_mtx = np.inner(matrix, objective_x_weights) score = np.squeeze(np.asarray(rank_mtx)) return rank.rank_values(score, reverse=True), score
[docs]class RatioMOORA(SKCDecisionMakerABC): r"""Ratio based MOORA method. In MOORA the set of ratios are suggested to be normalized as the square roots of the sum of squared responses as denominators, but you can use any scaler. These ratios, as dimensionless, seem to be the best choice among different ratios. These dimensionless ratios, situated between zero and one, are added in the case of maximization or subtracted in case of minimization: .. math:: Ny_i = \sum_{i=1}^{g} Nx_{ij} - \sum_{i=1}^{g+1} Nx_{ij} with: :math:`i = 1, 2, ..., g` for the objectives to be maximized, :math:`i = g + 1, g + 2, ...,n` for the objectives to be minimized. Finally, all alternatives are ranked, according to the obtained ratios. References ---------- :cite:p:`brauers2006moora` """ _skcriteria_parameters = [] @doc_inherit(SKCDecisionMakerABC._evaluate_data) def _evaluate_data(self, matrix, objectives, weights, **kwargs): rank, score = ratio(matrix, objectives, weights) return rank, {"score": score} @doc_inherit(SKCDecisionMakerABC._make_result) def _make_result(self, alternatives, values, extra): return RankResult( "RatioMOORA", alternatives=alternatives, values=values, extra=extra )
# ============================================================================= # Reference Point Moora # =============================================================================
[docs]def refpoint(matrix, objectives, weights): """Execute reference point MOORA without any validation.""" # max and min reference points rpmax = np.max(matrix, axis=0) rpmin = np.min(matrix, axis=0) # merge two reference points acoording objectives mask = np.where(objectives == Objective.MAX.value, objectives, 0) reference_point = np.where(mask, rpmax, rpmin) # create rank matrix rank_mtx = np.max(np.abs(weights * (matrix - reference_point)), axis=1) score = np.squeeze(np.asarray(rank_mtx)) return rank.rank_values(score), score, reference_point
[docs]class ReferencePointMOORA(SKCDecisionMakerABC): r"""Rank the alternatives by distance to a reference point. The reference point is selected with the Min-Max Metric of Tchebycheff. .. math:: \min_{j} \{ \max_{i} |r_i - x^*_{ij}| \} This reference point theory starts from the already normalized ratios as suggested in the MOORA method, namely formula: .. math:: \overline{X}_{ij} = \frac{X_{ij}}{\sqrt{\sum\limits_{j=1}^m X_{ij}^{2}}} Preference is given to a reference point possessing as coordinates the dominating coordinates per attribute of the candidate alternatives and which is designated as the *Maximal Objective Reference Point*. This approach is called realistic and non-subjective as the coordinates, which are selected for the reference point, are realized in one of the candidate alternatives. References ---------- :cite:p:`brauers2012robustness` """ _skcriteria_parameters = [] @doc_inherit(SKCDecisionMakerABC._evaluate_data) def _evaluate_data(self, matrix, objectives, weights, **kwargs): rank, score, reference_point = refpoint(matrix, objectives, weights) return rank, {"score": score, "reference_point": reference_point} @doc_inherit(SKCDecisionMakerABC._make_result) def _make_result(self, alternatives, values, extra): return RankResult( "ReferencePointMOORA", alternatives=alternatives, values=values, extra=extra, )
# ============================================================================= # FULL MULTIPLICATIVE FORM # =============================================================================
[docs]def fmf(matrix, objectives, weights): """Execute Full Multiplicative Form without any validation.""" weighted_matrix = np.log(np.multiply(matrix, weights)) if Objective.MAX.value in objectives: max_columns = weighted_matrix[:, objectives == Objective.MAX.value] Aj = np.sum(max_columns, axis=1) else: Aj = 1.0 if Objective.MIN.value in objectives: min_columns = weighted_matrix[:, objectives == Objective.MIN.value] Bj = np.sum(min_columns, axis=1) else: Bj = 0.0 score = Aj - Bj return rank.rank_values(score, reverse=True), score
[docs]class FullMultiplicativeForm(SKCDecisionMakerABC): r"""Non-linear, non-additive ranking method method. Full Multiplicative Form does not use weights and does not require normalization. To combine a minimization and maximization of different criteria in the same problem all the method uses the formula: .. math:: U'_j = \frac{\prod_{g=1}^{i} x_{gi}} {\prod_{k=i+1}^{n} x_{kj}} Where :math:`j` = the number of alternatives; :math:`i` = the number of objectives to be maximized; :math:`n − i` = the number of objectives to be minimize; and :math:`U'_j`: the utility of alternative j with objectives to be maximized and objectives to be minimized. To avoid underflow, instead the multiplication of the values we add the logarithms of the values; so :math:`U'_j`:, is finally defined as: .. math:: U'_j = \sum_{g=1}^{i} \log(x_{gi}) - \sum_{k=i+1}^{n} \log(x_{kj}) Notes ----- The implementation works Instead the multiplication of the values we add the logarithms of the values to avoid underflow. Raises ------ ValueError: If some objective is for minimization or some value in the matrix is <= 0. References ---------- :cite:p:`brauers2012robustness` """ _skcriteria_parameters = [] @doc_inherit(SKCDecisionMakerABC._evaluate_data) def _evaluate_data(self, matrix, objectives, weights, **kwargs): if np.any(matrix <= 0): raise ValueError( "FullMultiplicativeForm can't operate with values <= 0" ) rank, score = fmf(matrix, objectives, weights) return rank, {"score": score} @doc_inherit(SKCDecisionMakerABC._make_result) def _make_result(self, alternatives, values, extra): return RankResult( "FullMultiplicativeForm", alternatives=alternatives, values=values, extra=extra, )
# ============================================================================= # MULTIMOORA # =============================================================================
[docs]def multimoora(matrix, objectives, weights): """Execute weighted product model without any validation.""" ratio_rank, ratio_score = ratio(matrix, objectives, weights) refpoint_rank, refpoint_score, reference_point = refpoint( matrix, objectives, weights ) fmf_rank, fmf_score = fmf(matrix, objectives, weights) rank_matrix = np.vstack([ratio_rank, refpoint_rank, fmf_rank]).T alternatives = len(matrix) score = np.zeros(alternatives) # comparamos alternativa a alternativa y vemos cual domina a cual # la mas dominante va primero, la menos dominante va ultima for idx_a, idx_b in it.combinations(range(alternatives), 2): # retrieve the two ranks alt_a, alt_b = rank_matrix[[idx_a, idx_b]] # calculate the dominance dominance = rank.dominance(alt_a, alt_b, reverse=True) # if is the same rank we don't increment any alternative if dominance.eq == 0: dom_idx = idx_a if dominance.aDb > dominance.bDa else idx_b score[dom_idx] += 1 ranking = rank.rank_values(score, reverse=True) return ( ranking, score, rank_matrix, ratio_score, refpoint_score, fmf_score, reference_point, )
[docs]class MultiMOORA(SKCDecisionMakerABC): r"""Combination of RatioMOORA, RefPointMOORA and FullMultiplicativeForm. These three methods represent all possible methods with dimensionless measures in multi-objective optimization and one can not argue that one method is better than or is of more importance than the others; so for determining the final ranking the implementation maximizes how many times an alternative *i* dominates and alternative *j*. Raises ------ ValueError: If some objective is for minimization or some value in the matrix is <= 0. References ---------- :cite:p:`brauers2012robustness` """ _skcriteria_parameters = [] @doc_inherit(SKCDecisionMakerABC._evaluate_data) def _evaluate_data(self, matrix, objectives, weights, **kwargs): if np.any(matrix <= 0): raise ValueError("MultiMOORA can't operate with values <= 0") ( rank, score, rank_matrix, ratio_score, refpoint_score, fmf_score, reference_point, ) = multimoora(matrix, objectives, weights) return rank, { "score": score, "rank_matrix": rank_matrix, "ratio_score": ratio_score, "refpoint_score": refpoint_score, "fmf_score": fmf_score, "reference_point": reference_point, } @doc_inherit(SKCDecisionMakerABC._make_result) def _make_result(self, alternatives, values, extra): return RankResult( "MultiMOORA", alternatives=alternatives, values=values, extra=extra, )