# DCORES 2016 Abstracts

Full Papers

Paper Nr: | 1 |

Title: | ## Identification of new Equality Constraints for Integer Programming Problems |

Authors: | ## Asghar Moeini |

Abstract: | Characterizing the smallest dimension polytope containing all integer solution of an integer programming problem can be a very challenging task. Frequently, this task is facilitated by identifying linear equality constraints that all integer solutions must satisfy. Typically, some of these constraints are readily available but others need to be discovered by more technical means. This paper develops a method to assist modeler to obtain such equality constraints. The set of new equality constraints is not unique and the proposed method generates a set of these new equality constraints for some instances of the underlying problem. These generated constraints may, or may not, be easily extendable to the general case of the underlying problem. For the latter case, a mixed-integer program is developed to detect an extendable new constraint. Furthermore, this mixed-integer model allows modeler to check if there is a new constraint satisfying problem specific criteria. These criteria can restrict the coefficients to be 1,0, and −1 or having a sparse constraint. In order to elaborate the proposed method, a set of new equality constraints defining a previously published “Base polytope” are derived. Subsequently, exploiting these results, some techniques are proposed to tighten integer program problems. Finally, relaxation of widely used TSP formulations are compared against one another and strengthened with help of the newly discovered equality constraints. |

Paper Nr: | 3 |

Title: | ## Preference Dissagrigation Model of ELECTRE TRI-NC and Its Application on Identifying Prefered Climates for Tourism |

Authors: | ## Parisa Madhooshiarzanagh |

Abstract: | Multiple criteria sorting methods assign alternatives to pre-ordered categories. The ELECTRE TRI-NC method is an outranking method that compares alternatives in several ordered categories. This method allocates alternatives into ordered set of categories based on pessimistic and optimistic assignment rules. In order to use ELECTRE TRI-NC we need the Decision Maker (DM) to define some preference parameters like weight of criteria, credibility threshold, preference threshold and indifference thresholds which is a hard task for her/him. In this research a preference disaggregation method in ELECTRE TRI-NC approach is proposed to elicit the criteria weights and credibility threshold using some assignment example. In order to validate the proposed method, it is applied to infer subset of parameters in a real world example “Identifying most favourable touristic place” (Mailly et al. 2014). The model is applied in climate problem for 100 different assignment examples and infers different weight vector and credibility threshold. The inferred parameters are used to sort 62,482 touristic locations into four categories. Moreover, the robustness and validation analysis have been done on the results to discuss about the effectiveness of the model. |