Outranking Model Research Articles

An ACO-based Hyper-heuristic for Sequencing Many-objective Evolutionary Algorithms that Consider Different Ways to Incorporate the DM's Preferences

Many-objective optimization is an area of interest common to researchers, professionals, and practitioners because of its real-world implications. Preference incorporation into Multi-Objective Evolutionary Algorithms (MOEAs) is one of the current approaches to treat Many-Objective Optimization Problems (MaOPs). Some recent studies have focused on the advantages of embedding preference models based on interval outranking into MOEAs; several models have been proposed to achieve it. Since there are many factors influencing the choice of the best outranking model, there is no clear notion of which is the best model to incorporate the preferences of the decision maker into a particular problem. This paper proposes a hyper-heuristic algorithm—named HyperACO—that searches for the best combination of several interval outranking models embedded into MOEAs to solve MaOPs. HyperACO is able not only to select the most appropriate model but also to combine the already existing models to solve a specific MaOP correctly. The results obtained on the DTLZ and WFG test suites corroborate that HyperACO can hybridize MOEAs with a combined preference model that is suitable to the problem being solved. Performance comparisons with other state-of-the-art MOEAs and tests for statistical significance validate this conclusion.

Z-number dominance, support and opposition relations for multi-criteria decision-making

The outranking multi-criteria decision-making (MCDM) method focuses on the systematic comparison of alternatives and the non-compensation among criteria to conduct decision analysis. Z-numbers are powerful tools for characterizing decision-making information and identifying information reliability. This paper aims to explore Z-number outranking theories and the corresponding MCDM method on the basis of the idea of Elimination and Choice Translating Reality (ELECTRE) III, which is a very popular and capable outranking model. The concordance and discordance indices of Z-numbers are defined by processing their bimodal uncertainty fully. And an objective computation method is investigated to determine the values of thresholds in these indices. Further, three types of novel outranking relations, including dominance, support and opposition relations, for Z-numbers are presented by comparing these indices systematically. Then, an extended MCDM method with the distillation and flow ranking rules is proposed by detecting the outranking relations among alternatives under multiple criteria and carrying out the outranking aggregation and exploitation. To verify the applicability and effectivity of the proposed method, an illustrative example is provided, and a simulation test and a comparison discussion are conducted

Preference incorporation into many-objective optimization: An Ant colony algorithm based on interval outranking

In this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multi-objective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of the DM's preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM's preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with four competitive multi-objective optimizers: The Indicator-based Many-Objective ACO, the Multi-objective Evolutionary Algorithm Based on Decomposition, the Reference Vector-Guided Evolutionary Algorithm using Improved Growing Neural Gas, and the Indicator-based Multi-objective Evolutionary Algorithm with Reference Point Adaptation. The numerical results show that IO-ACO approximates the RoI better than leading metaheuristics based on approximating the Pareto frontier alone.

Combining a dynamic simulation tool and a multi-criteria decision aiding algorithm for improving existing District Heating

The work aims to evaluate the recovering potential of excess heat in the return pipe of a district heating (DH) for heating some substations.The proposed method combines a DH simulation tool and a multi-criteria decision aiding algorithm. It is based on the analysis of the measured return temperatures at each sub-station in order to identify those with high potential of efficiency gains by using the return flow (with support of the supply pipe when needed). Combinations of substations from this set of eligible ones define potential scenarios of connection to the return pipe. The impacts of each scenario on the DH operational performance and the energy savings are evaluated with a detailed hydro-thermal model. The technical parameters and the energy efficiency are not the only points of view in the selection process “of best compromise” scenarios for the improvement of the DH, so that we propose a complex decision aiding process, involving multiple criteria, dealing with different points of view (economic, energy, technical…) and different decision makers. The evaluations of the scenarios on the criteria are summed up in a so-called performance table and aggregated by an outranking model (MR-Sort) to identify relevant scenarios.This methodology is illustrated by the example of a part of the DH in Nantes (France). Interpretation of data from substations of a specific branch showed the potential of connecting some of them to the return pipe. Six scenarios were generated and evaluated with four criteria. Then, the Multi-criteria Decision Aiding method associated to two actors who have different priorities lead to not obvious results at a first glance.

Selection of a sustainable third-party reverse logistics provider based on the robustness analysis of an outranking graph kernel conducted with ELECTRE I and SMAA

Pressure from legislation and customers has motivated companies to consider reverse logistics (RL) in their operations. Since it is a complex procedure that requires an adequate system, the recent trend consists in outsourcing RL to third-party reverse logistics providers (3PRLPs). This paper provides the background of sustainable triple bottom line theory with focus on economic, environmental, and social aspects under 3PRL concerns. The relevant sustainability criteria are used in a case study conducted in cooperation with an Indian automotive remanufacturing company. To select the most preferred service provider, we use a hybrid method combining a variant of ELECTRE I accounting for the effect of reinforced preference, the revised Simos procedure, and Stochastic Multi-criteria Acceptability Analysis. The incorporated approach exploits all parameters of an outranking model compatible with the incomplete preference information of the Decision Maker. In particular, it derives the newly defined kernel acceptability and membership indices that can be interpreted as a support given to the selection of either a particular subset of alternatives or a single option. The proposed ELECTRE-based method enriches the spectrum of multiple criteria decision analysis approaches that can be used to effectively approach the problem of the 3PRLP selection. As indicated by the extensive review presented in the paper, this application field was so far dominated by Analytic Hierarchy Process and TOPSIS, whose weaknesses can be overcome by applying the outranking methods.

A credit ranking model for a parafinancial company based on the ELECTRE-III method and a multiobjective evolutionary algorithm

Credit rating is an assessment performed by lenders or financial institutions to determine a person’s creditworthiness based on the proposed terms of the loan. Frequently, these institutions use rating models to obtain estimates for the probabilities of default for their clients (companies, organizations, government, and individuals) and to assess the risk of credit portfolios. Numerous statistical and data mining methods are used to develop such models. In this paper, the potential of a multicriteria decision-aiding approach is studied. As a first step, the proposed methodology models the problem as a multicriteria evaluation process with multiple and in some cases, conflicting dimensions, which are integrated to derive sound recommendation for DMs. The second step of the methodology involves building a multicriteria outranking model based on ELECTRE III method. An evolutionary algorithm is used to exploit the outranking model. The methodology is applied to a small-scale financial institution operating in the agricultural sector. We compare loan applications based on their attributes and the credit profile of the customer or credit applicant. Our methodology offers the flexibility of combining heterogeneous information together with the preferences of decision makers (DMs), generating both relative and fixed rules for selecting the best loan applications among new and existing customers, which is an improvement over traditional methods The results reveal that outranking models are well suited to credit rating, providing good ranking results and suitable understanding on the relative importance of the evaluation criteria.

Integrated framework for preference modeling and robustness analysis for outranking-based multiple criteria sorting with ELECTRE and PROMETHEE

We introduce an integrated framework for preference modeling and robustness analysis in outranking-based multiple criteria sorting. The preference information supplied by the Decision Maker (DM) is composed of parts of desired recommendation and imprecise requirements that the delivered outcomes should satisfy. Its allowed forms are: imprecise assignment examples, desired class cardinalities, and assignment-based pairwise comparisons. The exploitation of all instances of the outranking model compatible with these preferences results in three types of outcomes. These raise robustness concerns in terms of the stability of a suggested assignment for each alternative, an observed size of each class, and a comparison between recommendation delivered for pairs of alternatives. The correspondence between different types of inputs and outputs facilitates the dialogue with the DM and enhances her/his confidence in the suggested recommendation. While referring only to a semantic meaning of an outranking relation, we present the procedures for translating the preference information into parameters of compatible outranking model instances and for deriving various kinds of sorting results. Then, we implement this general framework in the context of outranking models specific for ELECTRE and PROMETHEE. Finally, we show how preference modeling and robustness analysis can be performed and greatly simplified with a set of preference model instances providing precise assignments for the alternatives. The framework proposed for this case is based on Mixed-Integer Linear Programming (MILP), being independent of the underlying model and method. Application of the approaches is demonstrated on the case of classifying Polish research units into four quality classes.

A simulated annealing-based permutation method and experimental analysis for multiple criteria decision analysis with interval type-2 fuzzy sets

The aim of this paper is to develop a simulated annealing-based permutation method for multiple criteria decision analysis within the environment of interval type-2 fuzzy sets. The outranking methodology constitutes one of the most fruitful approaches in multiple criteria decision making and has been applied in numerous real-world problems. The permutation method is a classical outranking model, which generalizes Jacquet–Lagreze's permutation method and is based on a pairwise criterion comparison of the alternatives. Because modeling of the uncertainty in the decision-making process becomes increasingly important, an extension to the interval type-2 fuzzy environment is a useful generalization of the permutation method and is appropriate for handling uncertain and imprecise information in practical decision-making situations. This paper produces a signed-distance-based comparison among the comprehensive rankings of alternatives for concordance and discordance analyses. An integrated nonlinear programming model is constructed for estimation of the criterion weights and the optimal ranking order of the alternatives under incomplete preference information. To enhance the implementation efficiency, a simulated annealing-based permutation method and its meta-heuristic algorithm are developed to produce a polynomial time solution for the total completion time problem. Furthermore, computational experiments with notably large amounts of simulation data are conducted to test the solution approach and validate the correctness of the approximate solution compared with the optimal all-permutation-based result.

A classification approach based on the outranking model for multiple criteria ABC analysis

The multiple criteria ABC analysis is widely used in inventory management, and it can help organizations to assign inventory items into different classes with respect to several evaluation criteria. Many approaches have been proposed in the literature for addressing such a problem. However, most of these approaches are fully compensatory in multiple criteria aggregation. This means that an item scoring badly on one or more key criteria could be placed in good classes because these bad performances could be compensated by other criteria. Thus, it is necessary to consider the non-compensation in the multiple criteria ABC analysis. To the best of our knowledge, the ABC classification problem with non-compensation among criteria has not been studied sufficiently. We thus propose a new classification approach based on the outranking model to cope with such a problem in this paper. However, the relational nature of the outranking model makes the search for the optimal classification solution a complex combinatorial optimization problem. It is very time-consuming to solve such a problem using mathematical programming techniques when the inventory size is large. Therefore, we combine the clustering analysis and the simulated annealing algorithm to search for the optimal classification. The clustering analysis groups similar inventory items together and builds up the hierarchy of clusters of items. The simulated annealing algorithm searches for the optimal classification on different levels of the hierarchy. The proposed approach is illustrated by a practical example from a Chinese manufacturer. Furthermore, we validate the performance of the approach through experimental investigation on a large set of artificially generated data at the end of the paper.

A decision support system to find the best water allocation strategies in a Mediterranean river basin in future scenarios of global change

Global change refers to climate changes, but also demographic, technological and economic changes. Predicted water scarcity will be critical in the coastal Mediterranean region, especially for provision to mid-sized and large-sized cities. This paper studies the case of the city of Tarragona, located at the Mediterranean area of north-eastern Spain (Catalonia). Several scenarios have been constructed to evaluate different sectorial water allocation policies to mitigate the water scarcity induced by global change. Future water supply and demand predictions have been made for three time spans. The decision support system presented is based on the outranking model, which constructs a partial pre-order based on pairwise preference relations among all the possible actions. The system analyses a hierarchical structure of criteria, including environmental and economic criteria. We compare several adaptation measures including alternative water sources, inter-basin water transfer and sectorial demand management coming from industry, agriculture and domestic sectors. Results indicate that the most appropriate water allocation strategies depend on the severity of the global change effects.

Many-Objective Portfolio Optimization of Interdependent Projects with ‘a priori’ Incorporation of Decision-Maker Preferences

Project portfolio selection is one of the most important problems faced by any organization. The decision process involves multiple conflicting criteria, and has been commonly addressed by implemen ting a two-phase procedure. The first step identifies the efficient solution set; the second step supports the decision maker in se lecting only one portfolio solution from the efficient set. However, several recent studies show the advantages gained by optimizing towards a region of interest (according to the decision maker's preferences) instead of approximating the complete Pareto se t. However, these works have not faced synergism and its variants, such as cannibalization and redundancy. In this paper we introduce a new approach called Non-Outranked Ant Colony Optimization , which optimizes interdependent project portfolios with a priori articulation of decision-maker preferences based on an outranking model. Several experimental tests show the advantages of our proposal over the two-phase approach, providing reasonable evidence of its potential for solving real-world high-scale problems with many objective s.

DATA CONSTRUCTION PROCESS AND QUALIFLEX-BASED METHOD FOR MULTIPLE-CRITERIA GROUP DECISION MAKING WITH INTERVAL-VALUED INTUITIONISTIC FUZZY SETS

Based on Jacquet-Lagreze's permutation method, QUALIFLEX is an outranking model that investigates all possible permutations of alternatives with respect to the consequences of all criteria. The purpose of this paper is to develop a QUALIFLEX-based method for multiple criteria group decision making within a decision environment of interval-valued intuitionistic fuzzy sets. We conduct a statistical inference approach with finite population correction to construct interval-valued intuitionistic fuzzy numbers. In addition, we incorporate the relative importance of decision makers and fuse individual opinions to form collective ratings using a modified method with weighted interval estimations. In view of diversiform preference types (weak order, strict order, difference order, interval bound, and ratio bound), we represent multiple decision makers' various forms of preference structures and assess criterion weights under incomplete information. By means of score functions, accuracy functions, membership-uncertainty indices, and hesitation-uncertainty indices, a ranking procedure is employed to identify a criterion-wise preference of alternatives. A QUALIFLEX-based model is then established to measure the level of concordance of the complete preference order for handling multiple criteria group decisions. The feasibility of the proposed method is illustrated by a practical problem relating to the selection of a landfill site. As indicated in the application, the proposed method is useful for handling complicated group decision-making problems that involve comprehensive criteria and limited alternatives.

Evolutionary multi-objective optimization for inferring outranking model’s parameters under scarce reference information and effects of reinforced preference

AbstractMethods based on fuzzy outranking relations constitute one of the main approaches to multiple criteria decision problems. The use of ELECTRE methods require the elicitation of a large number of parameters (weights and different thresholds); but direct eliciting is often a demanding task for the decision-maker (DM). For handling intensity-ofpreference effects on concordance levels, a generalized concordance model was proposed by Roy and Slowinski which is more complex than previous outranking models. In this paper, an evolutionary multi-objective-based indirect elicitation of the complete ELECTRE III model-parameter set is proposed. The evolutionary multi-objective inference method is successfully extended to inferring reinforced-preference model parameters. Wide experimental evidence is provided to support the proposal, which performs well even working on small size reference sets.

Intuitionistic Fuzzy QUALIFLEX Method for Optimistic and Pessimistic Decision Making

Intuitionistic fuzzy sets are suitable for capturing imprecise or uncertain decision information in multiple criteria decision analysis. In addition, optimism and pessimism generally affect the manner in which subjective judgments are construed. This paper proposes an outranking model, a QUALIFLEX method, for relating optimism and pessimism within the intuitionistic fuzzy decision environment. This paper treats the influences of optimism and pessimism differently by using the unipolar bivariate model. In addition, the proposed method investigates all possible permutations of alternatives with respect to the consequences of all criteria. A ranking procedure is employed to compare intuitionistic fuzzy values by using the inclusion comparison probability.

An acyclic outranking model to support group decision making within organizations

A model to support group decision making within the board of any organization to select an alternative from a short list is proposed using a pairwise relation: consensus relation.This relation avoids elementary cyclicity which is a general shortcoming of previous models and satisfies transitivity under special conditions (weak transitivity). This relation is represented by a triangle-free graph and has important implications for Public Choice Theory such as the special relevance of the 2/3 majority rule and for Multicriteria Decision Making (MCDM) to improve outranking models.The proposed model can be easily applied as shown by the example presented.The contributions obtained from this model do not only include the selection of the recommended alternative(s) but also very useful representations and measures of the level of cultural consensus and dissent of the board members which can be used to improve their composition and behavior.

Multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm

Abstract Most multicriteria decision methods need the definition of a significant amount of preferential information from a decision agent. The preference disaggregation analysis paradigm infers the model’s parameter values from holistic judgments provided by a decision agent. Here, a new method for inferring the parameters of a fuzzy outranking model for multicriteria sorting is proposed. This approach allows us to use most of the preferential information contained in a reference set. The central idea is to characterize the quality of the model by measuring discrepancies and concordances amongst (i) the preference relations derived from the outranking model, and (ii) the preferential information contained in the reference set. The model’s parameters are inferred from a multiobjective optimization problem, according to some additional preferential information from a decision agent. Once the model has been fitted, sorting decisions about new objects are performed by using a fuzzy indifference relation. This proposal performs very well in some examples.

Multi-objective optimisation of an outranking model for public resources allocation on competing projects

This paper develops a model for composing social-oriented project portfolios. The information concerning the quality of the projects is in the form of a project-ranking, which can be obtained by the application of a proper multi-criteria method, but the ranking does not assume an appropriate evaluation of social impact. Inspired by outranking methods, the model provides a preference relation over project portfolios related to project rank positions, single-project costs, and the Decision-Maker's aversion to expensive projects. A best portfolio is primarily found through a multi-objective optimisation that regards violations to pre-established decision-maker's preferences and the competing portfolios' cardinalities. The overall solution is obtained by developing an evolutionary method, which is found to perform very well in some test examples.

Choosing realistic values of indifference, preference and veto thresholds for use with environmental criteria within ELECTRE

Abstract The ELECTRE III outranking model is particularly suited to aiding the choice between project alternatives on the basis of mainly environmental criteria. The model requires values of three criterion thresholds, the indifference threshold (q), the preference threshold (p) and the veto threshold (v). These allow the uncertainties inherent in the criteria valuations to be incorporated into the decision process. There is, at present, a high degree of subjectivity involved in determining these thresholds, which are expressed in terms of the error/uncertainty associated with the valuations of each of the criteria under scrutiny. If, however, the ELECTRE III outranking model is to be used within a formal environmental appraisal system, the thresholds which govern the outranking relationship of one project option over another must take account of the effect on human beings of the difference between any two criterion scores. The authors suggest a new method for applying the standard ELECTRE III model to decision-aid problems within the formal mechanism of environmental impact assessment. This involves a new, more comprehensive approach for specifying realistic limits for p, q and v, within the context of an environmental appraisal, where both criterion error/uncertainty and human sensitivity to differing levels of the criterion are taken into account. Threshold valuations for noise impacts from a highway project are used to illustrate the proposed method.