Inferring Preferences for Multi-Criteria Ordinal Classification Methods Using Evolutionary Algorithms

In the real world there are many problems which involve the optimization of multiple objective functions at the same time. These are known as Multi-objective Optimization Problems (MOPs). Solving this kind of problems implies generating a set of good solutions, commonly known as Pareto-optimal solutions. The Multi-Objective Evolutionary Algorithms (MOEAs) have been extensively used to address this type of problems, since it allowing to get a set of the Pareto solutions in a particular run. Nevertheless, finding this solution set does not resolve the problem since the Decision-Maker (DM) still must select from that set the solution that matches more with his/her preferences. Determine the Region of Interest (RoI), in accordance with the DM’s preferences, is an option that would make easy the selection process. The RoI has been defined as the region on the Pareto frontier which suits better to the DM's preferences. In order to help the DM in the selection process, different approaches in literature have added preferential information into the optimization process to lead the search towards the RoI. Such is the case of the approach presented by (Cruz-Reyes et al., 2017) called Hybrid Multi-Criteria Sorting Genetic Algorithm (H-MCSGA). This method addresses the preferences incorporation a priori into a MOEA to characterize the RoI by a multicriteria sorting method called THESEUS (Fernandez et al., 2011). H-MCSGA consists by two phases. First, a metaheuristic is used to create a set of solutions (reference set) that are assigned to ordered classes by the DM. The objective of this process is that the DM's preferences are indirectly reflected in this set. In the second phase, THESEUS is incorporated into an evolutionary algorithm to sort the new solutions created during optimization process. For this, THESEUS uses the reference set, generating selective pressure in the direction of the RoI. The performance of H-MCSGA was verified using nine instances of a public project portfolio problem. The achieve results show that H-MCSGA reach a good definition of the RoI and outperforms the well-known NSGA-II (Deb et al., 2002). A first interactive version of the H-MCSGA is presented in (Cruz-Reyes et al., 2014), where the reference set is updated, only once, while exploration process. Consequently, the DM’s preferences are updated. In examples on the portfolio problem, this proposal maintains its superiority over the NSGAII. Finally, an interactive method more robust is proposed in (Cruz-Reyes et al., 2016) called the Interactive Multi-Criteria Sorting Genetic Algorithm (I-MCSGA). This method allows the DM to assimilate progressively respecting the problem and to clarify his/her preferences. I-MCSGA was assessed on project portfolio optimization problems. This algorithm was measure against with NSGA-II in three and four objectives problems and in nine and sixteen objectives problems with A2-NSGA-III (Jain, Deb, 2013). I-MCSGA presented better outcomes than these algorithms in regard to Pareto-dominance and to its ability to accomplish the RoI. The automatic-enhancement procedure results efficient to include new solutions into the reference set, aiding THESEUS to propose more suitable assignments. Moreover, the proposed procedure to update preferences interactively is efficient to validate the enhanced reference set, still when the real DM was supplanted by the preference model proposed by (Fernandez et al., 2011). Therefore, I-MCSGA shown its capacity to identify the RoI and, to address optimization problems with a few and many numbers of objectives, effectively. Future research directions should be leads towards extend the experimentation to problems where the true Pareto frontier is known, the use of others multicriteria sorting methods and the comparing with others most recent MOEAs. This with the aim of validating the outcomes of these approach with greater certainty.

Incorporation of implicit decision-maker preferences in multi-objective evolutionary optimization using a multi-criteria classification method

Hyperheuristics for indirect elicitation of outranking model’s parameters in Project Portfolio Optimization

A novel hybrid simplified group BWM and multi-criteria sorting approach for stock portfolio selection

Chapter 2 - Multiple-Criteria Decision-Making sorting method

A hierarchical interval outranking approach with interacting criteria

Integrating machine learning models to learn potentially non-monotonic preferences for multi-criteria sorting from large-scale assignment examples

In the future, Enhanced Geothermal System (EGS) power generation will be a hot spot for new energy investment development. How to optimize the EGS power generation investment program is an important issue to be solved by the government and enterprises. In order to improve the accuracy of the EGS investment project evaluation, this paper proposes a technical route to optimize the EGS power generation investment program. It comprehensively considers the ambiguity of the decision attributes and the conflict between the indicators. The index is calculated using the entropy method and the order relationship method. Comprehensive weights; using triangular fuzzy numbers instead of exact numbers to reduce the loss of decision information; using a multi-criteria compromised sorting method to obtain trade-off solutions to solve the problem that investment plans cannot be accepted by all decision makers when there are multiple conflicting indicators. Finally, taking an enterprise’s EGS power generation project as an example, the effectiveness and rationality of the optimized technology route for the EGS power generation investment program are verified.

In multi-criteria sorting methods, it is often difficult for decision makers to precisely define their preferences. It is even harder to express them into parameters values. The idea of this work is to automatically find the parameters of a sorting model using classification examples in the contexts of traditional sorting and interval sorting. Interval sorting, i.e., the possible assignment of alternatives into several successive categories, is defined in this paper. The sorting method we are working with is FlowSort, which is based on the PROMETHEE methodology. Starting with an evaluation table and known allocations, we propose a heuristic based on a genetic algorithm (GA) to identify the weights, indifference and preference thresholds but also profiles characterising the categories. We illustrate both the performances of the algorithm and the quality of the solutions on three standard datasets in both cases.

This paper describes a new Preference-based Interactive Evolutionary (PIE) algorithm for multi-objective optimization which exploits the advantages of both evolutionary algorithms and multiple criteria decision making approaches. Our algorithm uses achievement scalarizing functions and the potential of population based evolutionary algorithms to help the decision maker to direct the search towards the desired Pareto optimal solution. Starting from an approximated nadir point, the PIE algorithm improves progressively the objective function values of a solution by finding a better solution at each iteration that improves the previous one. The decision maker decides from which solution, in which direction, and at what distance from the Pareto front to find the next solution. Thus, the PIE algorithm is guided interactively by the decision maker. A flexible approach is obtained with the use of archive sets to store all the solutions generated during an evolutionary algorithm's run, as it allows the decision maker to freely navigate and inspect previous solutions if needed. The PIE algorithm is demonstrated using a pollution monitoring station problem and shown to be effective in helping the decision maker to find a solution that satisfies her/his preferences.

Strategic behavior in multi-criteria sorting with trust relationships-based consensus mechanism: Application in supply chain risk management

We formulate and solve a real-world shape design optimization problem of an air intake ventilation system in a tractor cabin by using a preference-based surrogate-assisted evolutionary multi-objective optimization algorithm. We are motivated by practical applicability and focus on two main challenges faced by practitioners in industry: 1) meaningful formulation of the optimization problem reflecting the needs of a decision maker and 2) finding a desirable solution based on a decision maker's preferences when solving a problem with computationally expensive function evaluations. For the first challenge, we describe the procedure of modelling a component in the air intake ventilation system with commercial simulation tools. The problem to be solved involves time consuming computational fluid dynamics simulations. Therefore, for the second challenge, we extend a recently proposed Kriging-assisted evolutionary algorithm K-RVEA to incorporate a decision maker's preferences. Our numerical results indicate efficiency in using the computing resources available and the solutions obtained reflect the decision maker's preferences well. Actually, two of the solutions dominate the baseline design (the design provided by the decision maker before the optimization process). The decision maker was satisfied with the results and eventually selected one as the final solution.

Assessment of digital economy development with the new multicriteria sorting method: DCMSort

It has been found that significant benefits can be achieved if suppliers are involved in the early phase of new product development process. However, in practice, this approach do not always bright in the desired benefits, if does not have a negative influence on the buyer firm's performance. Trying to solve this problem, this paper describes a new management model based on a multicriteria sorting method. First, the index system for the evaluation of suppliers is constructed from the perspectives of quality, cost, delivery, development potentiality, technical capabilities, and cooperation capability. Second, by introducing the preferences of the decision maker, the suppliers are assigned to predefined ordered categories according to a new multicriteria sorting method based on PROMETHEE. At last, the suppliers are compared by means of the single criterion net flows, so as to identify potential reasons for differences in performance in order to improve suppliers. The usability and validity of the model are demonstrated by an empirical analysis.

Nowadays enterprises face the necessity of taking many decisions related to their everyday activities. Usually, these decisions are made over real world problems whose solutions contribute to the achievement of desire results. The most common strategy followed to provide assistance in such situations is through the development of optimizations models that reflects the needs of an enterprise but also that incorporates particular preferences of the Decision Maker (DM) who is meant to select the best solution. According to the revised literature, the strategies that have been used so far to model preferences are based on goal attainment, utility functions, preference relations, outranking and fuzzy logic. Of particular interest are the outranking approaches which exploits outranking relations to give answer to Multi-objective Optimization Problems (MOPs); such approach has allowed the development of computable preference models, based on a predefined set of parameters, that reflect the interests of a DM. The most practical way that can be used to set the parameter values for that preference model is through Preference Disaggregation Methods (PDM), which are methods that based on a battery of examples provided by the DM elicits the entire set of parameters. Recently it has been observed that the preferences of a DM are strongly influenced by abstract aspects of his/her personality, e.g. his/her level of tolerance. In this direction, the personality and the emotional state are relevant elements that provide in some way an added value to these preferences, and they could produce more descriptive and approximate solutions to the reasoning of the individual. Hence, it is acceptable to think that the personality should influence the values of the parameters that define a specific preference model that is used to characterize a DM. This work analyzes the effects of personality over parameter values of preference models. It presents an architecture that takes as input aspects of a personality and use them to modify the parameter values of a preference model. The elements considered were ELECTRE III, a well-known model that takes into account the preferences of a DM, a proposed personality model which uses the most recurrent models of the theory of personality theory to provide a computable measure of the tolerance of an individual, and a proposed methodology to modify the parameters of ELECTRE III due to the personality. In this cognitive process, it was possible to identify the parameters where the personality can influence preferences. The case study presented in this research is a basic case of purchases in an online super market, where a virtual assistant interacts with the decision maker emulating their behavior when selecting products based on their preferences and personality, in order to facilitate the decision maker chooses the most convenient solution. The main objective in the proposed research is the study of the impact of the influence of personality on preferences within a decisional context. To prove the above, an experimental design is proposed, it simulates series of purchases based on lists of initial product requests to determine whether the purchases of the resulting products are close to the products originally requested.