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

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.

Some recent works have established the importance of handling abundant reference information in multi-criteria sorting problems. More valid information allows a better characterization of the agent’s assignment policy, which can lead to an improved decision support. However, sometimes information for enhancing the reference set may be not available, or may be too expensive. This paper explores an automatic mode of enhancing the reference set in the framework of the THESEUS multi-criteria sorting method. Some performance measures are defined in order to test results of the enhancement. Several theoretical arguments and practical experiments are provided here, supporting a basic advantage of the automatic enhancement: a reduction of the vagueness measure that improves the THESEUS accuracy, without additional efforts from the decision agent. The experiments suggest that the errors coming from inadequate automatic assignments can be kept at a manageable level.

When optimizing a mechanical device, the symmetry principle provides important guidance. Minimum gearbox mass and maximum gearbox efficiency are two single objectives that need to be achieved when designing a gearbox, and they are not compatible. In order to address the multi-objective optimization (MOO) problem with the above single targets involved in building a two-stage helical gearbox with second-stage double gear sets, this work presents a novel application of the multi-criteria decision-making (MCDM) method. This study’s objective is to identify the best primary design elements that will increase the gearbox efficiency while lowering the gearbox mass. To carry this out, three main design parameters were selected: the first stage’s gear ratio and the first and second stages’ coefficients of wheel face width (CWFW). Furthermore, a study focusing on two distinct goals was carried out: the lowest possible gearbox mass and the highest possible gearbox efficiency. Furthermore, the two stages of the MOO problem are phase 1 and phase 2, respectively. Phase 2 solves the single-objective optimization issue to minimize the difference between variable levels and the MOO problem to determine the optimal primary design factors. To solve the MOO problem, the EAMR (Evaluation by an Area-based Method of Ranking) method was also chosen. The following are important features of this study: First, a MCDM method (EAMR technique) was successfully applied to solve a MOO problem for the first time. Secondly, this work explored the power losses during idle motion to calculate the efficiency of a two-stage helical gearbox with second-stage double gear sets. This study’s findings were used to identify the optimal values for three important design variables to design a two-stage helical gearbox with second-stage double gear sets.

Lexicographic optimization-based approaches to learning a representative model for multi-criteria sorting with non-monotonic criteria

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

On the adaptation of reference sets using niching and pair-potential energy functions for multi-objective optimization

A fuzzy multi-criteria decision-making model based on simple additive weighting method and relative preference relation

In order to address the Multi-Objective Optimization Problem (MOOP) in building a two-stage helical gearbox, this work presents a novel application of the Multi-Criterion Decision-Making (MCDM) method. The aim of the study is to determine the optimal primary design factors that will increase gearbox efficiency while decreasing gearbox volume. Three main design parameters were chosen for assessment in this work: the first stage’s gear ratio, and the first and second stages’ Coefficients of Wheel Face Width (CWFW). In addition, the MOOP is divided into two phases: phase 1 solves the single-objective optimization problem to reduce the gap between variable levels, and phase 2 solves the MOOP to determine the optimal primary design factors. Furthermore, the Entropy approach was picked to compute the weight criteria, and the MARCOS method was chosen as an MCDM method to handle the multi-objective optimization issue. The following are important characteristics of the study: Firstly, the MCDM method (MARCOS technique) was successfully applied to solve a MOOP for the first time. Secondly, this work has looked into power losses during idle motion to calculate the efficiency of a two-stage helical gearbox. The results of the study were used in the design of a two-stage helical gearbox in order to identify the optimal values for three important design parameters.

A multi-agent system is presented here. Agent decisions are based on economic partial utilities. It's a new computational tool using cellular and agent-based models. Decision processes are represented through computational agents. Land-use and land cover changes are represented through a cellular model. It belongs to kind of models called Multi-Agent Systems model of Land-Use Cover Change. Decisions concern the estate development in the neighborhood of the agents. Space is discretized in heterogeneous cells where heterogeneous agents interact together (directly or via space). Based on partial utility probabilities, several stochastic simulations are achieved. These simulations are then summarized, replicated and a parameter sensitivity analysis provided. The main parameters influencing the decisions of an agent depend on his type (ecologist, etc.) and on the expected economic activities in his neighborhood. Little information is assumed to be known about the mechanisms determining the parameter values guiding the decisions of the agents, except their type. The whole system constitutes a general virtual model, mostly independent from initial conditions and real data. Sensitivity analysis are used to explore behavioral paths and influencing parameters. In summary, the main contribution of this paper consists in: (i) defining a simulation-based framework for modeling the decisions of many heterogeneous economic agents involved in spatial interactions; (ii) capturing the decision process using general utility-based equations; (iii) providing a sensitivity analysis of initial parameter values. An example of possible application investigating strategies of various categories of agents (institutions, landowners, homeowners, etc.) facing an intense residential development is provided. The framework consists of abstracting institutional characteristics of actual local Urbanism Plan procedures in France. This model constitutes a first step to be further specified.

A multi-agent system is presented here. Agent decisions are based on economic partial utilities. It’s a new computational tool using cellular and agent-based models. Decision processes are represented through computational agents. Land-use and land cover changes are represented through a cellular model. It belongs to kind of models called Multi-Agent Systems model of Land-Use Cover Change. Decisions concern the estate development in the neighborhood of the agents. Space is discretized in heterogeneous cells where heterogeneous agents interact together (directly or via space). Based on partial utility probabilities, several stochastic simulations are achieved. These simulations are then summarized, replicated and a parameter sensitivity analysis provided. The main parameters influencing the decisions of an agent depend on his type (ecologist, etc.) and on the expected economic activities in his neighborhood. Little information is assumed to be known about the mechanisms determining the parameter values guiding the decisions of the agents, except their type. The whole system constitutes a general virtual model, mostly independent from initial conditions and real data. Sensitivity analysis are used to explore behavioral paths and influencing parameters. In summary, the main contribution of this paper consists in: (i) defining a simulation-based framework for modeling the decisions of many heterogeneous economic agents involved in spatial interactions; (ii) capturing the decision process using general utility-based equations; (iii) providing a sensitivity analysis of initial parameter values. An example of possible application investigating strategies of various categories of agents (institutions, landowners, homeowners, etc.) facing an intense residential development is provided. The framework consists of abstracting institutional characteristics of actual local Urbanism Plan procedures in France. This model constitutes a first step to be further specified. Copyright S (This abstract was borrowed from another version of this item.)

n modern aircraft design, increased attention is being paid to the conceptual and preliminary design phases so as to increase the odds of creating a design that will ultimately be successful at the completion of the design process. Since aerospace systems are complex systems with interacting disciplines and technologies, the decision makers dealing with such design problems are involved in balancing multiple, potentially conflicting attributes/criteria, transforming a large amount of customer supplied guidelines into a solidly defined set of requirement definitions. As a result, the criteria have to be all simultaneously taken into account and a compromise essentially becomes part of the decision making process. Various methods and techniques are available to deal with such sort of multi-criteria decision making (MCDM) problems. In the 1970’s, Saaty proposed the Analytic Hierarchy Process (AHP), which facilitates the MCDM problems that have a hierarchical structure of attributes by reducing complex decisions to a series of pair-wise comparisons. In this method, the preference information is elicited as the pair-wise comparisons between attributes or alternatives and treated using the eigenvector method. The other straightforward method to handle the MCDM problem is the Overall Evaluation Criterion (OEC) technique, presented in Ref 3. The OEC is a single metric and is obtained by summing multiple non-dimensional attribute metrics normalized by the metric values of a relevant baseline. Another commonly used MCDM technique is the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). The “best” solution chosen by TOPSIS is the alternative that is the closest to the positive ideal solution and the furthest from the negative ideal solution. The separation between each alternative solution and the ideal solution, which is determined by the weighted criteria, is rather sensitive to criterion weights, so typically several weighting scenarios are investigated to determine the final solution. Among these developed MCDM methods, different methods have different underlying assumptions, information requirements, analysis models, and decision rules that are designed for solving a certain class of decision making problems. This implies that it is critical to use the most appropriate method to solve the problem under consideration since the use of unsuitable method always leads to misleading design decisions. Consequently, bad design decisions will result in big loss to the society, such as property damage or personal injury. Thus, it is necessary to review the existing MCDM methods, discuss in depth their advantages, disadvantages, applicability, computational complexity, etc. in order to make right decision when choosing the right method for the given problem. In this paper a hybrid MCDM method is developed to deal with the problem under consideration. Relative weights of the evaluation criteria are elicited by using the eigenvector method to describe the decision maker’s preference information. The TOPSIS method is used to analyze the qualitative and quantitative data of input parameters and find the solution to the given problem. An aircraft technology selection problem is conducted as a proof of implementation to demonstrate the functionality and effectiveness of the proposed methodology.

A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method

In this paper, the complex multi-objective optimization problem is investigated for the train operation process. To sovle the multi-objective optimization problem, the fruit fly optimization algorithm (FOA) is adopted. Fistly, a new method of distance fusion, which fuses the Mahalanobis distance and the Euclidean distance, is proposed to solve the problem that the classical Mahalanobis distance and Euclidean distance can't effectively calculate the actual distance between the individual and the extremum individual solution set caused by the correlation ambiguity of characteristic variables. Then, to maintain the population diversity, the preference information is adopted so that the optimal solution provided by FOA can significantly move to the desired region. Hence, both problems can be overcome by the improved FOA based on fusion distance and preference information. Finally, simulation results are carried out to show the efficacy of the proposed method.

Predicting the three-dimensional structure of a protein from its amino acid sequence is an important issue in the field of computational biology and bioinformatics. It remains as an unsolved problem and attract enormous researchers' interests. Different from most conventional methods, we model the protein structure prediction (PSP) problem as a multi-objective optimization problem. A three-objective energy function based on three physical terms is designed to evaluate a protein conformation. A multi-objective evolutionary strategy algorithm coupled with preference information is proposed in this study. The preference information is used in the survival criteria, focusing on the exploration of search process. The experimental results based on five proteins in PDB library demonstrate the effectiveness of proposed method. The analysis of Pareto fronts indicates that the preference information can make solutions diverse in genotypic space. Thus, the proposed method gives a new perspective for solving PSP problems.

This paper presents a new preference based interactive evolutionary algorithm (I-SIBEA) for solving multiobjective optimization problems using weighted hypervolume. Here the decision maker iteratively provides her/his preference information in the form of identifying preferred and/or non-preferred solutions from a set of nondominated solutions. This preference information provided by the decision maker is used to assign weights of the weighted hypervolume calculation to solutions in subsequent generations. In any generation, the weighted hypervolume is calculated and solutions are selected to the next generation based on their contribution to the weighted hypervolume. The algorithm is compared with a recently developed interactive evolutionary algorithm, W-Hype on some benchmark multiobjective optimization problems. The results show significant promise in the use of the I-SIBEA algorithm. In addition, the performance of the algorithm is demonstrated using a human decision maker to show its flexibility towards changes in the preference information. The I-SIBEA algorithm is found to flexibly exploit the preference information from the decision maker and generate solutions in the regions preferable to her/him.