Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection
Graphical abstractDisplay Omitted HighlightsWe consider a constrained three-objective optimization portfolio selection problem.We solve the problem by means of evolutionary multi-objective optimization.New mutation, crossover and reparation operators are designed for this problem.They are tested in several algorithms for a data set from the Spanish stock market.Results for two performance metrics reveal the effectiveness of the new operators. In this paper, we consider a recently proposed model for portfolio selection, called Mean-Downside Risk-Skewness (MDRS) model. This modelling approach takes into account both the multidimensional nature of the portfolio selection problem and the requir…
NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point
Most interactive methods developed for solving multiobjective optimization problems sequentially generate Pareto optimal or nondominated vectors and the decision maker must always allow impairment in at least one objective function to get a new solution. The NAUTILUS method proposed is based on the assumptions that past experiences affect decision makers’ hopes and that people do not react symmetrically to gains and losses. Therefore, some decision makers may prefer to start from the worst possible objective values and to improve every objective step by step according to their preferences. In NAUTILUS, starting from the nadir point, a solution is obtained at each iteration which dominates t…
An Interactive Evolutionary Multiobjective Optimization Method: Interactive WASF-GA
In this paper, we describe an interactive evolutionary algorithm called Interactive WASF-GA to solve multiobjective optimization problems. This algorithm is based on a preference-based evolutionary multiobjective optimization algorithm called WASF-GA. In Interactive WASF-GA, a decision maker (DM) provides preference information at each iteration simple as a reference point consisting of desirable objective function values and the number of solutions to be compared. Using this information, the desired number of solutions are generated to represent the region of interest of the Pareto optimal front associated to the reference point given. Interactive WASF-GA implies a much lower computational…
IRA-EMO : Interactive Method Using Reservation and Aspiration Levels for Evolutionary Multiobjective Optimization
We propose a new interactive evolutionary multiobjective optimization method, IRA-EMO. At each iteration, the decision maker (DM) expresses her/his preferences as an interesting interval for objective function values. The DM also specifies the number of representative Pareto optimal solutions in these intervals referred to as regions of interest one wants to study. Finally, a real-life engineering three-objective optimization problem is used to demonstrate how IRA-EMO works in practice for finding the most preferred solution. peerReviewed
On the Use of Preferential Weights in Interactive Reference Point Based Methods
We introduce a new way of utilizing preference information specified by the decision maker in interactive reference point based methods. A reference point consists of aspiration levels for each objective function. We take the desires of the decision maker into account more closely when projecting the reference point to become nondominated. In this way we can support the decision maker in finding the most satisfactory solutions faster. In practice, we adjust the weights in the achievement scalarizing function that projects the reference point. We demonstrate our idea with an example and we summarize results of computational tests that support the efficiency of the idea proposed.
Incorporating preference information in interactive reference point methods for multiobjective optimization
In this paper, we introduce new ways of utilizing preference information specified by the decision maker in interactive reference point based methods. A reference point consists of desirable values for each objective function. The idea is to take the desires of the decision maker into account more closely when projecting the reference point onto the set of nondominated solutions. In this way we can support the decision maker in finding the most satisfactory solutions faster. In practice, we adjust the weights in the achievement scalarizing function that projects the reference point. We identify different cases depending on the amount of additional information available and demonstrate the c…
E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method
Interactive multiobjective optimization methods cannot necessarily be easily used when (industrial) multiobjective optimization problems are involved. There are at least two important factors to be considered with any interactive method: computationally expensive functions and aspects of human behavior. In this paper, we propose a method based on the existing NAUTILUS method and call it the Enhanced NAUTILUS (E-NAUTILUS) method. This method borrows the motivation of NAUTILUS along with the human aspects related to avoiding trading-off and anchoring bias and extends its applicability for computationally expensive multiobjective optimization problems. In the E-NAUTILUS method, a set of Pareto…
A two-slope achievement scalarizing function for interactive multiobjective optimization
The use of achievement (scalarizing) functions in interactive multiobjective optimization methods is very popular, as indicated by the large number of algorithmic and applied scientific papers that use this approach. Key parameters in this approach are the reference point, which expresses desirable objective function values for the decision maker, and weights. The role of the weights can range from purely normalizing to fully preferential parameters that indicate the relative importance given by the decision maker to the achievement of each reference value. Technically, the influence of the weights in the solution generated by the achievement scalarizing function is different, depending on …
A new preference handling technique for interactive multiobjective optimization without trading-off
Because the purpose of multiobjective optimization methods is to optimize conflicting objectives simultaneously, they mainly focus on Pareto optimal solutions, where improvement with respect to some objective is only possible by allowing some other objective(s) to impair. Bringing this idea into practice requires the decision maker to think in terms of trading-off, which may limit the ability of effective problem solving. We outline some drawbacks of this and exploit another idea emphasizing the possibility of simultaneous improvement of all objectives. Based on this idea, we propose a technique for handling decision maker’s preferences, which eliminates the necessity to think in terms of t…