When making decisions with multiple criteria, a decision maker often thinks in terms of an aspiration point or levels of achievement for the criteria. In multiple objective mathematical programming, solution methods based on aspiration points can generate nondominated solutions using a variety of scalarizing functions. These reference point solution methods commonly use a scalarizing function t...

Generalized scalarizing problems, called GENS and GENSLex, for obtaining Pareto optimal solutions of multicriteria optimization problems are presented in the paper. The basic properties of these scalarizing problems are described. The existence of single-criterion problems with differentiable objective functions and constraints, which are equivalent to GENS and GENSLex scalarizing problems, are...

A web-based Decision Support System WebOptim for solving multiple objective optimization problems is presented. Its basic characteristics are: user-independent, multisolver-admissibility, method-independent, heterogeneity, web-accessibility. Core system module is an original generalized interactive scalarizing method. It incorporates a number of thirteen interactive methods. Most of the known s...

In this paper, we discuss the idea of incorporating preference information into evolutionary multiobjective optimization and propose a preference-based evolutionary approach that can be used as an integral part of an interactive algorithm. One algorithm is proposed in the paper. At each iteration, the decision maker is asked to give preference information in terms of her/his reference point con...

A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units (DMUs) to select the factor weights which are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. For dealing with this difficulty and assessing all the DMUs on the sam...

In multiobjective optimization methods, the multiple conflicting objectives are typically converted into a single objective optimization problem with the help of scalarizing functions and such functions may be constructed in many ways. We compare both theoretically and numerically the performance of three classification-based scalarizing functions and pay attention to how well they obey the cla...

In this paper, we discuss the idea of incorporating preference information into evolutionary multi-objective optimization and propose a preference-based evolutionary approach that can be used as an integral part of an interactive algorithm. One algorithm is proposed in the paper. At each iteration, the decision maker is asked to give preference information in terms of his or her reference point...