In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.

This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used instead of traditional techniques. These multiple reference points can easily be implemented in a parallel algorithmic framework. The reference points can be uniformly distributed wit...

DINAS is an interactive system to aid solving various multiobje~tive transshipment problems with facility focation using IBM-PC XT:AT or compatibles. DINAS utilizes the so-called aspiration-based (or reference point) approach to interactive handling of multiple objectives. In this approach the decision maker forms his/her requirements in terms of aspiration and reservation levels, i.e. specifie...

The Reference Point Method (RPM) is an interactive technique for multiple criteria optimization problems. It is based on optimization of the scalarizing achievement function built as the augmented maxmin aggregation of individual outcomes with respect to the given reference levels. Actually, the worst individual achievement is optimized, but regularized with the term representing the average ac...

In this paper, an interactive version of the ParEGO algorithm is introduced for identifying most preferred solutions for computationally expensive multiobjective optimization problems. It enables a decision maker to guide the search with her preferences and change them in case new insight is gained about the feasibility of the preferences. At each interaction, the decision maker is shown a subs...

In the interactive algorithms for multicriteria optimization the decision maker (DM) may express his/her preferences among the separate Pareto optimal solutions with the help of the values of the scalarizing problem parameters. The DM must choose the final (most preferred) solution and be responsible for this selection. The interactive methods are the best developed and wide spread methods. Thi...

This article reports an experimental analysis on stochastic local search for approximating the Pareto set of bi-objective unconstrained binary quadratic programming problems. First, we investigate two scalarizing strategies that iteratively identify a high-quality solution for a sequence of sub-problems. Each sub-problem is based on a static or adaptive definition of weighted-sum aggregation co...

The interactive algorithms are often used [2] to solve multicriteria linear integer programming problems (MCIP). These algorithms [3, 6, 7, 11, 13] are modifications of interactive approaches solving multicriteria linear problems that include the integrality constraints. Linear integer programming problems are used as scalarizing problems in these interactive algorithms. These problems are NP-d...