multiobjective programming

In the presented paper, we investigate efficient solutions to optimization problems with multiple criteria and bounded trade-offs. A nonlinear optimization problem to find the relationships between the upper bound for trade-offs and objective functions is presented. Due to this problem, we determine some properly efficient points that are closer to the ideal point. To this end,  we apply the extended form of the generalized Tchebycheff norm. Note that all the presented results work for general problems and no convexity assumption is needed.

We suggest an a priori method by introducing the concept of AP - equitable efficiency. The preferences matrix AP , which is based on the partition P of the index set of the objective functions, is given by the decision-maker. We state the certain conditions on the matrix AP that guarantee the preference relation ⪯eAP to satisfy the strict monotonicity and strict P -transfer principle axioms. A problem most frequently encountered in multiobjective optimization is that the set of Pareto optimal solutions provided by the optimization pro-cess is a large set. Hence, the decision-making based on selecting a unique preferred solution becomes difficult. Considering models with Ar P -equitable efficiency and A∞ P -equitable efficiency can help the decision-maker for over-coming this difficulty, by shrinking the solution set.

‎In recent years the binary quadratic program has grown in‎ ‎combinatorial optimization‎. ‎Quadratic programming can‎ ‎be formulated as a semidefinite programming problem‎. ‎In this paper‎, ‎we consider the general form of‎ ‎binary semidefinite programming problems (BSDP)‎.‎ ‎We show the optimal solutions of the BSDP belong to the efficient set of a semidefinite multiobjective programming problem (SDMOP)‎. ‎Although‎ ‎finding all efficient points for multiobjective is not an easy problem‎, ‎but‎‎solving a continuous problem would be easier than a discrete variable problem‎. ‎In this paper‎, ‎we solve an SDMOP‎, ‎as an auxiliary‎, ‎instead of BSDP‎. We show the performance of our method by generating and solving random problems.

In this paper, multiobjective optimization problems with nondifferentiable quasiconvex functions are considered. We obtain some duality results and a linear representation for the considered problems. Since the well-known strong duality result is not valid for the problems, we present a weaker form of it, named quasi-strong duality result.

Traditional Data Envelopment Analysis (DEA) models evaluate the efficiency of decision making units (DMUs) with common crisp input and output data. However, the data in real applications are often imprecise or ambiguous. This paper transforms fuzzy fractional DEA model constructed using fuzzy arithmetic, into the conventional crisp model. This transformation is performed considering the goal programming that is one of the Multi Objective Programming (MOP) methods. Therefore, in this research the one linear programming model measures the fuzzy efficiencies of DMUs with fuzzy input and fuzzy output data.