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In this paper, we introduce new concepts of ε-weak efficient solutions and ε-efficient solutions for a nonconvex multiobjective fractional programming problem involving n-set functions. Using an ε-parametric approach and a new theorem of alternative for nonconvex n-set functions, some necessary and sufficient conditions for ε-approximate solutions axe derived. [ABSTRACT FROM AUTHOR]

The use of evolutionary strategies (ESs) to solve problems with multiple objectives [known as vector optimization problems (VOPs)] has attracted much attention recently. Being population-based approaches, ESs offer a means to find a set of Pareto-optimal solutions in a single run. Differential evolution (DE) is an ES that was developed to handle optimization problems over continuous domains. The objective of this paper is to introduce a novel Pareto-frontier differential evolution (PDE) algorithm to solve VOPs. The solutions provided by the proposed algorithm for two standard test problems, outperform the ‘strength Pareto evolutionary algorithm’, one of the state-of-the-art evolutionary algorithm for solving VOPs. [ABSTRACT FROM AUTHOR]

Bilevel programming involves two optimization problems where the constraint region of the first-level problem is implicitly determined by another optimization problem. This model has been applied to decentralized planning problems involving a decision process with a hierarchical structure. In this paper, we consider the bilevel linear fractional/linear programming problem, in which the objective function of the first-level is linear fractional, the objective function of the second level is linear, and the common constraint region is a polyhedron. For this problem, taking into account the relationship between the optimization problem of the second level and its dual, a global optimization approach is proposed that uses an exact penalty function based on the duality gap of the second-level problem. [ABSTRACT FROM AUTHOR]

During the last years nature inspired intelligent techniques have become attractive for analyzing large data sets and solving complex optimization problems. In this paper, one of the most interesting of them, the Ant Colony Optimization (ACO), is used for the construction of a hybrid algorithmic scheme which effectively handles the Pap Smear Cell classification problem. This algorithmic approach is properly combined with a number of nearest neighbor based approaches for performing the requested classification task, through the solution of the so-called optimal feature subset selection problem. The proposed complete algorithmic scheme is tested in two sets of data. The first one consists of 917 images of pap smear cells and the second set consists of 500 images, classified carefully by expert cyto-technicians and doctors. Each cell is described by 20 numerical features, and the cells fall into seven (7) classes, four (4) representing normal cells and three (3) abnormal cases. Nevertheless, from the medical diagnosis viewpoint, a minimum requirement corresponds to the general two-class problem of correct separation between normal from abnormal cells. [ABSTRACT FROM AUTHOR]