Considering a vector optimization problem to which properly efficient solutions are defined by using convex cone-monotone scalarization functions, we attach to it, by means of perturbation theory, new vector duals. When the primal problem, the scalarization function and the perturbation function are particularized, different dual vector problems are obtained, some of them already known in the l...

Ordinal Optimization is a tool to reduce the computational burden in simulation-based optimization problems. The major effort in this field so far focuses on single-objective optimization. In this paper we extend this to multi-objective optimization, and develop Vector Ordinal Optimization, which is different from the one introduced in Ref. 1. Alignment probability and ordered performance curve...

In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval are generalized to the case of ...

Given a set S of n points in the plane, the disjoint two-rectangle covering problem is to find a pair of disjoint rectangles such that their union contains S and the area of the larger rectangle is minimized. In this paper we consider two variants of this optimization problem: (1) the rectangles are free to rotate but must remain parallel to each other, and (2) one rectangle is axis-parallel bu...

Lower bounds of stability, pseudostability and quasistability radii of lexicographic set in vector combinatorial problem on systems of subsets of finite set with partial criteria of more general kinds have been found. Many specialists are engaged in study of stability of discrete optimization problems to perturbations of their parameters (see [1-3]). Need for investigation of stability of optim...

This manuscript is on the theory and numerical procedures of vector optimization w.r.t. various ordering structures, on recent developments in this area and, most important, on their application to medical engineering. In vector optimization one considers optimization problems with a vectorvalued objective map and thus one has to compare elements in a linear space. If the linear space is the fi...

In an attempt to solve multiobjective optimization problems, many traditional methods scalarize an objective vector into a single objective by a weight vector. In these cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands a user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers m...

We have proposed tolerant fuzzy c-means clustering (TFCM) from the viewpoint of handling data more flexibly. This paper presents a new type of tolerant fuzzy c-means clustering with L1-regularization. L1-regularization is wellknown as the most successful techniques to induce sparseness. The proposed algorithm is different from the viewpoint of the sparseness for tolerance vector. In the origina...

A new application for support vector machines is their use for meta-modeling feasible regions in constrained optimization problems. We here describe a solution for the still unsolved problem of a standardized integration of such models into (evolutionary) optimization algorithms with the help of a new decoder based approach. This goal is achieved by constructing a mapping function that maps the...

Ant Colony Optimization (ACO) [2] is a nondeterministic algorithm framework that mimics the foraging behavior of ants to solve difficult optimization problems. Several researchers have successfully applied ant based algorithm framework in different fields of engineering, but never in VLSI testing. In this paper, we first describe the basics of ACO. We then consider the problem of simultaneously...