A discrete polynomial curve is defined as a set of points lying between two polynomial curves. This paper deals with the problem of fitting a discrete polynomial curve to given integer points in the presence of outliers. We formulate the problem as a discrete optimization problem in which the number of points included in the discrete polynomial curve, i.e., the number of inliers, is maximized. ...

In this paper, the problem of observing the state of a class of discrete nonlinear system is addressed. The design of the observer is dealt with using H∞ performance techniques, taking into account disturbance and noise attenuation. The result is an LMI optimization problem that can be solved by standard optimization techniques. A design strategy is proposed based on the available disturbances ...

This paper treats the solution of nonlinear optimization problems involving discrete decision variables, also known as generalized disjunctive programming (GDP) or mixed-integer nonlinear programming (MINLP) problems, that arise in process engineering. The key idea is to eliminate the discrete decision variables by adding a set of continuous variables and constraints that represent the discrete...

Helly’s theorem says that if every d + 1 elements of a given finite set of convex objects in IR have a common point, then there is a point common to all of the objects in the set. We define three new types of Helly theorems: discrete Helly theorems where the common point should belong to an a-priori given set, lexicographic Helly theorems where the common point should not be lexicographically g...

Latin hypercube designs (LHDs) are widely used in many applications. As the number of design points or factors becomes large, the total number of LHDs grows exponentially. The large number of feasible designs makes the search for optimal LHDs a difficult discrete optimization problem. To tackle this problem, we propose a new population-based algorithm named LaPSO that is adapted from the standa...

in this paper, a new continuous ant colony optimization (caco) algorithm is proposed for optimal reservoir operation. the paper presents a new method of determining and setting a complete set of control parameters for any given problem, saving the user from a tedious trial and error based approach to determine them. the paper also proposes an elitist strategy for caco algorithm where best solut...

Censored quantile regressions (CQR) are a valuable tool in economics and engineering. The computation of estimators is highly complex and the performance of standard methods is not satisfactory, in particular if a high degree of censoring is present. Due to an interpolation property the computation of CQR estimates corresponds to the solution of a large scale discrete optimization problem. This...

This paper describes valuation-based systems for representing and solving discrete optimization problems. The information in an optimization problem is represented using variables, sample spaces of variables, a set of values, and func­ tions that map sample spaces of sets of variables to the set of values. The func­ tions, called valuations, represent the factors of an objective function. Solvi...

In this paper, we are interested in the application to video segmentation of the discrete shape optimization problem

For the first time, a running time analysis of a multi-objective evolutionary algorithm for a discrete optimization problem is given. To this end, a simple pseudo-Boolean problem (Lotz: leading ones trailing zeroes) is defined and a population-based optimization algorithm (FEMO). We show, that the algorithm performs a black box optimization in Θ(n log n) function evaluations where n is the numb...