There is a lack of a representative set of test problems for comparing global optimization methods. To remedy this a classiication of essentially un-constrained global optimization problems into unimodal, easy, moderately diicult, and diicult problems is proposed. The problem features giving this classiication are the chance to miss the basin of the global minimum, the dispersion of minima, and...

In this paper we discuss weak sharp minima for vector optimization problems with polynomial data. Exploiting the imposed polynomial structure together with powerful tools of variational analysis and semialgebraic geometry and under some slight assumptions, we establish (Hölder type) bounded and global weak sharp minima with explicitly calculated exponents.

We have shown recently that, when certain quite general conditions are satisfied, the set of local minima in the optical merit function space forms a network where they are all connected through optimization paths generated from saddle points having a Morse index of 1. A new global optimization method, that makes use of this linking network to systematically detect all minima, is presented. The...

Associative memory Hamiltonian structure prediction potentials are not overly rugged, thereby suggesting their landscapes are like those of actual proteins. In the present contribution we show how basin-hopping global optimization can identify low-lying minima for the corresponding mildly frustrated energy landscapes. For small systems the basin-hopping algorithm succeeds in locating both lower...

Given unit points charges on the surface of a unit conducting sphere, what configuration of charges minimizes the Coulombic energy SigmaN i>(j=1)1/r(ij)? Due to an exponential rise in good local minima, finding global minima for this problem, or even approaches to do so has proven extremely difficult. For N=10(h2+hk+k2)+2 recent theoretical work based on elasticity theory, and subsequent numeri...

Introduction: A variety of field-map estimation techniques using 3-pt multi-echo acquisitions have been developed for reliable water-fat separation [1-6]. The field-map is mainly estimated by finding a minimum of a cost function, defined as , the difference between measured data and estimated data with field-map values varying, which is periodic with period 1/∆TE . However, there still exists a...

An empirical two-plus-three-body atomistic potential, derived by fitting experimental data pertaining to bulk aluminium, has been applied to study the structures and growth patterns of small aluminium clusters. The high dimensionality of the nuclear configuration space for clusters results in an extremely large number of isomers – local minima on the potential energy hypersurface. Global optimi...

This report presents P scg , a new global optimization method for training mul-tilayered perceptrons. Instead of local minima, global minima of the error function are found. This new method is hybrid in the sense that it combines three very diierent optimization techniques: Random Line Search, Scaled Conjugate Gradient and a 1-dimensional minimization algorithm named P. The best points of each ...

Locating the global minimum of a complex potential energy surface is facilitated by considering a homotopy, namely, a family of surfaces that interpolate continuously from an arbitrary initial potential to the system under consideration. Different strategies can be used to follow the evolving minima. It is possible to enhance the probability of locating the global minimum through a heuristic ch...

This paper presents an improved technique for accelerating the process of doing logic programming in discrete Hopfield neural network by integrating fuzzy logic and modifying activation function. Generally Hopfield networks are suitable for solving combinatorial optimization problems and pattern recognition problems. However Hopfield neural networks also face some limitations; one of the major ...