The Morse potential is a simple model pair potential that has a single parameter $\rho$ which determines the width of the potential well and allows a wide variety of materials to be modelled. Morse clusters provide a particularly tough test system for global optimization algorithms, and one that is highly relevant to methods that are … Read more
We show how to derive error estimates between a function and its interpolating polynomial and between their corresponding derivatives. The derivation is based on a new definition of well-poisedness for the interpolation set, directly connecting the accuracy of the error estimates with the geometry of the points in the set. This definition is equivalent to … Read more
Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices present a fascinating mathematical challenge. Such problems arise often in theory and practice, particularly in engineering design, and are amenable to a rich blend of classical mathematical techniques and contemporary optimization theory. This essay presents a personal choice of some central mathematical ideas, outlined for … Read more
We develop Quasi-Newton methods for distributed parameter estimation problems, where the forward problem is governed by a set of partial differential equations. A Tikhonov style regularization approach yields an optimization problem with a special structure, where the gradients are calculated using the adjoint method. In many cases standard Quasi-Newton methods (such as L-BFGS) are not … Read more
In this paper we report results on the problem of docking two large proteins by means of a two-phase monotonic basin hopping method. Given an appropriate force field which is used to measure the interaction energy between two biomolecules which are considered as rigid bodies, we used a randomized global optimization methods based upon the … Read more
We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for “infinite-dimensional second-order cone programs.” We consider as an example a … Read more
We present a new formulation of the truss topology problem that results in unique design and unique displacements of the optimal truss. This is reached by adding an upper level to the original optimization problem and formulating the new problem as an MPCC (Mathematical Program with Complementarity Constraints). We derive optimality conditions for this problem … Read more
We recently discovered 5 new putative globally optimum configurations for Morse clusters at $\rho=8$. This report contains some algorithmic details as well as the structures determined with our method. Citation Technical Report DSI 3-2003, Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Firenze, 2003. Article Download View New global optima for Morse clusters … Read more
A single facility has to be located in competition with fixed existing facilities of similar type. Demand is supposed to be concentrated at a finite number of points, and consumers patronise the facility to which they are attracted most. Attraction is expressed by some function of the quality of the facility and its distance to … Read more
The effectiveness of a layout design cannot be completely measured if the operational characteristics of the manufacturing system are ignored. There is, therefore, a need to develop integrated manufacturing system design models. In this paper, the integration of unit load and material handling considerations in facility layout design is presented. This integration is based on … Read more