DIPARTIMENTO   DI   INFORMATICA
Università di Torino

Research Report Year 2000

Operational Research

Linear Programming, Integer Linear Programming, Global Optimization

  People   Research Activities   Publications   Software Products   Research Grants

People

Cantoni Lionello

Associate Professor

cantoni(at)di.unito.it

Locatelli Marco

Researcher

locatell(at)di.unito.it

Research activity in 2000

  1. Efficiency and efficacy of a symmetric variant of the Simplex method are in course of evaluation
  2. Development of methodologies in learning processes headed by the computer (AUDIP project)
  3. Development, implementation and experimentation of global optimization algorithms in order to detect the minimal energy configuration according to the Lennard-Jones potential function. The minimal energy of a cluster of identical and uncharged atoms, where the energy between any pair of atoms is represented by the Lennard-Jones pair potential, is searched. This problem, widely explored in the literature, not only in the field of optimization but also in the field of chemistry, is a very difficult one because of the exponential growth of the number of local minima as the number of atoms increases. The problem has been faced by an approach based on a two-phase local search where the first phase minimizes a modified potential and the second one the original potential. The modified potential tends to favour, in a mild or strong way according to the choice of some parameters, spherical and compact structures. The results obtained are quite good especially for what concerns the most difficult configurations (respectively with 38, 75, 98, 102 atoms). In such cases the number of local searches required to detect the best configurations is improved by one, two and sometimes even three order of magnitudes with respect to the previously best reported results.
  4. Theoretical analysis of the properties of optimal clusters. While a lower bound on the minimal distance between atoms in an optimal cluster is known for Lennard-Jones clusters, it was not known for clusters based on the Morse pair potential, which resembles the Lennard-Jones potential but introduces a higher degree of flexibility by the introduction of a parameter which can be varied in order to better model real situations. Such a lower bound for Morse clusters has been now computed.
  5. Simulated Annealing algorithms. In this field results about the convergence and the rate of convergence of such algorithms have been derived. The main results have been obtained by constraining both the choice of the next candidate point and the value of the temperature to the distance of the current function value from the global optimum value or an estimate of it.
  6. Concave optimization. Convergence and finiteness properties of some algorithms for concave optimization over polytopes have been studied. The algorithms are Branch & Bound ones where branching is obtained by conical or simplicial subdivisions.

2000 Publications

Locatelli M. Convergence of a simulated annealing algorithm for continuous global optimization. JOURNAL OF GLOBAL OPTIMIZATION. Vol. 18, pp. 219-233, 2000.

Locatelli M. Simulated annealing algorithms for continuous global optimization: convergence conditions. JOURNAL OF OPTIMIZATION THEORY & APPLICATIONS, Vol. 104, pp. 121-133, 2000.

Locatelli M., Raber U. A finiteness result for the simplicial branch-and-bound algorithm based on w-subdivisions. JOURNAL OF OPTIMIZATION THEORY & APPLICATIONS Vol. 107, pp. 81-88, 2000.

Locatelli M., Raber U. On the convergence of the simplicial branch-and-bound algorithm based on w-subdivisions. JOURNAL OF OPTIMIZATION THEORY & APPLICATIONS, Vol. 107, pp. 69-79, 2000.

Locatelli M., Thoai N.V. Finite exact branch-and-bound algorithms for concave minimization over polytopes. JOURNAL OF GLOBAL OPTIMIZATION, Vol. 18, pp. 107-128, 2000.

Software Products

Name

Type

Name of prototype

Description

Year

Cantoni L. and Gedda M.

Software for learning, exercising, and reviewing

AUDIP: Teoria dei giochi

The software has been developed for the Operational Research course students; its purpose is the interactive learning, simulation and review of the course topics. It is available online.

2000

Locatelli M. and Schoen F.

Software for experimenting with the Lennard-Jones clusters

Fast Global Optimization of difficutl Lennard-Jones Clusters

The software is to support the problem of the Lennard Jones clusters computation. It is available online to those interested in the analysis of this problems following the approach proposed in the paper titled "Fast Global Optimization of difficutl Lennard-Jones Clusters"

2000

 

Research grants

Title of project

Project leader

Funding Organization

Kind of grant

Per la standardizzazione delle aule didattiche

L. Cantoni

Università di Torino

ex 60%

Ricerca e applicazione di nuove tecnologie M/S per l'implementazione e la somministrazione di moduli AUDIP loro integrazione

L. Cantoni

Università di Torino

ex 60%

 

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