Fabio Schoen

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We present a new computational approach to the problem of placing n identical non overlapping disks in the unit square in such a way that their radius is maximized. The problem has been studied in a large number of papers, both from a theoretical and from a computational point of view. In this paper we conjecture that the problem possesses a so-called(More)
In this paper we propose a Monotonic Basin Hopping approach and its population-based variant Population Basin Hopping to solve the problem of packing equal and unequal circles within a circular container with minimum radius. Extensive computational experiments have been performed both to analyze the problem at hand, and to choose in an appropriate way the(More)
University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom San Diego Supercomputer Center, University of California, San Diego, USA Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, I-10149 Torino, Italy Dipartimento di Sistemi e Informatica, Università di Firenze, Via di S.Marta, 3, I-50139 Firenze 185, Italy(More)
When dealing with extremely hard global optimization problems, i.e. problems with a large number of variables and a huge number of local optima, heuristic procedures are the only possible choice. In this situation, lacking any possibility of guaranteeing global optimality for most problem instances, it is quite difficult to establish rules for(More)
It is widely believed that in order to solve large scale global optimization problems an appropriate mixture of local approximation and global exploration is necessary. Local approximation, if first order information on the objective function is available, is efficiently performed by means of local optimization methods. Unfortunately, global exploration, in(More)
In this paper we derive a lower bound, independent from the number of atoms N , for the minimal interatomic distances between atoms in a cluster whose total energy is modelled by means of the so called Morse potential. A similar result was previously proven for Lennard-Jones clusters but the proof can not be extended to Morse clusters. Besides the(More)
One of the most consistently deleted chromosomal regions in solid tumours is 11q23-q25, which consequently has been postulated to harbour one or more tumour suppressor loci. Despite large efforts to identify the responsible genes, the goal remains elusive, but as knowledge accumulates new candidates are emerging. The present study was undertaken in an(More)