Linear Programming, Integer Linear Programming, Global Optimization


DIPARTIMENTO DI INFORMATICA Università di Torino

Research Report Year 2002

Operational Research

People Research Activities Publications Software Products Research Grants

People People

Last and first name	Position	Email
Cantoni Lionello	Associate Professor	cantoni(at)di.unito.it
Locatelli Marco	Associate Professor	locatell(at)di.unito.it
Grosso Andrea Cesare	Researcher	grosso(at)di.unito.it

Research activity in 2002

Development, implementation and experimentation of global optimization algorithms in order to detect the minimal energy configuration according to the Lennard-Jones potential function as well as for other relevant potentials such as the Morse potential. 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 or the Morse pair potential, is searched. This problems are widely explored in the literature, they are very challenging from the optimization point of view and have important applications in the field of chemistry. Currently, the combination of two-phase local searches, previously successully employed, with other methods, such as basin-hopping, is tested with quite encouraging results. The research has also been extended to the search for minimal energy configurations of water molecules and to the docking protein problem.
The properties of objective functions which make them difficult for global optimization have been analysed. A set of properties (such as multimodality at different levels, width of oscillations) have been considered and appropriate tools to take them into account have been searched for.
Max-clique problems, i.e. finding the maximum clique (the complete subgraph of a graph with highest cardinality) are very challenging optimization problems. An analysis of existing methods based on a continuous formulation of such problem revealed their equivalence with particular combinatorial heuristics. Such heuristics have been further developed and lead to the detection of the global optimum or at least of the best known value for many benchmark problems. Some recent developments allowed to detect optimal solutions for a class of benchmark problems which posed serious difficulties to most approaches in the literature.
The concept of undominated D.C. (Difference of Convex) Decompositions for general quadratic functions has been introduced and it has been shown how these decompositions allow to find better bounds in branch-and-bound approaches.

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