Andrea Grosso

Finding maximin latin hypercube designs by Iterated Local Search heuristics

The maximin LHD problem calls for arranging N points in a k-dimensional grid so that no pair of points share a coordinate and the distance of the closest pair of points is as large as possible. In this paper we propose to tackle this problem by heuristic algorithms belonging to the Iterated Local Search (ILS) family and show through some computational experiments that the proposed algorithms compare very well with different heuristic approaches in the established literature.

Simple ingredients leading to very efficient heuristics for the maximum clique problem

Abstract Starting from an algorithm recently proposed by Pullan and Hoos, we formulate and analyze iterated local search algorithms for the maximum clique problem. The basic components of such algorithms are a fast neighbourhood search (not based on node evaluation but on completely random selection) and simple, yet very effective, diversification techniques and restart rules. A detailed computational study is performed in order to identify strengths and weaknesses of the proposed algorithms and the role of the different components on several classes of instances. The tested algorithms are very fast and reliable: most of the DIMACS benchmark instances are solved within very short CPU times. For one of the hardest tests, a new putative optimum was discovered by one of our algorithms. Very good performances were also shown on recently proposed and more difficult instances. It is important to remark that the heuristics tested in this paper are basically parameter free (the appropriate value for the unique parameter is easily identified and was, in fact, the same value for all problem instances used in this paper).

A Population-based Approach for Hard Global Optimization Problems based on Dissimilarity Measures

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 discriminating among different algorithms. We think that in order to judge the quality of new global optimization methods, different criteria might be adopted like, e.g.: 1.efficiency – measured in terms of the computational effort necessary to obtain the putative global optimum2.robustness – measured in terms of “percentage of successes”, i.e. of the number of times the algorithm, re-started with different seeds or starting points, is able to end up at the putative global optimum3.discovery capability – measured in terms of the possibility that an algorithm discovers, for the first time, a putative optimum for a given problem which is better than the best known up to now. Of course the third criterion cannot be considered as a compulsory one, as it might be the case that, for a given problem, the best known putative global optimum is indeed the global one, so that no algorithm will ever be able to discover a better one. In this paper we present a computational framework based on a population-based stochastic method in which different candidate solutions for a single problem are maintained in a population which evolves in such a way as to guarantee a sufficient diversity among solutions. This diversity enforcement is obtained through the definition of a dissimilarity measure whose definition is dependent on the specific problem class. We show in the paper that, for some well known and particularly hard test classes, the proposed method satisfies the above criteria, in that it is both much more efficient and robust when compared with other published approaches. Moreover, for the very hard problem of determining the minimum energy conformation of a cluster of particles which interact through short-range Morse potential, our approach was able to discover four new putative optima.

Logical topologies design over WDM wavelength routed networks robust to traffic uncertainties

We develop a novel methodology for the design of the optimal logical topology configuration over a WDM wavelength routed network, when some or all the traffic relations are affected by a degree of uncertainty. Our optimal topology design algorithm relies on the application of the tabu search optimization meta-heuristic.

Hypertensive retinopathy revisited: some answers, more questions

Hypertension is associated with cardiovascular risk and systemic target organ damage. Retinopathy is considered one of the indicators of target organ damage. This review focuses on recent studies on hypertensive retinopathy and their implications for clinical care. Early recognition of hypertensive retinopathy signs remains an important step in the risk stratification of hypertensive patients.

Solving the problem of packing equal and unequal circles in a circular container

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 parameter values for the proposed methods. Different improvements with respect to the best results reported in the literature have been detected.

Solution of the single machine total tardiness problem

The paper deals with the solution of the single machine total tardiness model. It improves and generalizes an important rule to decompose the model into two subproblems. It also provides a O(n2) procedure to implement this rule and its generalization. Those two rules, along with some known results, are incorporated in a branch and bound algorithm that efficiently handles instances with up to 300 jobs and uses the original and maximally increased due dates to solve the original problem. Several properties that justify the modified due date version of our algorithm and produce an easy-to-implement new lower bound are established. The paper also provides an explanation why using the increased due dates may improve the efficiency of certain algorithms. Copyright

Branch and cut algorithms for detecting critical nodes in undirected graphs

In this paper we deal with the critical node problem, where a given number of nodes has to be removed from an undirected graph in order to maximize the disconnections between the node pairs of the graph. We propose an integer linear programming model with a non-polynomial number of constraints but whose linear relaxation can be solved in polynomial time. We derive different valid inequalities and some theoretical results about them. We also propose an alternative model based on a quadratic reformulation of the problem. Finally, we perform many computational experiments and analyze the corresponding results.

Solving molecular distance geometry problems by global optimization algorithms

Abstract In this paper we consider global optimization algorithms based on multiple local searches for the Molecular Distance Geometry Problem (MDGP). Three distinct approaches (Multistart, Monotonic Basin Hopping, Population Basin Hopping) are presented and for each of them a computational analysis is performed. The results are also compared with those of two other approaches in the literature, the DGSOL approach (Moré, Wu in J. Glob. Optim. 15:219–234, 1999) and a SDP based approach (Biswas et al. in An SDP based approach for anchor-free 3D graph realization, Technical Report, Operations Research, Stanford University, 2005).

Hypertensive retinopathy: there's more than meets the eye

Hypertension is associated with increased cardiovascular risk, leading to systemic end-organ damage, including retinopathy. However, the recent European Society of Hypertension–European Society of Cardiology and World Health Organization–International Society of Hypertension 2003 guidelines propose new prognostic indications for the classification of hypertensive retinopathy. In particular, grades I and II are no longer included among signs of end-organ damage, and only grades III and IV are retained as associated clinical conditions for the stratification of global cardiovascular risk. This review article will focus on the wider implications of clinical markers of microvascular damage in the retina, with specific reference to hypertension and end-organ damage. Early recognition of retinal changes remains an important step in the risk stratification of hypertensive patients.