Search results for "Mathematical optimization"
showing 10 items of 1300 documents
OLS Identification of network topologies
2011
Abstract In many applications, it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model. The problem of reducing the complexity is addressed by fixing a certain degree of sparsity and finding the…
Obtaining the best value for money in adaptive sequential estimation
2010
Abstract In [Kujala, J. V., Richardson, U., & Lyytinen, H. (2010). A Bayesian-optimal principle for learner-friendly adaptation in learning games. Journal of Mathematical Psychology , 54(2), 247–255], we considered an extension of the conventional Bayesian adaptive estimation framework to situations where each observable variable is associated with a certain random cost of observation. We proposed an algorithm that chooses each placement by maximizing the expected gain in utility divided by the expected cost. In this paper, we formally justify this placement rule as an asymptotically optimal solution to the problem of maximizing the expected utility of an experiment that terminates when the…
Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems
1994
In this paper we introduce qualification conditions for multivalued functions in Banach spaces involving the A-approximate subdifferential, and we show that these conditions guarantee metric regularity of multivalued functions. The results are then applied for deriving Lagrange multipliers of Fritz—John type and Kuhn—Tucker type for infinite non-smooth vector optimization problems.
Randomized heuristics for the Capacitated Clustering Problem
2017
In this paper, we investigate the adaptation of the Greedy Randomized Adaptive Search Procedure (GRASP) and Iterated Greedy methodologies to the Capacitated Clustering Problem (CCP). In particular, we focus on the effect of the balance between randomization and greediness on the performance of these multi-start heuristic search methods when solving this NP-hard problem. The former is a memory-less approach that constructs independent solutions, while the latter is a memory-based method that constructs linked solutions, obtained by partially rebuilding previous ones. Both are based on the combination of greediness and randomization in the constructive process, and coupled with a subsequent l…
A matheuristic for the Team Orienteering Arc Routing Problem
2015
In the Team OrienteeringArc Routing Problem (TOARP) the potential customers are located on the arcs of a directed graph and are to be chosen on the basis of an associated profit. A limited fleet of vehicles is available to serve the chosen customers. Each vehicle has to satisfy a maximum route duration constraint. The goal is to maximize the profit of the served customers. We propose a matheuristic for the TOARP and test it on a set of benchmark instances for which the optimal solution or an upper bound is known. The matheuristic finds the optimal solutions on all, except one, instances of one of the four classes of tested instances (with up to 27 vertices and 296 arcs). The average error o…
High resolution in currents reconstruction applying the extrapolation matrix and spectrum replies
2007
A faster method for the reconstruction of currents has been proposed. For this a new algorithm has been used which extrapolates a 2D signal in less time than the iterative method of Papoulis. Results exposed in this paper show the likeness of the reconstructed currents with the new algorithm with those of the iterative method and the improvement that might be obtained in these new currents with regard to the iterative one. Furthermore, results show the higher speed of the new matrix method.
What is the Best Method of Matrix Adjustment? A Formal Answer by a Return to the World of Vectors
2003
The principle of matrix adjustment methods consists into finding what is the matrix which is the closest to an initial matrix but with respect of the column and row sum totals of a second matrix. In order to help deciding which matrix-adjustment method is the better, the article returns to the simpler problem of vector adjustment then back to matrices. The information-lost minimization (biproportional methods and RAS) leads to a multiplicative form and generalize the linear model. On the other hand, the distance minimization which leads to an additive form tends to distort the data by giving a result asymptotically independent to the initial matrix. The result allows concluding non-ambiguou…
Simulated Annealing in Bayesian Decision Theory
1992
Since the seminal paper by Kirkpatrick, Gelatt and Vechhi (1983), a number of papers in the scientific literature refer to simulated annealing as a powerful random optimization method which promises to deliver, within reasonable computing times, optimal or nearly optimal solutions to complex decision problems hitherto forbidding. The algorithm, which uses the physical process of annealing as a metaphor, is special in that, at each iteration, one may move with positive probability to solutions with higher values of the function to minimize, rather than directly jumping to the point with the smallest value within the neighborhood, thus drastically reducing the chances of getting trapped in lo…
Wait-and-switch relaxation model: Relationship between nonexponential relaxation patterns and random local properties of a complex system
2006
The wait-and-switch stochastic model of relaxation is presented. Using the ``random-variable'' formalism of limit theorems of probability theory we explain the universality of the short- and long-time fractional-power laws in relaxation responses of complex systems. We show that the time evolution of the nonequilibrium state of a macroscopic system depends on two stochastic mechanisms: one, which determines the local statistical properties of the relaxing entities, and the other one, which determines the number (random or deterministic) of the microscopic and mesoscopic relaxation contributions. Within the proposed framework we derive the Havriliak-Negami and Kohlrausch-Williams-Watts funct…
Measuring the Spatial Dispersion of Evolutionary Search Processes: Application to Walksat
2002
In this paper, we propose a simple and efficient method for measuring the spatial dispersion of a set of points in a metric space. This method allows the quantifying of the population diversity in genetic algorithms. It can also be used to measure the spatial dispersion of any local search process during a specified time interval. We then use this method to study the way Walksat explores its search space, showing that the search for a solution often includes several stages of intensification and diversification.