Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Invariant Embedding Technique and Its Applications for Improvement or Optimization of Statistical Decisions
2010
In the present paper, for improvement or optimization of statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a performance index is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rule, which has smaller risk than any of the well-known decision rules. To illustrate the proposed technique, applica…
A New Approach to the Stock Location Assignment Problem by Multidimensional Scaling and Seriation
1999
The problem of the best stock location assignment in a warehouse has a fundamental role while optimising picking activities. In the present paper, this problem has been faced by considering seven variables to compute similarity between items. In this context, the problem of the choice of the most adequate similarity (or dissimilarity) measure between units while applying Multidimensional Scaling (MDS), has been examined. Besides the right metric, the possibility of applying a Seriation algorithm has been also considered. By using both MDS and seriation not just a single target can be considered, but we are able to manage with a plenty of variables; on the contrary with techniques used in li…
On smoothing problems with one additional equality condition
2009
Two problems of approximation in Hilbert spaces are considered with one additional equality condition: the smoothing problem with a weight and the smoothing problem with an obstacle. This condition is a generalization of the equality, which appears in the problem of approximation of a histogram in a natural way. We characterize the solutions of these smoothing problems and investigate the connection between them. First published online: 14 Oct 2010
Edge Orientation and the Design of Problem-Specific Crossover Operators for the OCST Problem
2012
In the Euclidean optimal communication spanning tree problem, the edges in optimal trees not only have small weights but also point with high probability toward the center of the graph. These characteristics of optimal solutions can be used for the design of problem-specific evolutionary algorithms (EAs). Recombination operators of direct encodings like edge-set and NetDir can be extended such that they prefer not only edges with small distance weights but also edges that point toward the center of the graph. Experimental results show higher performance and robustness in comparison to EAs using existing crossover strategies.
On the Bias and Performance of the Edge-Set Encoding
2009
The edge-set encoding of trees directly represents trees as sets of their edges. Nonheuristic operators for edge-sets manipulate trees' edges without regard for their weights, while heuristic operators consider edges' weights when including or excluding them. In the latter case, the operators generally favor edges with lower weights, and they tend to generate trees that resemble minimum spanning trees. This bias is strong, which suggests that evolutionary algorithms (EAs) that employ heuristic operators will succeed when optimum solutions resemble minimum spanning trees (MSTs) but fail otherwise. The one-max tree problem is a scalable test problem for trees where the optimum solution can be…
On Optimal Solutions for the Optimal Communication Spanning Tree Problem
2009
This paper presents an experimental investigation into the properties of the optimal communication spanning tree (OCST) problem. The OCST problem seeks a spanning tree that connects all the nodes and satisfies their communication requirements at a minimum total cost. The paper compares the properties of random trees to the properties of the best solutions for the OCST problem that are found using an evolutionary algorithm. The results show, on average, that the optimal solution and the minimum spanning tree (MST) share a higher number of links than the optimal solution and a random tree. Furthermore, optimal solutions for OCST problems with randomly chosen distance weights share a higher n…
Energy Efficient Consensus Over Complex Networks
2015
The need to extract large amounts of information from the environment to have precise situation awareness and then react appropriately to certain events has led to the emergence of complex and heterogeneous sensor networks. In this context, where the sensor nodes are usually powered by batteries, the design of new methods to make inference processes efficient in terms of energy consumption is necessary. One of these processes, which is present in many distributed tasks performed by these complex networks, is the consensus process. This is the basis for certain tracking algorithms in monitoring and control applications. To improve the energy efficiency of this process, in this paper we propo…
Parallel Simulated Annealing: Getting Super Linear Speedups
2005
The study described in this paper tries to improve and combine different approaches that are able to speed up applications of the Simulated Annealing model. It investigates separately two main aspects concerning the degree of parallelism an implementation can egectively exploit at the initial andfinal periods of an execution. As for case studies, it deals with two implementations: the Job shop Scheduling problem and the poryblio selection problem. The paper reports the results of a large number of experiments, carried out by means of a transputer network and a hypercube system. They give useful suggestions about selecting the most suitable values of the intervention parameters to achieve su…
Gradient-based shape optimisation of ultra-wideband antennas parameterised using splines
2010
Methodology enabling the gradient-based optimisation of antennas parameterised using B-splines is presented. Use of the spline parametrisation allows us to obtain versatile new shapes, whereas the geometry can be represented with a small set of design variables. Moreover, good control over admissible geometries is retained. Advantages of gradient-based optimisation methods are quick convergence, and the fact that the obtained design can be guaranteed to be a local optimum. Focus of this study is to present techniques that enable the computation of exact gradients of the discrete problem, even though the complexity of the geometries does not permit establishing analytical expressions for the…
Stability Analysis of Large Scale Networks of Autonomous Work Systems with Delays
2011
This paper considers the problem of stability analysis for a class of production networks of autonomous work systems with delays in the capacity changes. The system under consideration does not share information between work systems and the work systems adjust capacity with the objective of maintaining a desired amount of local work in progress (WIP). Attention is focused to derive explicit sufficient delay-dependent stability conditions for the network using properties of matrix norm. Finally, numerical results are provided to demonstrate the proposed approach.