Search

Algorithms that make use of the gradient, i.e., the direction of maximum improvement, to search for the optimum of a single-objective function have been around for decades. They are commonly accepted to be important and have been applied to tackle single-objective optimization problems in many fields. For multiobjective optimization problems, much less is known about the gradient and its algorithmic use. In this paper, we aim to contribute to the understanding of gradients for numerical, i.e., real-valued, multiobjective optimization. Specifically, we provide an analytical parametric description of the set of all nondominated, i.e., most promising, directions in which a solution can be moved such that the objective values either improve or remain the same. This result completes previous work where this set is described only for one particular case, namely when some of the nondominated directions have positive, i.e., nonimproving, components and the final set can be computed by taking the subset of directions that are all nonpositive. In addition we use our result to assess the utility of using gradient information for multiobjective optimization where the goal is to obtain a Pareto set of solutions that approximates the optimal Pareto set. To this end, we design and consider various multiobjective gradient-based optimization algorithms. One of these algorithms uses the description of the multiobjective gradient provided here. Also, we hybridize an existing multiobjective evolutionary algorithm (MOEA) with the various multiobjective gradient-based optimization algorithms. During optimization, the performance of the gradient-based optimization algorithms is monitored and the available computational resources are redistributed to allow the (currently) most effective algorithm to spend the most resources. We perform an experimental analysis using a few well-known benchmark problems to compare the performance of different optimization methods. The results underline that the use of a population of solutions that is characteristic of MOEAs is a powerful concept if the goal is to obtain a good Pareto set, i.e., instead of only a single solution. This makes it hard to increase convergence speed in the initial phase using gradient information to improve any single solution. However, in the longer run, the use of gradient information does ultimately allow for better fine-tuning of the results and thus better overall convergence. [ABSTRACT FROM PUBLISHER]

High availability communication networks with very low failure rates are often designed by using physical diversity, i.e., the traffic between a given pair of nodes is routed by using several physically disjoint paths. The selection of the pair of routes that maximizes the connectivity of a node is not an easy problem, because such connectivity cannot be expressed as an additive function of the availability of links and nodes in the path pairs. Previous algorithms for searching the optimal route use additive costs, which can be a loose assumption either when high failure rates can be locally present, or when fully disjoints paths do not exist. In this paper, we construct a Bayesian network to encode the probabilistic relation between the connectivity of a node and the availability of nodes and links. The problem of selecting an optimal pair of routes becomes equivalent to optimizing the structure of the Bayesian network. By introducing appropriate approximations on the double route availability equations, we propose a new algorithm, which outperforms other classical methods when there are sporadic high error rate elements in the network. Simulations and an application example in an electric transport telecontrol network show the performance of the method when compared to standard search. [ABSTRACT FROM AUTHOR]

This paper presents a novel parametric representation for bidirectional texture functions. Our method mainly relies on two original techniques, namely, multivariate spherical radial basis functions (SRBFs) and optimized parameterization. First, since the surface appearance of a real-world object is frequently a mixed effect of different physical factors, the proposed sum-of-products model based on multivariate SRBFs especially provides an intrinsic and efficient representation for heterogenous materials. Second, optimized parameterization particularly aims at overcoming the major disadvantage of traditional fixed parameterization. By using a parametric model to account for variable transformations, the parameterization process can be tightly integrated with multivariate SRBFs into a unified framework. Finally, a hierarchical fitting algorithm for bidirectional texture functions is developed to exploit spatial coherence and reduce computational cost. Our experimental results further reveal that the proposed representation can easily achieve high-quality approximation and real-time rendering performance. [ABSTRACT FROM AUTHOR]

In this article, we show that when targets are closely spaced, traditional tracking algorithms can be adjusted to perform better under a performance measure that disregards identity. More specifically, we propose an adjusted version of the joint probabilistic data association (JPDA) filter, which we call set JPDA (SJPDA). Through examples and theory we motivate the new approach, and show its possibilities. To decrease the computational requirements, we further show that the SJPDA filter can be formulated as a continuous optimization problem which is fairly easy to handle. Optimal approximations are also discussed, and an algorithm, Kullback–Leibler SJPDA (KLSJPDA), which provides optimal Gaussian approximations in the Kullback–Leibler sense is derived. Finally, we evaluate the SJPDA filter on two scenarios with closely spaced targets, and compare the performance in terms of the mean optimal subpattern assignment (MOSPA) measure with the JPDA filter, and also with the Gaussian-mixture cardinalized probability hypothesis density (GM-CPHD) filter. The results show that the SJPDA filter performs substantially better than the JPDA filter, and almost as well as the more complex GM-CPHD filter. [ABSTRACT FROM PUBLISHER]