Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights

In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage orienteering problem with stochastic weights

Feature Generation by Simple-FLDA for Pattern Recognition

Abstract—In this paper, a new feature generation method for pattern recognition is proposed, which is approximately derived from geometrical interpretation of the Fisher linear discriminant analysis (FLDA). In a field of pattern recognition or signal processing, the principal component analysis (PCA) is popular for data compression and feature extraction. Furthermore, iterative learning algorithms for obtaining eigenvectors in PCA have been presented in such fields, including neural networks. Their effectiveness has been demonstrated in many applications. However, recently the FLDA has been used in many fields, especially face image analysis. The drawback of FLDA is a long computational time based on a large-sized covariance matrix and the issue that the within-class covariance matrix is usually singular. Generally FLDA has to carry out minimization of a within-class variance. However in this case the inverse matrix of the within-class covariance matrix cannot be obtained, since data dimension is generally higher than the number of data and then it includes many zero eigenvalues. In order to overcome this difficulty, a new iterative feature generation method, a simple FLDA is introduced and its effectiveness is demonstrated for pattern recognition problems. I

Two-Stage Robust Optimization for the Orienteering Problem with Stochastic Weights

In this paper, the two-stage orienteering problem with stochastic weights is studied, where the first-stage problem is to plan a path under the uncertain environment and the second-stage problem is a recourse action to make sure that the length constraint is satisfied after the uncertainty is realized. First, we explain the recourse model proposed by Evers et al. (2014) and point out that this model is very complex. Then, we introduce a new recourse model which is much simpler with less variables and less constraints. Based on these two recourse models, we introduce two different two-stage robust models for the orienteering problem with stochastic weights. We theoretically prove that the two-stage robust models are equivalent to their corresponding static robust models under the box uncertainty set, which indicates that the two-stage robust models can be solved by using common mathematical programming solvers (e.g., IBM CPLEX optimizer). Furthermore, we prove that the two two-stage robust models are equivalent to each other even though they are based on different recourse models, which indicates that we can use a much simpler model instead of a complex model for practical use. A case study is presented by comparing the two-stage robust models with a one-stage robust model for the orienteering problem with stochastic weights. The numerical results of the comparative studies show the effectiveness and superiority of the proposed two-stage robust models for dealing with the two-stage orienteering problem with stochastic weights

Real-time feature-based image morphing for memory-efficient impostor rendering and animation on GPU

Real-time rendering of large animated crowds consisting of thousands of virtual humans is important for several applications including simulations, games, and interactive walkthroughs but cannot be performed using complex polygonal models at interactive frame rates. For that reason, methods using large numbers of precomputed image-based representations, called impostors, have been proposed. These methods take advantage of existing programmable graphics hardware to compensate for computational expense while maintaining visual fidelity. Thanks to these methods, the number of different virtual humans rendered in real time is no longer restricted by computational power but by texture memory consumed for the variety and discretization of their animations. This work proposes a resource-efficient impostor rendering methodology that employs image morphing techniques to reduce memory consumption while preserving perceptual quality, thus allowing higher diversity or resolution of the rendered crowds. Results of the experiments indicated that the proposed method, in comparison with conventional impostor rendering techniques, can obtain 38 % smoother animations or 87 % better appearance quality by reducing the number of key-frames required for preserving the animation quality via resynthesizing them with up to 92 % similarity on real time