The Binary Space Partitioning-Tree Process

The Mondrian process represents an elegant and powerful approach for space partition modelling. However, as it restricts the partitions to be axis-aligned, its modelling flexibility is limited. In this work, we propose a self-consistent Binary Space Partitioning (BSP)-Tree process to generalize the Mondrian process. The BSP-Tree process is an almost surely right continuous Markov jump process that allows uniformly distributed oblique cuts in a two-dimensional convex polygon. The BSP-Tree process can also be extended using a non-uniform probability measure to generate direction differentiated cuts. The process is also self-consistent, maintaining distributional invariance under a restricted subdomain. We use Conditional-Sequential Monte Carlo for inference using the tree structure as the high-dimensional variable. The BSP-Tree process's performance on synthetic data partitioning and relational modelling demonstrates clear inferential improvements over the standard Mondrian process and other related methods

How Many Communities Are There?

Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called communities. The approach is inherently related to clustering with mixture models; and raises a similar model selection problem for the number of communities. The Bayesian information criterion (BIC) is a popular solution, however, for stochastic blockmodels, the conditional independence assumption given the communities of the endpoints among different edges is usually violated in practice. In this regard, we propose composite likelihood BIC (CL-BIC) to select the number of communities, and we show it is robust against possible misspecifications in the underlying stochastic blockmodel assumptions. We derive the requisite methodology and illustrate the approach using both simulated and real data. Supplementary materials containing the relevant computer code are available online.Comment: 26 pages, 3 figure

Uncertainty management in multiobjective hydro-thermal self-scheduling under emission considerations

In this paper, a stochastic multiobjective framework is proposed for a day-ahead short-term Hydro Thermal Self-Scheduling (HTSS) problem for joint energy and reserve markets. An efficient linear formulations are introduced in this paper to deal with the nonlinearity of original problem due to the dynamic ramp rate limits, prohibited operating zones, operating services of thermal plants, multi-head power discharge characteristics of hydro generating units and spillage of reservoirs. Besides, system uncertainties including the generating units\u27 contingencies and price uncertainty are explicitly considered in the stochastic market clearing scheme. For the stochastic modeling of probable multiobjective optimization scenarios, a lattice Monte Carlo simulation has been adopted to have a better coverage of the system uncertainty spectrum. Consequently, the resulting multiobjective optimization scenarios should concurrently optimize competing objective functions including GENeration COmpany\u27s (GENCO\u27s) profit maximization and thermal units\u27 emission minimization. Accordingly, the ε-constraint method is used to solve the multiobjective optimization problem and generate the Pareto set. Then, a fuzzy satisfying method is employed to choose the most preferred solution among all Pareto optimal solutions. The performance of the presented method is verified in different case studies. The results obtained from ε-constraint method is compared with those reported by weighted sum method, evolutionary programming-based interactive Fuzzy satisfying method, differential evolution, quantum-behaved particle swarm optimization and hybrid multi-objective cultural algorithm, verifying the superiority of the proposed approach

A Review on Energy Consumption Optimization Techniques in IoT Based Smart Building Environments

In recent years, due to the unnecessary wastage of electrical energy in residential buildings, the requirement of energy optimization and user comfort has gained vital importance. In the literature, various techniques have been proposed addressing the energy optimization problem. The goal of each technique was to maintain a balance between user comfort and energy requirements such that the user can achieve the desired comfort level with the minimum amount of energy consumption. Researchers have addressed the issue with the help of different optimization algorithms and variations in the parameters to reduce energy consumption. To the best of our knowledge, this problem is not solved yet due to its challenging nature. The gap in the literature is due to the advancements in the technology and drawbacks of the optimization algorithms and the introduction of different new optimization algorithms. Further, many newly proposed optimization algorithms which have produced better accuracy on the benchmark instances but have not been applied yet for the optimization of energy consumption in smart homes. In this paper, we have carried out a detailed literature review of the techniques used for the optimization of energy consumption and scheduling in smart homes. The detailed discussion has been carried out on different factors contributing towards thermal comfort, visual comfort, and air quality comfort. We have also reviewed the fog and edge computing techniques used in smart homes