Deterministic policies based on maximum regrets in MDPs with imprecise rewards

Markov Decision Process Models (MDPs) are a powerful tool for planning tasks and sequential decision-making issues. In this work we deal with MDPs with imprecise rewards, often used when dealing with situations where the data is uncertain. In this context, we provide algorithms for finding the policy that minimizes the maximum regret. To the best of our knowledge, all the regret-based methods proposed in the literature focus on providing an optimal stochastic policy. We introduce for the first time a method to calculate an optimal deterministic policy using optimization approaches. Deterministic policies are easily interpretable for users because for a given state they provide a unique choice. To better motivate the use of an exact procedure for finding a deterministic policy, we show some (theoretical and experimental) cases where the intuitive idea of using a deterministic policy obtained after “determinizing” the optimal stochastic policy leads to a policy far from the exact deterministic policy.

On Optimistic and Pessimistic Bilevel Optimization Models for Demand Response Management

This paper investigates bilevel optimization models for demand response management, and highlights the often overlooked consequences of a common modeling assumption in the field. That is, the overwhelming majority of existing research deals with the so-called optimistic variant of the problem where, in case of multiple optimal consumption schedules for a consumer (follower), the consumer chooses an optimal schedule that is the most favorable for the electricity retailer (leader). However, this assumption is usually illegitimate in practice; as a result, consumers may easily deviate from their expected behavior during realization, and the retailer suffers significant losses. One way out is to solve the pessimistic variant instead, where the retailer prepares for the least favorable optimal responses from the consumers. The main contribution of the paper is an exact procedure for solving the pessimistic variant of the problem. First, key properties of optimal solutions are formally proven and efficiently solvable special cases are identified. Then, a detailed investigation of the optimistic and pessimistic variants of the problem is presented. It is demonstrated that the set of optimal consumption schedules typically contains various responses that are equal for the follower, but bring radically different profits for the leader. The main procedure for solving the pessimistic variant reduces the problem to solving the optimistic variant with slightly perturbed problem data. A numerical case study shows that the optimistic solution may perform poorly in practice, while the pessimistic solution gives very close to the highest profit that can be achieved theoretically. To the best of the authors’ knowledge, this paper is the first to propose an exact solution approach for the pessimistic variant of the problem.

THE STUDY USING ENSEMBLE LEARNING FOR RECOMMENDING BETTER FUTURE INVESTMENTS

Generally, House estimation record addresses the summarized esteem changes of private housing. While at a single-family house cost desire, it needs more exact procedure reliant on the spot, house type, size, structure year, close by improvements, and some various parts which could impact house demand and deftly. With limited dataset and data incorporates, a sensible and composite data pre-taking care of, creative component planning methodology is assessed in this paper. People are careful when they are endeavouring to buy another house with their money related plans and market strategies. The objective of the paper is to measure the sensible house costs for non-house holders reliant on their financial courses of action and their desires. By analysing the earlier item, entry ranges and besides alerts enhancements, guessed costs will be evaluated. The paper includes expectations utilizing diverse Regression procedures like Ridge, LASSO, Random Forest, SVM (support-vector machine), KNN (k-nearest neighbours), Ada Boost Regression, Stacking (decision tree, lasso and random forest), Decision Tree. House estimation figure on an instructive file has been done by using all the recently referenced systems to find the best among them. The reason of this paper is to help the vendor with assessing the selling cost of a house perfectly and to assist people with foreseeing the time slap to store up a house. A part of the related segments that influence the cost were furthermore taken into examinations, for instance, states of being, thought, area and territory, etc.

Finding globally optimal macrostructure in multiple relation, mixed-mode social networks

From the outset, computational sociologists have stressed leveraging multiple relations when blockmodeling social networks. Despite this emphasis, the majority of published research over the past 40 years has focused on solving blockmodels for a single relation. When multiple relations exist, a reductionist approach is often employed, where the relations are stacked or aggregated into a single matrix, allowing the researcher to apply single relation, often heuristic, blockmodeling techniques. Accordingly, in this article, we develop an exact procedure for the exploratory blockmodeling of multiple relation, mixed-mode networks. In particular, given (a) [Formula: see text] actors, (b) [Formula: see text] events, (c) an [Formula: see text] binary one-mode network depicting the ties between actors, and (d) an [Formula: see text] binary two-mode network representing the ties between actors and events, we use integer programming to find globally optimal [Formula: see text] image matrices and partitions, where [Formula: see text] and [Formula: see text] represent the number of actor and event positions, respectively. Given the problem’s computational complexity, we also develop an algorithm to generate a minimal set of non-isomorphic image matrices, as well as a complementary, easily accessible heuristic using the network analysis software Pajek. We illustrate these concepts using a simple, hypothetical example, and we apply our techniques to a terrorist network.

The use of Weber’s focal-directorial plane curves as approximation of top view contour curves at architectural buildings objects

One of the major aims when researching some problems in architectural design of buildings is to fully understand and adequately apply the underlying scientific foundations that architects use in their projects. In this paper we analyze the application possibilities of the Weber?s focal-directorial curves in the approximation of ground-base contour line of architectural objects i.e. buildings. Thus, a Weber?s curve with m foci and n directrices was defined. Furthermore, particular qualifiers were introduced in order to estimate the level of adequacy of the conducted approximation. The importance of the research can be sought in the fact that the exact procedure has been created with its applicability in architectural-urban design of contemporary forms as well as in the domain of the historical heritage and conservation in the sense of the creating proper geometrical models for further computer aided use.

Categorisation of Telecom Circles in India

Ever since mobile has revolutionized the telecom scenario in India, experts often ask a pertinent question: is the old assignment of twenty-two telecom circles into four categories valid even now? It has become important in the light of variable rates of revenue sharing in different circles as per the policy of the Government of India (GoI). The extant literature is silent on the exact procedure followed by the GoI in classifying the circles, apart from mentioning the rationale of decreasing attractiveness. So we revisit the categorization process afresh from two perspectives: gross domestic product (GDP) and diffusion of mobile telephony. The GDP based clustering of the circles is quite straightforward. However, for the mobile diffusion based method, we take help of a dynamic model based on revenue potential. Interestingly, both the methods generate results, which are almost similar to the existing classification done by the GoI way back in 1999. Thus, our exercise provides a big relief to the policy-makers, thereby pre-empting the demands for immediate relook at the categorization.