Thermal station modelling and optimal control based on deep learning

To solve the mismatch between heating quantity and demand of thermal stations, an optimized control method based on depth deterministic strategy gradient was proposed in this paper. In this paper, long short-time memory deep learning algorithm is used to model the thermal power station, and then the depth deterministic strategy gradient control algorithm is used to solve the water supply flow sequence of the primary side of the thermal power station in combination with the operation mechanism of the central heating system. In this paper, a large number of historical working condition data of a thermal station are used to carry out simulation experiment, and the results show that the method is effective, which can realize the on-demand heating of the thermal station a certain extent and improve the utilization rate of heat.

Risk strategy analysis for an online rental problem of durable equipment with a transaction cost

This study introduces the second-hand market into the famous ski-rental model, presents an online rental problem of durable equipment with a transaction cost, and designs an optimal deterministic competitive strategy. The traditional competitive analysis is based on the worst-case scenario; hence, its results are too conservative. Even though investors want to manage and control their risks in reality, in some cases, they are willing to undertake higher risk to obtain greater benefits. Considering this situation, this study designs a risk strategy combining the decision makers’ risk tolerance with certain and probabilistic forecasts. Numerical analysis shows that the proposed risk strategy can improve the competitive ratio. This study introduces the idea of risk compensation into traditional competitive analysis and designs strategies for online rental of durable equipment based on forecast. The decision maker selects a strategy according to risk tolerance and forecast. If the forecast is correct, then a reward is obtained; otherwise, the risk is guaranteed to be within the decision maker’s risk tolerance. The optimal restricted ratio, that is, the competitive ratio of a risk strategy, is less than the optimal competitive ratio of a deterministic strategy. Therefore, the performance of the proposed risk strategy is better than a deterministic strategy. At the same time, the risk strategy based on the probabilistic forecast represents an extension of the strategy based on a certain forecast. In other words, the risk strategy based on a certain forecast is a special case of the risk strategy based on the probabilistic forecast.

Microgrid Planning Considering the Supply Adequacy of Critical Loads under the Uncertain Formation of Sub-Microgrids

A microgrid can be partitioned into several autonomous sub-microgrids in case of multiple faults in natural disasters. How to guarantee the supply adequacy of critical loads in sub-microgrids is a problem that should be considered at the planning stage. This paper proposes a microgrid planning model considering the supply adequacy of critical loads under the uncertain formation of sub-microgrids. The proposed model minimizes the total cost during the project life, which includes the construction cost and operation cost for the candidate distributed energy resources (DERs). The supply adequacy of critical loads in sub-microgrids is taken into account in the model. As we only know the critical load areas, the locations of switches which divide the microgrid into sub-microgrids are unknown at the planning stage. Considering this uncertainty, the microgrid planning issue is finally formulated as a robust model against the worst formation of sub-microgrids. The developed model is tested on two systems: IEEE 33-bus and 123-bus distribution systems. Simulation indicates (1) the proposed method is more robust than deterministic strategy as critical load loss is intolerable in sub-microgrids; (2) the investment cost is the same with that of the deterministic case when the number of sub-microgrids is within two.

A Force-Directed Algorithm for Drawing Directed Graphs Symmetrically

Symmetry is one of the most important aesthetic criteria on graph drawing. It is quite necessary to measure the extent to which the drawings can be considered symmetric. For this purpose, a symmetric metric based on vertex coordinate calculation is proposed in this paper. It is proven theoretically and experimentally that the proposed metric is robust to contraction, expansion, and rotation of drawings. This robustness conforms to human perception of symmetry. Star-subgraphs and cycles are two common structures in digraphs. Both of them have inherent symmetry which should be displayed in drawings. For this purpose, a force-directed algorithm named FDS is proposed which can draw star-subgraphs and cycles as symmetrically as possible. FDS algorithm draws cycles as circles whose positions are fixed to provide a scaffolding for overall layout, renders non-leaf vertices by a standard force-directed layout, and places leaf vertices on concentric circles via a deterministic strategy. A series of experiments are carried out to test FDS algorithm. The results show that FDS algorithm draws digraphs more symmetrically than the existing state-of-the-art algorithms and performs efficiency comparable to O(nlog⁡n) YFHu algorithm.

Deep Learning for Multi-Facility Location Mechanism Design

Moulin [1980] characterizes the single-facility, deterministic strategy-proof mechanisms for social choice with single-peaked preferences as the set of generalized median rules. In contrast, we have only a limited understanding of multi-facility strategy-proof mechanisms, and recent work has shown negative worst case results for social cost. Our goal is to design strategy-proof, multi-facility mechanisms that minimize expected social cost. We first give a PAC learnability result for the class of multi-facility generalized median rules, and utilize neural networks to learn mechanisms from this class. Even in the absence of characterization results, we develop a computational procedure for learning almost strategy-proof mechanisms that are as good as or better than benchmarks from the literature, such as the best percentile and dictatorial rules.

MANY-VALUED LOGIC OF INFORMAL PROVABILITY: A NON-DETERMINISTIC STRATEGY

Mathematicians prove theorems in a semi-formal setting, providing what we’ll call informal proofs. There are various philosophical reasons not to reduce informal provability to formal provability within some appropriate axiomatic theory (Leitgeb, 2009; Marfori, 2010; Tanswell, 2015), but the main worry is that we seem committed to all instances of the so-called reflection schema: B(φ) → φ (where B stands for the informal provability predicate). Yet, adding all its instances to any theory for which Löb’s theorem for B holds leads to inconsistency.Currently existing approaches (Shapiro, 1985; Horsten, 1996, 1998) to formalizing the properties of informal provability avoid contradiction at a rather high price. They either drop one of the Hilbert-Bernays conditions for the provability predicate, or use a provability operator that cannot consistently be treated as a predicate.Inspired by (Kripke, 1975), we investigate the strategy which changes the underlying logic and treats informal provability as a partial notion. We use non-deterministic matrices to develop a three-valued logic of informal provability, which avoids some of the above mentioned problems.