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We develop a time series model to forecast weekly peak power demand for three main states of Australia for a yearly timescale, and show the crucial role of environmental factors in improving the forecasts. More precisely, we construct a seasonal autoregressive integrated moving average (SARIMA) model and reinforce it by employing the exogenous environmental variables including, maximum temperature, minimum temperature, and solar exposure. The estimated hybrid SARIMA-regression model exhibits an excellent mean absolute percentage error (MAPE) of 3.41 % . Moreover, our analysis demonstrates the importance of the environmental factors by showing a remarkable improvement of 46.3 % in MAPE for the hybrid model over the crude SARIMA model which merely includes the power demand variables. In order to illustrate the efficacy of our model, we compare our outcome with the state-of-the-art machine learning methods in forecasting. The results reveal that our model outperforms the latter approach. [ABSTRACT FROM AUTHOR]

In this paper, we present some algebraic properties of a particular class of probability transition matrices, namely, Hamiltonian transition matrices. Each matrix $$P$$ in this class corresponds to a Hamiltonian cycle in a given graph $$G$$ on $$n$$ nodes and to an irreducible, periodic, Markov chain. We show that a number of important matrices traditionally associated with Markov chains, namely, the stationary, fundamental, deviation and the hitting time matrix all have elegant expansions in the first $$n-1$$ powers of $$P$$ , whose coefficients can be explicitly derived. We also consider the resolvent-like matrices associated with any given Hamiltonian cycle and its reverse cycle and prove an identity about the product of these matrices. As an illustration of these analytical results, we exploit them to develop a new heuristic algorithm to determine a non-Hamiltonicity of a given graph. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new hybrid algorithm for the Hamiltonian cycle problem by synthesizing the Cross Entropy method and Markov decision processes. In particular, this new algorithm assigns a random length to each arc and alters the Hamiltonian cycle problem to the travelling salesman problem. Thus, there is now a probability corresponding to each arc that denotes the probability of the event 'this arc is located on the shortest tour.' Those probabilities are then updated as in cross entropy method and used to set a suitable linear programming model. If the solution of the latter yields any tour, the graph is Hamiltonian. Numerical results reveal that when the size of graph is small, say less than 50 nodes, there is a high chance the algorithm will be terminated in its cross entropy component by simply generating a Hamiltonian cycle, randomly. However, for larger graphs, in most of the tests the algorithm terminated in its optimization component (by solving the proposed linear program). [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptation of the Cross Entropy (CE) method called Projection-Adapted CE (PACE) to solve a transmission expansion problem that arises in management of national and provincial electricity grids. The aim of the problem is to find an expansion policy that is both economical and operational from the technical perspective. Often, the transmission network expansion problem is mathematically formulated as a mixed integer nonlinear program that is very challenging algorithmically. The challenge originates from the fact that a global optimum should be found despite the presence, of possibly a huge number, of local optima. The PACE method shows promise in solving global optimization problems regardless of continuity or other assumptions. In our approach, we sample the integer variables using the CE mechanism, and solve LPs to obtain matching continuous variables. Numerical results, on selected test systems, demonstrate the potential of this approach. [ABSTRACT FROM AUTHOR]