The Stochastic Multipath Traveling Salesman Problem with Dependent Random Travel Costs

The objective of the stochastic multipath traveling salesman problem is to determine the expected minimum-cost Hamiltonian tour in a network characterized by the presence of different paths between each pair of nodes, given that a random travel cost with an unknown probability distribution is associated with each of these paths. Previous works have proved that this problem can be deterministically approximated when the path travel costs are independent and identically distributed. Such an approximation has been demonstrated to be of acceptable quality in terms of the estimation of an optimal solution compared with consolidated approaches such as stochastic programming with recourse, completely overcoming the computational burden of solving enormous programs exacerbated by the number of scenarios considered. Nevertheless, the hypothesis regarding the independence among the path travel costs does not hold when considering real settings. It is well known, in fact, that traffic congestion influences travel costs and creates dependence among them. In this paper, we demonstrate that the independence assumption can be relaxed and a deterministic approximation of the stochastic multipath traveling salesman problem can be derived by assuming just asymptotically independent travel costs. We also demonstrate that this deterministic approximation has strong operational implications because it allows the consideration of realistic traffic models. Computational tests on extensive sets of random and realistic instances indicate the excellent efficiency and accuracy of the deterministic approximation.

Stochastic optimal scheduling of hydropower compensation for wind and photovoltaic power output considering multiple uncertainties

<p>Multiple uncertainties, including from the uncertainty of a single power (wind power or photovoltaic power) output forecasting to the uncertainty of the combined power output of wind and photovoltaic forecasting to the power shortage after hydropower compensation for wind and photovoltaic power output, exist in the wind-photovoltaic-hydropower system. Furthermore, as the forecast is updated, the above uncertainty will evolve accordingly. Revealing the evolution of multiple uncertainties is of great significance for the hydropower compensation for the combined power output of wind and photovoltaic. We use a generalized martingale model of forecast evolution to describe the uncertainty of a single power output. We then superimpose the single power output to obtain the combined power output of wind and photovoltaic. we establish a stochastic programming with recourse model for optimal scheduling of the hydropower compensation for wind and photovoltaic power output. The results indicate that the uncertainty of the combined power output of wind and photovoltaic forecasting is less than that of wind power output forecasting, and greater than that of photovoltaic power output forecasting. After hydropower compensates for combined power output of wind and photovoltaic, compared with the uncertainty of combined wind and photovoltaic power output forecasting, the uncertainty of power shortage is greatly reduced by 90%, which has significant benefits. And with the dynamic update of the forecast, the uncertainty of the single power output forecast, the uncertainty of the combined power output forecast, and the uncertainty of the power shortage will decrease accordingly.</p>