Time scheduling of transit systems with transfer considerations using genetic algorithms.

Scheduling of a bus transit system must be formulated as an optimization problem, if the level of service to passengers is to be maximized within the available resources. In this paper, we present a formulation of a transit system scheduling problem with the objective of minimizing the overall waiting time of transferring and nontransferring passengers while satisfying a number of resource- and service-related constraints. It is observed that the number of variables and constraints for even a simple transit system (a single bus station with three routes) is too large to tackle using classical mixed-integer optimization techniques. The paper shows that genetic algorithms (GAs) are ideal for these problems, mainly because they (i) naturally handle binary variables, thereby taking care of transfer decision variables, which constitute the majority of the decision variables in the transit scheduling problem; and (ii) allow procedure-based declarations, thereby allowing complex algorithmic approaches (involving if then-else conditions) to be handled easily. The paper also shows how easily the same GA procedure with minimal modifications can handle a number of other more pragmatic extensions to the simple transit scheduling problem: buses with limited capacity, buses that do not arrive exactly as per scheduled times, and a multiple-station transit system having common routes among bus stations. Simulation results show the success of GAs in all these problems and suggest the application of GAs in more complex scheduling problems.

Effects of cardiac sympathetic innervation on coronary blood flow.

BACKGROUND: The role of cardiac sympathetic nerves in regulating coronary blood flow is controversial. We sought to determine the degree to which cardiac efferent sympathetic signals modulate coronary blood flow. The heterogeneous sympathetic reinnervation in transplanted hearts provides a model for studying the vasomotor responses to adrenergic stimulation in reinnervated and denervated coronary territories of the same heart. METHODS: We studied 14 cardiac-transplant recipients who had normal coronary arteries and no evidence of rejection and 8 normal subjects. We used positron-emission tomography with [(11)C]hydroxyephedrine, an analogue of norepinephrine, to delineate sympathetic innervation. Using [(13)N]ammonia, we measured myocardial blood flow at rest, during adenosine-induced hyperemia, and in response to sympathetic stimulation induced by cold pressor testing. RESULTS: In the transplant recipients, the uptake of [(11)C]hydroxyephedrine was greater in the territory served by the left anterior descending artery (0.15+/-0.01) than in those served by the right coronary artery (0.07+/-0.01, P<0.001) or the circumflex artery (0.09+/-0.01, P<0.001). The basal flow was similar in all three regions, as was the percent increase in flow during hyperemia. However, the increase in flow in response to cold pressor testing was higher in the territory of the left anterior descending artery (46+/-10 percent) than in those of the right coronary artery (16+/-5 percent, P=0.01) or the circumflex artery (23+/-6 percent, P=0.06), although the changes in hemodynamics and levels of circulating catecholamines were similar. No such regional differences were observed in the normal subjects. CONCLUSIONS: Increases in coronary blood flow in response to sympathetic stimulation correlated with the regional norepinephrine content in the cardiac sympathetic-nerve terminals. These findings suggest that cardiac adrenergic signals play an important part in regulating myocardial blood flow.