Methods to reduce dimensionality and identify candidate solutions in multi-objective signal timing problems

Adjusting traffic signal timings is a practical way for agencies to manage urban traffic without the need for significant infrastructure investments. Signal timings are generally selected to minimize the total control delay vehicles experience at an intersection, particularly when the intersection is isolated or undersaturated. However, in practice, there are many other potential objectives that might be considered in signal timing design, including: total passenger delay, pedestrian delays, delay inequity among competing movements, total number of stopping maneuvers, among others. These objectives do not tend to share the same relationships with signal timing plans and some of these objectives may be in direct conflict. The research proposes the use of a new multi-objective optimization (MOO) visualization technique—the mosaic plot—to easily quantify and identify significant tradeoffs between competing objectives using the set of Pareto optimal solutions that are normally provided by MOO algorithms. Using this tool, methods are also proposed to identify and remove potentially redundant or unnecessary objectives that do not have any significant tradeoffs with others in an effort to reduce problem dimensionality. Since MOO procedures will still be needed if more than one objective remains and MOO algorithms generally provide a set of candidate solutions instead of a single final solution, two methods are proposed to rank the set of Pareto optimal solutions based on how well they balance between the competing objectives to provide a final recommendation. These methods rely on converting the objectives to dimensionless values based on the optimal value for each specific objectives, which allows for direct comparison between and weighting of each. The proposed methods are demonstrated using a simple numerical example of an undersaturated intersection where all objectives can be analytically obtained. However, they can be readily applied to other signal timing problems where objectives can be obtained using simulation outputs to help identify the signal timing plan that provides the most reasonable tradeoff between competing objectives.