Constrain Path Optimization on Time-Dependent Road Networks

Time-Dependent Constrained Path Optimization (TD-CPO) takes the following input: (i) time-dependent (TD) road network, (ii) source ($s$), (iii) destination ($d$), (iv) departure time ($t$) and, (v) budget ($\mathcal{B}$). In TD graph, each edge is characterized by a time-dependent arrival time and a score function. TD-CPO aims to determine a loopless path $s$--$d$ departing from $s$ at time $t$ and arriving at $d$ on or before $t+\mathcal{B}$ while maximizing the score. TD-CPO has applications in urban navigation. TD-CPO is a variant of the Arc Orienteering Problem (AOP) known to be NP-hard in nature. The key computational challenge of TD-CPO is that we need to find the "longest path" in terms of score within the given budget constraint in a TD graph. Current works prune down the search space very aggressively. Thus, despite having low execution time, these algorithms often produce low-quality solutions. In contrast, our proposed approach $\mathcal{SCOPE}$ efficiently solves TD-CPO by exploiting road networks' spatial and temporal properties. The inherent computational structure of $\mathcal{SCOPE}$ enables trivial parallelization for improved performance. Our experiments indicate that $\mathcal{SCOPE}$ produces superior quality solutions (nearly $2x$) compared to the state-of-the-art algorithm while having comparable running times. Furthermore, $\mathcal{SCOPE}$ exhibits almost linear speedup as the number of CPUs (cores) increases (up to 24 CPUs).