No abstract

No abstract

No abstract

In recent years, well-designed bus rapid transit (BRT) systems have become a real alternative to more expensive rail-based public transportation systems around the world. However, once the BRT system is operational, its success often depends on the routes offered to passengers. Thus, the bus rapid transit route design problem (BRTRDP) is the problem of finding a set of routes and frequencies that minimizes the operational and passenger costs (travel time) while simultaneously satisfying the system’s technical constraints, such as meeting the demands for trips, bus frequencies, and lane capacities. To address this problem, we propose a mathematical formulation of the BRTRDP as a mixed-integer program (MIP) with an underlying network structure. However, because of the vast number of routes, solving the MIP via branch and bound is out of reach for most practical instances. Hence, we propose a decomposition strategy that, given a certain set of routes, decouples the route selection decisions from the BRT system performance evaluation. The latter evaluation is done by solving a linear optimization problem using a column generation scheme. We embedded this decomposition strategy in a hybrid genetic algorithm (HGA) and tested it in 14 instances ranging from 5 to 40 stations with different BRT system topologies. The results show that in 8 of 14 problems, the HGA was able to obtain a solution that is provably optimal within 0.20%. Additionally, in 4 of 14 instances, HGA obtained the optimal solution.

No abstract

We consider the problem of detecting a collection of critical node structures of a graph whose deletion results in the maximum deterioration of the graph's connectivity. The proposed approach is aimed to generalize other existing models whose scope is restricted to removing individual and unrelated nodes. We consider two common metrics to quantify the connectivity of the residual graph: the total number of connected node pairs and the size of the largest connected component. We first discuss the computational complexity of the problem and then introduce a general mixed-integer linear formulation, which depending on the kind of node structures, may have an exponentially large number of variables and constraints. To solve this potentially large model, we develop a branch-price-and-cut framework, along with some valid inequalities and preprocessing algorithms to strengthen the formulation and reduce the overall execution time. We use the proposed approach to solve the problem for the cases, where the node structures form cliques or stars and provide further directions on how to extend the framework for detecting other kinds of critical structures as well. Finally, we test the quality of our approach by solving a collection of real-life and randomly generated instances with various configurations, analyze the benefits of our model, and propose further enhancements. KEYWORDS branch-price-and-cut, combinatorial optimization, critical node problem, graph partitioning, mixed-integer programming, network interdiction Problem 2. Critical star detection problem (CSP). INSTANCE: A simple non-empty graph G = (V, E) and two nonnegative integers r and b. QUESTION: Is there a set  of at most b stars so that a connectivity measure over G[V ⧵ V()] is no greater than r. Theorem 2. CSP for both the CNP and LC measures is strongly NP-complete.The proof of this theorem, which can also be found in the Appendix A, uses a reduction from DOMINATING SET to CSP. Complexity of detecting critical connected subgraphsWe now prove a more general complexity result, in which the elements of set  induce connected subgraphs of G. We show that detecting critical disjoint connected subgraphs is NP-hard as well.Problem 3. Critical connected subgraph detection problem (CCSP). INSTANCE:A simple non-empty graph G = (V, E), a set of connected subgraphs  , and two nonnegative integers r and b.

Risk-informed asset management is key to maintaining optimal performance and efficiency of urban sewer systems. Although sewer system failures are spatiotemporal in nature, previous studies analyzed failure risk from a unidimensional aspect (either spatial or temporal), not accounting for bidimensional spatiotemporal complexities. This is owing to the insufficiency of good-quality data, which ultimately leads to under-/overestimation of failure risk. Here, we propose a generalized methodology/framework to facilitate a robust spatiotemporal analysis of urban sewer system failure risk, overcoming the intrinsic challenges of data imperfections-e.g., missing data, outliers, and imbalanced information. The framework includes a two-stage data-driven modeling technique that efficiently models the highly rightskewed sewer system failure data to predict the failure risk, leveraging a bidimensional spacetime approach. We implemented our analysis for Bogotá, the capital city of Colombia. We train, test, and validate a battery of machine learning algorithms-logistic regression, decision trees, random forests, and XGBoost-and select the best model in terms of goodnessof-fit and predictive accuracy. Finally, we illustrate the applicability of the framework in planning/scheduling sewer system maintenance operations using state-of-the-art optimization techniques. Our proposed framework can help stakeholders to analyze the failure-risk models' performance under different discrimination thresholds, and provide managerial insights on the model's adequate spatial resolution and appropriateness of decentralized management for sewer system maintenance.

Jose L. Walteros and Austin Buchanan