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Applications such as megaregional planning require efficient methods for solving traffic assignment problems (TAPs) on large-scale networks. We propose a decomposition heuristic that generates approximate TAP solutions by partitioning the…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
We present a new heuristic point-to-point routing algorithm based on contraction hierarchies (CH). Given an epsilon >= 0, we can prove that the length of the path computed by our algorithm is at most (1+epsilon) times the length of the…
In this paper, we propose an effective search procedure that interleaves two steps: subproblem generation and subproblem solution. We mainly focus on the first part. It consists of a variable domain value ranking based on reduced costs.…
The problem of mobile sequential recommendation is presented to suggest a route connecting some pick-up points for a taxi driver so that he/she is more likely to get passengers with less travel cost. Essentially, a key challenge of this…
Given a weighted graph $G$, a minimum weight $\alpha$-spanner is a least-weight subgraph $H\subseteq G$ that preserves minimum distances between all node pairs up to a factor of $\alpha$. There are many results on heuristics and…
On-time performance is a critical challenge in the airline industry, leading to large operational and customer dissatisfaction costs. The tail assignment problem builds the sequences of flights or routes followed by individual airplanes.…
In [Q. Liao et al., Commun. Math. Sci., 20(2022)], a linear-time Sinkhorn algorithm is developed based on dynamic programming, which significantly reduces the computational complexity involved in solving optimal transport problems. However,…
The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in…
In the Minimum Common String Partition Problem (MCSP), we are given two strings on input, and we want to partition both into the same collection of substrings, minimizing the number of the substrings in the partition. This combinatorial…
This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…
Establishing a low-dimensional representation of the data leads to efficient data learning strategies. In many cases, the reduced dimension needs to be explicitly stated and estimated from the data. We explore the estimation of dimension in…
A landmark based heuristic is investigated for reducing query phase run-time of the probabilistic roadmap (\PRM) motion planning method. The heuristic is generated by storing minimum spanning trees from a small number of vertices within the…
In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…
In this paper, we propose a novel mixed integer programming model to formulate integrated operating room planning and scheduling problems, where several mandatory and elective surgeries are to be assigned and scheduled in operating rooms on…
This paper focuses on the generalized grouping problem in the context of cellular manufacturing systems (CMS), where parts may have more than one process route. A process route lists the machines corresponding to each part of the operation.…
Backtracking has been widely used for solving problems in artificial intelligence (AI), including constraint satisfaction problems and combinatorial optimization problems. Good branching heuristics can efficiently improve the performance of…
We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set, potentially including additional nodes. This is a…
The column-and-constraint generation (CCG) method was introduced by \citet{Zeng2013} for solving two-stage adaptive optimization. We found that the CCG method is quite scalable, but sometimes, and in some applications often, produces…
In order for an e-commerce platform to maximize its revenue, it must recommend customers items they are most likely to purchase. However, the company often has business constraints on these items, such as the number of each item in stock.…