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Solving an optimization task in any domain is a very challenging problem, especially when dealing with nonlinear problems and non-convex functions. Many meta-heuristic algorithms are very efficient when solving nonlinear functions. A…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $\delta$, the goal is to find a value that is $\delta$-approximately minimum…
The latency location routing problem integrates the facility location problem and the multi-depot cumulative capacitated vehicle routing problem. This problem involves making simultaneous decisions about depot locations and vehicle routes…
Intelligent autonomous path planning is essential for enhancing the exploration efficiency of mobile robots operating in uneven terrains like planetary surfaces and off-road environments.In this paper, we propose the NNPP model for…
We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures,…
Mobility-on-demand (MoD) ridesharing is a promising way to improve the occupancy rate of personal vehicles and reduce traffic congestion and emissions. Maximizing the number of passengers served and maximizing a profit target are major…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
We investigate the problem of coordinating multiple automated vehicles (AVs) in confined areas. This problem can be formulated as an optimal control problem (OCP) where the motion of the AVs is optimized such that collisions are avoided in…
We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its…
This paper studies line planning for urban bus networks that face multiple resource limits such as budget, labor, and emission caps while using heterogeneous fleets. The objective is to maximize total reward from serving passengers by…
This paper proposes a hybrid genetic algorithm for solving the Multiple Traveling Salesman Problem (mTSP) to minimize the length of the longest tour. The genetic algorithm utilizes a TSP sequence as the representation of each individual,…
We propose a new model for formalizing reward collection problems on graphs with dynamically generated rewards which may appear and disappear based on a stochastic model. The *robot routing problem* is modeled as a graph whose nodes are…
Given an approximation algorithm $A$, we want to find the input with the worst approximation ratio, i.e., the input for which $A$'s output's objective value is the worst possible compared to the optimal solution's objective value. Such hard…
Designing high-performing metaheuristics for NP-hard combinatorial optimization problems, such as the Vehicle Routing Problem (VRP), remains a significant challenge, often requiring extensive domain expertise and manual tuning. Recent…
The Travelling Salesman Problem (TSP) is one of the most popular Combinatorial Optimization Problem. It is well solicited for the large variety of applications that it can solve, but also for its difficulty to find optimal solutions. One of…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…