Related papers: Long-term planning versus short-term planning in t…
We study the mechanism design problem of facility location on a metric space in the learning-augmented framework, where mechanisms have access to imperfect predictions of the optimal facility locations. Our objective is to design…
We consider a single-facility location problem, where agents are positioned on the real line and are partitioned into multiple disjoint districts. The goal is to choose a location (where a public facility is to be built) so as to minimize…
We study a non-cooperative two-sided facility location game in which facilities and clients behave strategically. This is in contrast to many other facility location games in which clients simply visit their closest facility. Facility…
In this note, we consider the capacitated facility location problem when the transportation costs of the instance satisfy the Monge property. We show that a straightforward dynamic program finds the optimal solution when the demands are…
This paper considers robot motion planning under temporal logic constraints in probabilistic maps obtained by semantic simultaneous localization and mapping (SLAM). The uncertainty in a map distribution presents a great challenge for…
This paper addresses the planning and control problem for nonlinear systems under Signal Temporal Logic (STL) specifications. We first decompose an STL task into finite local tasks. A sampling-based method generates sequences of local…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of…
The uncapacitated facility location has always been an important problem due to its connection to operational research and infrastructure planning. Byrka obtained an algorithm that is parametrized by $\gamma$ and proved that it is optimal…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
We consider assortment optimization over a continuous spectrum of products represented by the unit interval, where the seller's problem consists of determining the optimal subset of products to offer to potential customers. To describe the…
We consider $k$-Facility Location games, where $n$ strategic agents report their locations on the real line, and a mechanism maps them to $k\ge 2$ facilities. Each agent seeks to minimize her distance to the nearest facility. We are…
We study a joint facility location and cost planning problem in a competitive market under random utility maximization (RUM) models. The objective is to locate new facilities and make decisions on the costs (or budgets) to spend on the new…
As a starting point of our research, we show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
Capability planning problems are pervasive throughout many areas of human interest with prominent examples found in defense and security. Planning provides a unique context for optimization that has not been explored in great detail and…
We propose novel optimal designs for longitudinal data for the common situation where the resources for longitudinal data collection are limited, by determining the optimal locations in time where measurements should be taken. As for all…
Consider the Euclidean traveling salesman problem with $n$ random points on the plane. Suppose that one of the points is shifted to a new random location. This gives us a new optimal path. Consider such shifts for each of the $n$ points. Do…
In the strategic facility location problem, a set of agents report their locations in a metric space and the goal is to use these reports to open a new facility, minimizing an aggregate distance measure from the agents to the facility.…
We consider a strategic variant of the facility location problem. We would like to locate a facility on a closed interval. There are n agents located on that interval, divided into two types: type 1 agents, who wish for the facility to be…