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Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…
Recent methods in ergodic coverage planning have shown promise as tools that can adapt to a wide range of geometric coverage problems with general constraints, but are highly sensitive to the numerical scaling of the problem space. The…
The line coverage problem involves finding efficient routes for the coverage of linear features by one or more resource-constrained robots. Linear features model environments like road networks, power lines, and oil and gas pipelines. Two…
We consider the classic facility location problem in fully dynamic data streams, where elements can be both inserted and deleted. In this problem, one is interested in maintaining a stable and high quality solution throughout the data…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…
We study the maximum capture problem in facility location under random utility models, i.e., the problem of seeking to locate new facilities in a competitive market such that the captured user demand is maximized, assuming that each…
Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from the centers to given input points. Examples are $k$-Means, Geometric…
We study a robust version of the maximum capture facility location problem in a competitive market, assuming that each customer chooses among all available facilities according to a random utility maximization (RUM) model. We employ the…
Mixed-integer programming (MIP) extends linear programming by incorporating both continuous and integer decision variables, making it widely used in production planning, logistics scheduling, and resource allocation. However, MIP remains…
Distributing spatially located heterogeneous workloads is an important problem in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of non-negative integers) into rectangles,…
In this paper the capacitated hub location problem is formulated by a minimax regret model, which takes into account uncertain setup cost and demand. We focus on hub location with multiple allocations as a strategic problem requiring one…
The facility location problem (FLP) is a classical combinatorial optimization challenge aimed at strategically laying out facilities to maximize their accessibility. In this paper, we propose a reinforcement learning method tailored to…
Configuration integer programs (IP) have been key in the design of algorithms for NP-hard high-multiplicity problems since the pioneering work of Gilmore and Gomory [Oper. Res., 1961]. Configuration IPs have a variable for each possible…
We present a new multi-layer peeling technique to cluster points in a metric space. A well-known non-parametric objective is to embed the metric space into a simpler structured metric space such as a line (i.e., Linear Arrangement) or a…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the…
We propose explicitly incorporating large-scale load siting into a stochastic nodal power system capacity expansion planning model that concurrently co-optimizes generation, transmission and storage expansion. The potential operational…
The paper proposes a novel hybrid method for solving equilibrium problems and fixed point problems. By constructing specially cutting-halfspaces, in this algorithm, only an optimization program is solved at each iteration without the…
In this work, we consider a method of searching of the direction of a wireless network development (the places of new access points or base stations etc.) optimized with criteria of coverage of important territories and minimum cost of…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…