arXiv subjects

Qie He

Publications and source records attributed to Qie He.

5 recordsLinked to original sources

arXiv2022

Repair Crew Routing for Power Distribution Network Restoration

As extreme weather events become more frequent and disruptive, service restoration is increasingly important for many infrastructures, e.g., power grids and communication networks. In many studies on service restoration, the logistics issue of traveling over the road network, however, is often overlooked due to the complexity of considering multiple networks simultaneously, resulting in prolonged disruption time. In this work, we address such a problem arising in power systems, where technical crew and utility trucks travel to a number of sites to repair damaged equipment, with the goal of minimizing the total service disruption time within the service region. We call this problem the Power Restoration Traveling Repairman Problem (PRTRP). What makes it significantly more challenging than a typical routing problem is that the service disruption time in a location depends on the interaction of the routing sequence with both networks, i.e., the road network and the power grid. To solve the problem, we develop an exact method based on bi-directional dynamic programming. We then improve the method by reducing the search space with solution upper and lower bounds, and threshold rules derived from the precedence relations in the power grid. We also propose efficient heuristic variants of the method. We present computational results and compare our method with benchmark heuristics.

math.OC↗

arXiv2020

Optimal switching sequence for switched linear systems

We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of $n\times n$ matrices and an $n$-dimensional vector, find a sequence of $K$ matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the $K$ matrices and the given vector. This simple problem has many applications in operations research and control, yet a moderate-sized instance is challenging to solve to optimality for state-of-the-art optimization software. We propose a simple exact algorithm for this problem. Our algorithm runs in polynomial time when the given set of matrices has the oligo-vertex property, a concept we introduce in this paper for a finite set of matrices. We derive several sufficient conditions for a set of matrices to have the oligo-vertex property. Numerical results demonstrate the clear advantage of our algorithm in solving large-sized instances of the problem over one state-of-the-art global optimization solver. We also propose several open questions on the oligo-vertex property and discuss its potential connection with the finiteness property of a set of matrices, which may be of independent interest.

math.OC↗

arXiv2017

A joint routing and speed optimization problem

Fuel cost contributes to a significant portion of operating cost in cargo transportation. Though classic routing models usually treat fuel cost as input data, fuel consumption heavily depends on the travel speed, which has led to the study of optimizing speeds over a given fixed route. In this paper, we propose a joint routing and speed optimization problem to minimize the total cost, which includes the fuel consumption cost. The only assumption made on the dependence between the fuel cost and travel speed is that it is a strictly convex differentiable function. This problem is very challenging, with medium-sized instances already difficult for a general mixed-integer convex optimization solver. We propose a novel set partitioning formulation and a branch-cut-and-price algorithm to solve this problem. Our algorithm clearly outperforms the off-the-shelf optimization solver, and is able to solve some benchmark instances to optimality for the first time.

math.OC↗

arXiv2016

Optimized Treatment Schedules for Chronic Myeloid Leukemia

Over the past decade, several targeted therapies (e.g. imatinib, dasatinib, nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite an initial response to therapy, drug resistance remains a problem for some CML patients. Recent studies have shown that resistance mutations that preexist treatment can be detected in a substan- tial number of patients, and that this may be associated with eventual treatment failure. One proposed method to extend treatment efficacy is to use a combination of multiple targeted therapies. However, the design of such combination therapies (timing, sequence, etc.) remains an open challenge. In this work we mathematically model the dynamics of CML response to combination therapy and analyze the impact of combination treatment schedules on treatment efficacy in patients with preexisting resistance. We then propose an optimization problem to find the best schedule of multiple therapies based on the evolution of CML according to our ordinary differential equation model. This resulting optimiza- tion problem is nontrivial due to the presence of ordinary different equation constraints and integer variables. Our model also incorporates realistic drug toxicity constraints by tracking the dynamics of patient neutrophil counts in response to therapy. Using realis- tic parameter estimates, we determine optimal combination strategies that maximize time until treatment failure.

q-bio.TO↗

arXiv2016

On the computational complexity of minimum-concave-cost flow in a two-dimensional grid

We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all arcs, and the location of sources and sinks. The concave cost over each arc is assumed to be evaluated through an oracle machine, i.e., the oracle machine returns the cost over an arc in a single computational step, given the flow value and the arc index. We propose an algorithm whose running time is polynomial in the number of columns of the grid, for the following cases: (1) the grid has a constant number of rows, a constant number of different capacities over all arcs, and sources and sinks in at most two rows; (2) the grid has two rows and a constant number of different capacities over all arcs connecting rows; (3) the grid has a constant number of rows and all sources in one row, with infinite capacity over each arc. These are presumably the most general polynomially solvable cases, since we show the problem becomes NP-hard when any condition in these cases is removed. Our results apply to abundant variants and generalizations of the dynamic lot sizing model, and answer several questions raised in serial supply chain optimization.

cs.DS↗