Gino J. Lim

A Capacitated Network Flow Optimization Approach for Short Notice Evacuation Planning

We present a capacity constrained network flow optimization approach for finding evacuation paths, flows and schedules so as to maximize the total evacuees for short notice evacuation planning (SNEP). Due to dynamic nature of this optimization problem, we first construct a time-expanded network that expands the static network over the planning horizon for every time interval. Since the resulting evacuation networks become extremely large to solve, we have developed Evacuation Scheduling Algorithm (ESA) to expedite the solution process. ESA utilizes Dijkstra’s algorithm for finding the evacuation paths and a greedy algorithm for finding the maximum flow of each path and the schedule to execute the flow for each time interval. We show that the complexity of ESA is O(|Nc|·n2)+O(|Nc|·m·T). Numerical experiments show a tremendous advantage of ESA over an exact algorithm (CCEP) in computation time by running up to 41,682 faster than CCEP. In many test network instances, CCEP failed to find a solution within 12hours while ESA converged to a solution in less than 0.03seconds.

Iterative solution methods for beam angle and fluence map optimization in intensity modulated radiation therapy planning

We present computational approaches for optimizing beam angles and fluence maps in Intensity Modulated Radiation Therapy (IMRT) planning. We assume that the number of angles to be used for the treatment is given by the treatment planner. A mixed integer programming (MIP) model and a linear programming (LP) model are used to find an optimal set of beam angles and their corresponding fluence maps. The MIP model is solved using the branch-and-bound method while the LP model is solved using the interior point method. In order to reduce the computational burden for solving the optimization models, we introduce iterative beam angle elimination algorithms in which an insignificant beam angle is eliminated in each iteration. Other techniques are also explored including feasible set reduction for LP and data reduction. Experiments are made to show the computational advantage of the iterative methods for optimizing angles using real patient cases.

An Optimization Framework for Conformal Radiation Treatment Planning

An optimization framework for three-dimensional conformal radiation therapy is presented. In conformal therapy, beams of radiation are applied to a patient from different directions, where the aperture through which the beam is delivered from each direction is chosen to match the shape of the tumor, as viewed from that direction. Wedge filters may be used to produce a gradient in beam intensity across the aperture. Given a set of equispaced beam angles, a mixed-integer linear program can be solved to determine the most effective angles to be used in a treatment plan, the weight (exposure time) to be used for each beam, and the type and orientation of wedges to be used. Practical solution techniques for this problem are described; they include strengthening of the formulation and solution of smaller approximate problems obtained by a reduced parametrization of the treatment region. In addition, techniques for controlling the dose-volume histogram implicitly for various parts of the treatment region using hot-and cold-spot control parameters are presented. Computational results are given that show the effectiveness of the proposed approach on practical data sets.

Uncertainty incorporated beam angle optimization for IMPT treatment planning

PURPOSE Beam angle optimization (BAO) by far remains an important and challenging problem in external beam radiation therapy treatment planning. Conventional BAO algorithms discussed in previous studies all focused on photon-based therapies. Impact of BAO on proton therapy is important while proton therapy increasingly receives great interests. This study focuses on potential benefits of BAO on intensity-modulated proton therapy (IMPT) that recently began available to clinical cancer treatment. METHODS The authors have developed a novel uncertainty incorporated BAO algorithm for IMPT treatment planning in that IMPT plan quality is highly sensitive to uncertainties such as proton range and setup errors. A linear programming was used to optimize robust intensity maps to scenario-based uncertainties for an incident beam angle configuration. Unlike conventional intensity-modulated radiation therapy with photons (IMXT), the search space for IMPT treatment beam angles may be relatively small but optimizing an IMPT plan may require higher computational costs due to larger data size. Therefore, a deterministic local neighborhood search algorithm that only needs a very limited number of plan objective evaluations was used to optimize beam angles in IMPT treatment planning. RESULTS Three prostate cancer cases and two skull base chordoma cases were studied to demonstrate the dosimetric advantages and robustness of optimized beam angles from the proposed BAO algorithm. Two- to four-beam plans were optimized for prostate cases, and two- and three-beam plans were optimized for skull base cases. By comparing plans with conventional two parallel-opposed angles, all plans with optimized angles consistently improved sparing at organs at risks, i.e., rectum and femoral heads for prostate, brainstem for skull base, in either nominal dose distribution or uncertainty-based dose distributions. The efficiency of the BAO algorithm was demonstrated by comparing it with alternative methods including simulated annealing and genetic algorithm. The numbers of IMPT plan objective evaluations required were reduced by up to a factor of 5 while the same optimal angle plans were converged in selected comparisons. CONCLUSIONS Uncertainty incorporated BAO may introduce pronounced improvement of IMPT plan quality including dosimetric benefits and robustness over uncertainties, based on the five clinical studies in this paper. In addition, local search algorithms may be more efficient in finding optimal beam angles than global optimization approaches for IMPT BAO.

Evaluation and mitigation of the interplay effects of intensity modulated proton therapy for lung cancer in a clinical setting

PURPOSE The primary aim of this study was to evaluate the impact of the interplay effects of intensity modulated proton therapy (IMPT) plans for lung cancer in the clinical setting. The secondary aim was to explore the technique of isolayered rescanning to mitigate these interplay effects. METHODS AND MATERIALS A single-fraction 4-dimensional (4D) dynamic dose without considering rescanning (1FX dynamic dose) was used as a metric to determine the magnitude of dosimetric degradation caused by 4D interplay effects. The 1FX dynamic dose was calculated by simulating the machine delivery processes of proton spot scanning on a moving patient, described by 4D computed tomography during IMPT delivery. The dose contributed from an individual spot was fully calculated on the respiratory phase that corresponded to the life span of that spot, and the final dose was accumulated to a reference computed tomography phase by use of deformable image registration. The 1FX dynamic dose was compared with the 4D composite dose. Seven patients with various tumor volumes and motions were selected for study. RESULTS The clinical target volume (CTV) prescription coverage for the 7 patients was 95.04%, 95.38%, 95.39%, 95.24%, 95.65%, 95.90%, and 95.53% when calculated with the 4D composite dose and 89.30%, 94.70%, 85.47%, 94.09%, 79.69%, 91.20%, and 94.19% when calculated with the 1FX dynamic dose. For these 7 patients, the CTV coverage calculated by use of a single-fraction dynamic dose was 95.52%, 95.32%, 96.36%, 95.28%, 94.32%, 95.53%, and 95.78%, with a maximum monitor unit limit value of 0.005. In other words, by increasing the number of delivered spots in each fraction, the degradation of CTV coverage improved up to 14.6%. CONCLUSIONS A single-fraction 4D dynamic dose without rescanning was validated as a surrogate to evaluate the interplay effects of IMPT for lung cancer in the clinical setting. The interplay effects potentially can be mitigated by increasing the amount of isolayered rescanning in each fraction delivery.

Daily scheduling of nurses in operating suites

This article provides a new multi-objective integer programming model for the daily scheduling of nurses in operating suites. The model is designed to assign nurses to different surgery cases based on their specialties and competency levels, subject to a series of hard and soft constraints related to nurse satisfaction, idle time, overtime, and job changes during a shift. To find solutions, two methodologies were developed. The first is based on the idea of a solution pool and the second is a variant of modified goal programming. The model and the solution procedures were validated using real data provided by the University of Texas MD Anderson Cancer Center in Houston, Texas. The results show that the two methodologies can produce schedules that satisfy all demand with 50% less overtime and 50% less idle time when benchmarked against current practice.

An ant colony optimization approach for solving an operating room surgery scheduling problem

We focus on surgery scheduling problem under open scheduling strategy.We consider multiple resources constraints involved in three-stage surgery flow.We propose ACO algorithm with the objective of minimizing makespan.Our ACO is compared with a simulation based scheduling on five test cases.The proposed ACO outperforms in makespan, overtime and balanced resource utilization. Operating room surgery scheduling deals with determining operation start times of surgeries on hand and allocating the required resources to the scheduled surgeries, considering several constraints to ensure a complete surgery flow, the resource availability, and specialties and qualifications of human resources. This task plays a crucial role in providing timely treatments for the patients while ensuring the balance in the hospitals resource utilization. By observing similarities between operating room surgery scheduling and a multi-resource constraint flexible job shop scheduling problem (FJSSP) in manufacturing, this article proposes an Ant Colony Optimization (ACO) approach to efficiently solve such surgery scheduling problems based on the knowledge gained in FJSSP. Numerical experiments are performed on five surgery test cases with different problem sizes and resource availability. The performance of the ACO algorithm was compared against schedules generated by a discrete event system simulation model built in SIMIO on five test cases. The results showed a superior performance of ACO in makespan, overtime, and the variation coefficient of working time.

Solution time reduction techniques of a stochastic dynamic programming approach for hazardous material route selection problem

We use a stochastic dynamic programming (SDP) approach to solve the problem of determining the optimal routing policies in a stochastic dynamic network. Due to its long time for solving SDP, we propose three techniques for pruning stochastic dynamic networks to expedite the process of obtaining optimal routing policies. The techniques include: (1) use of static upper/lower bounds, (2) pre-processing the stochastic dynamic networks by using the start time and origin location of the vehicle, and (3) a mix of pre-processing and upper/lower bounds. Our experiments show that while finding optimal routing policies in stochastic dynamic networks, the last two of the three strategies have a significant computational advantage over conventional SDP. Our main observation from these experiments was that the computational advantage of the pruning strategies that depend on the start time of the vehicle varies according to the time input to the problem. We present the results of this variation in the experiments section. We recommend that while comparing the computational performances of time-dependent techniques, it is very important to test the performance of such strategies at various time inputs.

Reliability analysis of evacuation routes under capacity uncertainty of road links

This article presents a reliability-based evacuation route planning model that seeks to find the relationship between the clearance time, number of evacuation paths, and congestion probability during an evacuation. Most of the existing models for network evacuation assume deterministic capacity estimates for road links without taking into account the uncertainty in capacities induced by myriad external conditions. Only a handful of models exist in the literature that account for capacity uncertainty of road links. A dynamic network–based evacuation model is extended by incorporating probabilistic arc capacity constraints and a minimum-cost network flow problem is formulated that finds a lower bound on the clearance time within the framework of a chance-constrained programming technique. Network breakdown minimization principles for traffic flow in evacuation planning problem are applied and a path-based evacuation routing and scheduling model is formulated. Given the horizon time for evacuation, the model selects the evacuation paths and finds flows on the selected paths that result in the minimum congestion in the network along with the reliability of the evacuation plan. Numerical examples are presented and the effectiveness of the stochastic models in evacuation planning is discussed. It is shown that the reliability-based evacuation plan is conservative compared with plans made using a deterministic model. Stochastic models guarantee that congestion can be avoided with a higher confidence level at the cost of an increased clearance time.

Multi-UAV Pre-Positioning and Routing for Power Network Damage Assessment

This paper presents a two-phase mathematical framework for efficient power network damage assessment using unmanned aerial vehicle (UAV). In the first phase, a two-stage stochastic integer programming optimization model is presented for damage assessment in which the first stage determines the optimal UAV locations anticipating an arrival of an extreme weather event, and the second stage is to adjust the UAV locations, if necessary, when the arrival time of the predicted extreme weather becomes closer with updated information. UAV paths to scan the power network are generated in the second phase to minimize operating costs and final damage assessment completion time of the UAVs. Computational techniques are developed to help reduce the solution time. Numerical experiments show that the proposed stochastic model outperforms the deterministic counterpart in terms of the total UAV pre-positioning setup cost. Additionally, sensitivity analysis discovered the relations among damage assessment time, UAV pre-positioning setup cost, and operating cost.