A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem

We present a column generation algorithm for solving the bi-objective multi-commodity minimum cost flow problem. This method is based on the bi-objective simplex method and Dantzig–Wolfe decomposition. The method is initialised by optimising the problem with respect to the first objective, a single objective multi-commodity flow problem, which is solved using Dantzig–Wolfe decomposition. Then, similar to the bi-objective simplex method, our algorithm iteratively moves from one non-dominated extreme point to the next one by finding entering variables with the maximum ratio of improvement of the second objective over deterioration of the first objective. Our method reformulates the problem into a bi-objective master problem over a set of capacity constraints and several single objective linear fractional sub-problems each over a set of network flow conservation constraints. The master problem iteratively updates cost coefficients for the fractional sub-problems. Based on these cost coefficients an optimal solution of each sub-problem is obtained. The solution with the best ratio objective value out of all sub-problems represents the entering variable for the master basis. The algorithm terminates when there is no entering variable which can improve the second objective by deteriorating the first objective. This implies that all non-dominated extreme points of the original problem are obtained. We report on the performance of the algorithm on several directed bi-objective network instances with different characteristics and different numbers of commodities

Growing Beagles and Foxhound-Boxer-Ingelheim Labrador Retriever mixed breeds show a forelimb-dominated gait and a cranial shift in weight support over time during a kinetic gait analysis

OBJECTIVETo collect kinetic gait reference data of dogs of 2 breeds in their growth period during walking and trotting gait, to describe their development, and to investigate the weight support pattern over time.ANIMALS8 Foxhound-Boxer-Ingelheim Labrador Retriever mixed breeds and 4 Beagles.PROCEDURESGround reaction force variables (GRFs), peak vertical force and vertical impulse, and temporal variables (TVs) derived therefrom; time of occurrence; and stance times were collected. Body weight distribution (BWD) was evaluated. Six measurements, each containing 1 trial in walking and 1 trial in trotting gait, were taken at age 10, 17, 26, 34, 52, and 78 weeks. The study period started July 17, 2013 and lasted until October 7, 2015. Area under the curve with respect to increase was applied. The difference of area under the curve with respect to increase values between breeds and gaits was analyzed using either the t test or the Mann-Whitney test. Generalized mixed linear models were applied.R E SU LTSSignificant differences in gait and breed comparisons were found. Growing dogs showed a forelimb-dominated gait. The development of GRF and TV values over the study period were described.CLINICAL RELEVANCEReference values for GRFs, TVs, and BWDs in growing dogs were given. A cranial shift in weight support over time was found during trotting gait. Smaller, younger dogs walked and trotted more inconsistently

Rapid autologous point-of-care transplantation of the adipose-derived stromal vascular fraction in a dog with cubarthrosis

A 1-year-old shepherd dog was presented in the veterinary hospital due to left-sided cubarthrosis and persisting weight-bearing lameness of the left forelimb after a fragmented coronoid process in the left elbow joint had been removed at the age of 6 months. An autologous point-of-care transplantation of adipose tissue-derived regenerative cells was performed using ARC System (InGeneron, Houston, TX, USA). Pre- and postoperative investigations included orthopaedic and radiographic examinations, gait analyses as well as two owner questionnaires, Liverpool Osteoarthritis in Dogs and Canine Brief Pain Inventory. After 1, 2, 3, 6 and 12 months of treatment, the dog showed an improvement of peak vertical force and vertical impulse in the gait analyses as well as. The Canine Brief Pain Inventory and the Liverpool Osteoarthritis in Dogs revealed an improvement of the quality of life within all further control visits up to 12 months after the therapy

Integrating column generation in a method to compute a discrete representation of the non-dominated set of multi-objective linear programmes

In this paper we propose the integration of column generation in the revised normal boundary intersection (RNBI) approach to compute a representative set of non-dominated points for multi-objective linear programmes (MOLPs). The RNBI approach solves single objective linear programmes, the RNBI subproblems, to project a set of evenly distributed reference points to the non-dominated set of an MOLP. We solve each RNBI subproblem using column generation, which moves the current point in objective space of the MOLP towards the non-dominated set. Since RNBI subproblems may be infeasible, we attempt to detect this infeasibility early. First, a reference point bounding method is proposed to eliminate reference points that lead to infeasible RNBI subproblems. Furthermore, different initialisation approaches for column generation are implemented, including Farkas pricing. We investigate the quality of the representation obtained. To demonstrate the efficacy of the proposed approach, we apply it to an MOLP arising in radiotherapy treatment design. In contrast to conventional optimisation approaches, treatment design using column generation provides deliverable treatment plans, avoiding a segmentation step which deteriorates treatment quality. As a result total monitor units is considerably reduced. We also note that reference point bounding dramatically reduces the number of RNBI subproblems that need to be solved

Considerations for using data envelopment analysis for the assessment of radiotherapy treatment plan quality

Data envelopment analysis (DEA) is a widely used method in operations research for the benchmarking and empirical assessment of productive efficiency. We have previously applied DEA for treatment plan analysis and demonstrated its ability to determine relative plan quality, however considerations regarding the optimal use of DEA were not considered in that work. In the current work we have extended the complexity of the DEA modelling to include an increased number of measures of treatment plan quality as well investigating the best method of accounting for patient geometry. Forty-one IMRT prostate treatment plans were retrospectively analysed using an input-oriented variable returns to scale DEA method. The impacts of DEA weight restrictions were analysed with reference to the ability of DEA to differentiate plan performance at a level of clinical significance. Patient geometry significantly influences plan quality and alternative methods for considering geometry in the DEA model were investigated. In this work we identify how best to use DEA for the relative assessment of prostate treatment plan quality

A matheuristic approach to solve the multi-objective beam angle optimisation problem in intensity modulated radiation therapy

Selecting a suitable set of beam angles is an important but difficult task in intensity modulated radiation therapy (IMRT) for cancer treatment. From a single objective point of view this problem, known as beam angle optimisation (BAO) problem, is solved by finding a beam angle configuration (BAC) that leads to the best dose distribution, according to some objective function. Because there exists a trade-off between the main goals in IMRT (to irradiate the tumour according to some prescription and to avoid surrounding healthy tissue) it makes sense to solve this problem from a multi-objective (MO) point of view. When doing so, a solution of the BAO problem is no longer a single BAC but instead a set of BACs which lead to a set of dose distributions that, depending on both dose prescription and physician preferences, can be selected as the preferred treatment. We solve this MO problem using a two-phase strategy. During the first phase, a deterministic local search algorithm is used to select a set of locally optimal BACs, according to a single objective function. During this search, an optimal dose distribution for each BAC, with respect to the single objective function, is calculated using an exact non-linear programming algorithm. During the second phase a set of non-dominated points is generated for each promising locally optimal BAC and a dominance analysis among them is performed. The output of the procedure is a set of (approximately) efficient BACs that lead to good dose distributions. To demonstrate the viability of the method, the two-phase strategy is applied to a prostate case

Numerical Stability of Path-based Algorithms For Traffic Assignment

In this paper we study numerical stability of path-based algorithms for the traffic assignment problem. These algorithms are based on decomposition of the original problem into smaller sub-problems which are optimised sequentially. Previously, path-based algorithms were numerically tested only in the setting of moderate requirements to the level of solution precision. In this study we analyse convergence of these methods when the convergence measure approaches machine epsilon of IEEE double precision format. In particular, we demonstrate that the straightforward implementation of one of the algorithms of this group (projected gradient) suffers from loss of precision and is not able to converge to highly precise solution. We propose a way to solve this problem and test the proposed adjusted version of the algorithm on various benchmark instances

A Framework for and Empirical Study of Algorithms for Traffic Assignment

Traffic congestion is an issue in most cities worldwide. Transportation engineers and urban planners develop various tra c management projects in order to solve this issue. One way to evaluate such projects is traffic assignment (TA). The goal of TA is to predict the behaviour of road users for a given period of time (morning and evening peaks, for example). Once such a model is created, it can be used to analyse the usage of a road network and to predict the impact of implementing a potential project. The most commonly used TA model is known as user equilibrium, which is based on the assumption that all drivers minimise their travel time or generalised cost. In this study, we consider the static deterministic user equilibrium TA model. The constant growth of road networks and the need of highly precise solutions (required for select link analysis, network design, etc) motivate researchers to propose numerous methods to solve this problem. Our study aims to provide a recommendation on what methods are more suitable depending on available computational resources, time and requirements on the solution. In order to achieve this goal, we implement a flexible software framework that maximises usage of common code and, hence, ensures comparison of algorithms on common ground. In order to identify similarities and differences of the methods, we analyse groups of algorithms that are based on common principles. In addition, we implement and compare several different methods for solving sub-problems and discuss issues related to accumulated numerical errors that might occur when highly accurate solutions are required

Prognostic indicators and outcomes of hospitalised COVID-19 patients with neurological disease: An individual patient data meta-analysis

BACKGROUND: Neurological COVID-19 disease has been reported widely, but published studies often lack information on neurological outcomes and prognostic risk factors. We aimed to describe the spectrum of neurological disease in hospitalised COVID-19 patients; characterise clinical outcomes; and investigate factors associated with a poor outcome. METHODS: We conducted an individual patient data (IPD) meta-analysis of hospitalised patients with neurological COVID-19 disease, using standard case definitions. We invited authors of studies from the first pandemic wave, plus clinicians in the Global COVID-Neuro Network with unpublished data, to contribute. We analysed features associated with poor outcome (moderate to severe disability or death, 3 to 6 on the modified Rankin Scale) using multivariable models. RESULTS: We included 83 studies (31 unpublished) providing IPD for 1979 patients with COVID-19 and acute new-onset neurological disease. Encephalopathy (978 [49%] patients) and cerebrovascular events (506 [26%]) were the most common diagnoses. Respiratory and systemic symptoms preceded neurological features in 93% of patients; one third developed neurological disease after hospital admission. A poor outcome was more common in patients with cerebrovascular events (76% [95% CI 67-82]), than encephalopathy (54% [42-65]). Intensive care use was high (38% [35-41]) overall, and also greater in the cerebrovascular patients. In the cerebrovascular, but not encephalopathic patients, risk factors for poor outcome included breathlessness on admission and elevated D-dimer. Overall, 30-day mortality was 30% [27-32]. The hazard of death was comparatively lower for patients in the WHO European region. INTERPRETATION: Neurological COVID-19 disease poses a considerable burden in terms of disease outcomes and use of hospital resources from prolonged intensive care and inpatient admission; preliminary data suggest these may differ according to WHO regions and country income levels. The different risk factors for encephalopathy and stroke suggest different disease mechanisms which may be amenable to intervention, especially in those who develop neurological symptoms after hospital admission