Multiple Cuts Research Articles

Accelerating benders decomposition: multiple cuts via multiple solutions

Benders decomposition (BD) is a well-known approach that has been successfully applied to various mathematical programming problems. According to previous studies, slow convergence is the main drawback of this method. In this paper, multi-solution of the master problem has been applied to accelerate the BD algorithm and improve both lower and upper bounds by simultaneously adding multiple feasibility and optimality cuts. A novel integration of Benders cuts was used to prevent the growth of master problem. Computational experiments were applied to a series of logistics facility location problems. Our numerical experiments resulted in a 61% decrease in the total number of iterations and up to 73% reduction in the solution time, confirming the outstanding performance of the proposed method.

Back analysis of the multilayer cylindrical HMA samples – height reduction method

ABSTRACTAlthough the complex modulus is one of the most basic properties used in pavement analysis and design, its accurate measurement for existing pavement layers has always been a challenging task. When samples cut out from the pavement asphalt layers are used for the hot mix asphalt (HMA) complex modulus tests, they are performed separately for each layer. This paper describes an original method for determining the complex moduli of individual asphalt layers. The new idea is tested by applying uniaxial loading–unloading cycle tests to the HMA specimens combined of multiple layers. It was observed that changing the thickness ratios in samples' layers, allows obtaining the sets of load and displacement values (F, u), which effectively enlarge the database needed for the back analysis. For now, the conducted analysis presented in the paper focused on numerical modelling of HMA specimens. The simulated numerical testing conditions were based on viscoelastic parameters of asphalt concrete samples whose values were determined in real laboratory tests. In the case of noisy results of laboratory test simulations with a stochastic Gaussian process, by applying multiple cuts and changing sample's height, the determined values of stiffness moduli of the individual layers do not vary from the reference values by more than 10%.

PCP24 - Projecting survival with cure mixture models: when are the data mature enough for reliable analysis?

Some novel cancer treatments can induce long sustained response leading to prolonged survival, potentially indicating a cure. Projection of overall survival (OS) with these treatments using standard parametric methods – often performed with very early cuts of the trial data – can produce a more rapid projected rate of death than expected. Cure mixture models have been proposed to better capture the full benefit of treatment. These models explicitly account for the possibility of some patients achieving a cure, and estimates the proportion cured that yields the mixture of cancer and non-cancer deaths providing best fit to the data. We use an example based on published survival with over ten years follow-up with immunotherapy for melanoma to illustrate the risks of premature application of cure models. The data show a clear flattening of the OS curve at around 20%, suggesting that the risk of cancer-related deaths has become negligible. We applied cure models and standard parametric fitting analyses on multiple simulated interim cuts of the data at yearly intervals. We found that while the cure model provided best fit to the observed curve, the estimated cure fraction and long term projected OS greatly exaggerated the effect of treatment. The estimated proportion cured aligned with the final observed plateau when the deceleration of mortality was manifested in the data. This highlights the risks of misleading projections with models that otherwise meet the usual evaluation criteria (e.g., fit statistics, close prediction of the data). The shape of the extrapolation and the plausibility of the estimated cure fraction are critical with these methods. With a strong prior belief of the existence of a potential cure, it is tempting to resort to cure models for early projection analyses; our findings suggest a more conservative approach is advisable.

Editorial of the Special Issue on Quantified Self and Personal Informatics

In recent years, we witnessed the spreading of a plethora of wearable and mobile technologies allowing for a continuous and “transparent” gathering of personal data [...]

Two‐stage minimax stochastic unit commitment

The study proposes a stochastic optimisation approach based on discrete scenarios and the minimax criterion to deal with demand uncertainty in the two-stage unit commitment problem. To avoid making an over-conservative decision, the approach is designed to assign a probability-based weight to each demand scenario and provide a unit commitment schedule that minimises the maximum possible-weighted generation cost. Unit commitment is determined in the first stage and the economic dispatch under the scenario that corresponds to the maximum possible-weighted generation cost is determined in the second stage. The problem is formulated as a type of min–max–min mixed integer programming model. By introducing an auxiliary variable, the model is further transformed into a minimisation problem. A Benders decomposition algorithm is developed to solve the problem. The Benders master problem determines the unit commitment decision, while the Benders subproblem determines the dispatch decision. Multiple Benders feasibility cuts are constructed when the Benders subproblem is infeasible. Valid inequalities are derived to improve the lower bound provided by the Benders master problem. Numerical results show the performance of the algorithm.

Conditional value at risk‐based stochastic unit commitment considering the uncertainty of wind power generation

This study presents a risk-averse stochastic unit commitment (SUC) model which considers the loss-of-load risk caused by wind power uncertainty. The expected cost of loss-of-load is usually considered in the conventional scenario-based SUC model. However, even if the expected risk of loss-of-load induced by all wind scenarios is low, the risk induced by some extreme scenarios can be very high. Thus, there is a strong will to better control the risk in these cases with high costs but low probabilities. In this study, the management of loss-of-load risk in worst scenarios is addressed by the conditional value-at-risk (CVaR). The proposed SUC model is built in a mixed-integer linear programming formulation and finally solved by a modified Benders decomposition algorithm with two enhancement strategies (Jensen's inequality and multiple cuts generated from all subproblems). Case studies demonstrate that the loss-of-load cost in extreme scenarios decreases after the inclusion of CVaR in the proposed SUC model. The proposed model can also provide multiple unit commitment schedules with different levels of loss-of-load risk. Using enhancement strategies in Benders decomposition drastically reduces the total number of iterations, verifying the effectiveness of the modified Benders decomposition algorithm.

An automated procedure for geometry creation and finite element mesh generation: Application to explicit grain structure models and machining distortion

Explicit grain structure models within finite element (FE) computational tools are essential for conducting crystal plasticity simulations to elucidate the three-dimensional (3D) topological effects of microstructural evolution on micromechanical fields during plastic deformation. Such full-field framework can predict not only texture evolution but also the development of intra- and inter-granular misorientation, grain shape, and grain boundary character distribution in polycrystalline metals. This paper develops an automated procedure for the geometry creation and FE mesh generation of explicit grain structures to facilitate full-field crystal plasticity modeling of complex shapes other than cuboids. The procedure consists of: (1) generation of a synthetic voxel-based microstructure of cuboidal shapes using the software called digital representation environment for the analysis of microstructure in 3D (DREAM.3D), (2) cutting of the model into a final shape by Boolean operations in Abaqus software, and (3) generation of volume FE mesh for the shaped polycrystalline aggregate using a custom-built toolset involving Patran software. Explicit grain structure FE models for micropillar compression and for microtube forming are created as examples. To further demonstrate the utility and robustness of the automated procedure for making multiple cuts while attaining the state of stress equilibrium after each cut, machining distortion of an Inconel 718 aircraft engine disk is modeled. The starting material for machining had a distribution of bulk residual stresses resulting from prior thermo-mechanical processing. Specifically, turning and broaching operations are carried out using the procedure. During machining, the disk distorts as material is removed, while bulk residual stress fields evolve to reach a new equilibrium. The disk distortion during the material removal is predicted using the developed automated procedure in Abaqus.

Factitious disorder with self inflicted injuries

A 45 year old Bangladeshi female presented with multiple deep cuts and scratch injuries on her body. It was evident from the detail history and observation that the injuries were done by the patient herself. The absences of any obvious external rewards lead to the diagnosis of the factitious disorder. Deception is a key component in both malingering and factitious disorder but in factitious disorder, getting attention or playing the sick role is the only motive.

Performance on the Test of Memory Malingering is predicted by the number of errors on its first 10 items on an inpatient epilepsy monitoring unit

Objective: Performance validity testing is an increasingly vital component of neuropsychological evaluation, though administration of stand-alone performance validity tests (PVTs) can be time-consuming. As the Test of Memory Malingering (TOMM) is among the most commonly used and researched PVTs, much work has focused on creating abbreviated versions while preserving diagnostic accuracy. A recent addition to this effort, errors on the first 10 items of Trial 1 (TOMMe10), was analyzed for its utility in predicting TOMM performance. Method: Subjects were 180 veterans seen on a long-term epilepsy monitoring unit. TOMM learning trials, Word Memory Test (WMT), and WAIS-IV Digit Span (for Reliable Digit Span; RDS) were administered as part of a larger battery. Performance invalidity was classified using established cut scores. Diagnostic classification statistics were calculated predicting TOMM, WMT, and RDS performance, including sensitivity, specificity, receiver operating characteristics (ROC), and positive and negative predictive values for multiple TOMMe10 cut scores. Results: A cut score of ≥2 errors on TOMMe10 yielded the highest sensitivity (.88) while maintaining ≥.90 specificity when predicting TOMM (also supported by ROC analysis). This cut score was also optimal when validated against combinations of PVTs (e.g. two of TOMM, WMT, and RDS; WMT and/or RDS). Conclusions: TOMMe10 shows great promise in predicting future TOMM performance. In settings where time with patients is at a premium, ≥2 errors on TOMMe10 may be used as an early TOMM discontinue criteria, allowing examiners to use their limited time more effectively. The use of TOMMe10 in settings with varying TOMM failure base rates was discussed.

A Reliable and Efficient Approach to Numerically Controlled Programming Optimization for Multiple Largest Tools Cutting Blisks Patch by Patch in the Blisks' Four-Axis Rough Machining

As an important component of gas turbine engines, a blisk (or an axial compressor) is complex in shape. The pressure and suction surfaces of the blisk blades are designed with free-form surfaces, and the space (or the channel) between two adjacent blades varies significantly. Thus, some blade patches can be machined with large-diameter cutters, and some patches have to be cut with small-diameter cutters. Usually, the blisk's material is high-strength stainless steel, titanium alloy, or difficult-to-cut material. The cutting force and temperature in roughing the blisks are high, and thus, the machine tool should be rigid and the cutters should be as large as possible. Therefore, the best industrial practice of rough-machining the blisks is to use multiple largest solid and indexable end-mills to cut them patch by patch on a four-axis computer numerically controlled (CNC) machine. The reasons are (a) four-axis CNC machines are more rigid than five-axis CNC machines, (b) multiple largest cutters are used for higher cutting speeds and feed rates and for less machining time and longer tool life, and (c) if indexable end-mills can be used, the tooling costs are further reduced. For the blisk finishing, a small cutter is often used on a five-axis CNC machine, which is not a topic of this work. However, due to complex shape of the blades, it is quite difficult to automatically optimize the blade surface partition so that each surface patch can be cut with a largest cutter in four-axis blisk rough machining. In the conventional way, numerically controlled (NC) programmers often employ small-diameter solid end-mills and plan their paths to cut the blades layer by layer in four-axis milling. Unfortunately, the machining efficiency of this way is low, and the end-mills wear out quickly. This work establishes a theoretical and completed solution. A simplified optimization model of the largest allowable diameter of the theoretical cutter at a cutter contact (CC) point is established, and an efficient and reliable solver is proposed. The blade surfaces are automated partitioned for largest cutters to the surfaces patch by patch in four-axis rough machining. This approach is efficient and reliable, and it is viable in theory and practical in industry.

Block spectral clustering for multiple graphs with inter-relation

Clustering methods for multiple graphs explore and exploit multiple graphs simultaneously to obtain a more accurate and robust partition of the data than that using single graph clustering methods. In this paper, we study the clustering of multiple graphs with inter-relation among vertices in different graphs. The main contribution is to propose and develop a block spectral clustering method for multiple graphs with inter-relation. Our idea is to construct a block Laplacian matrix for multiple graphs and make use of its eigenvectors to perform clustering very efficiently. Global optimal solutions are obtained in the proposed method and they are solutions of relaxation of multiple graphs ratio cut and normalized cut problems. In contrast, existing clustering methods cannot guarantee optimal solutions and their solutions are dependent on initial guesses. Experimental results on both synthetic and real-world data sets are given to demonstrate that the clustering accuracy achieved and computational time required by the proposed block clustering method are better than those by the testing clustering methods in the literature.

Rate of Convergence of the Bundle Method

The number of iterations needed by the bundle method for nonsmooth optimization to achieve a specified solution accuracy can be bounded by the product of the inverse of the accuracy and its logarithm, if the function is strongly convex. The result is true for the versions of the method with multiple cuts and with cut aggregation.

Scenario-based modeling for multiple allocation hub location problem under disruption risk: multiple cuts Benders decomposition approach

The hub location problem arises in a variety of domains such as transportation and telecommunication systems. In many real-world situations, hub facilities are subject to disruption. This paper deals with the multiple allocation hub location problem in the presence of facilities failure. To model the problem, a two-stage stochastic formulation is developed. In the proposed model, the number of scenarios grows exponentially with the number of facilities. To alleviate this issue, two approaches are applied simultaneously. The first approach is to apply sample average approximation to approximate the two stochastic problem via sampling. Then, by applying the multiple cuts Benders decomposition approach, computational performance is enhanced. Numerical studies show the effective performance of the SAA in terms of optimality gap for small problem instances with numerous scenarios. Moreover, performance of multi-cut Benders decomposition is assessed through comparison with the classic version and the computational results reveal the superiority of the multi-cut approach regarding the computational time and number of iterations.

Is percutaneous medial hamstring myofascial lengthening as anatomically effective and safe as the open procedure?

BackgroundMedial hamstring fractional lengthening is commonly performed in children with cerebral palsy (CP) to decrease contracture and/or to improve gait. Percutaneous procedures are gaining more and more popularity, even in the paediatric population, with equivocal results. The purpose of this paper was to determine the efficacy and safety of percutaneous medial hamstring myofascial lengthening (PHL).MethodsThis is a prospective randomised controlled trial including 31 knees from 18 consecutive patients with CP scheduled for medial hamstring lengthening in the setting of multilevel tendon lengthening procedures in a university hospital. Other concomitant lower extremity surgeries were not exclusionary. A first paediatric orthopaedic surgeon executes the PHL at one level, as recently described in the literature. Another surgeon opens and extends the wound to explore what had been cut during the PHL and completes fractional lengthening (OHL) of both the semimembranosus (SM) and semitendinosus (ST) when possible. Popliteal angle (PA) was assessed by a third surgeon immediately before PHL, after PHL and then after OHL, using a goniometer in a standardised reproducible manner. All three surgeons were blinded to the others’ findings. Primary endpoints included ease of performing PHL, the percentage of tendon-fascia/ muscle portion sectioned percutaneously and improvement of PA. Comparison between improvement of PA after PHL and OHL was done using a paired t-test with a 95% confidence interval.ResultsThe first surgeon was at ease in palpating and identifying the semimembranosus tendon before PHL in ten knees only. PHL led to an undesirable cut of the semimembranosus muscle fibres to more than 50% of the muscle section area in eight cases (<50% in 23 cases, between 50% and 75% in eight cases), and of the semitendinosus muscle fibres to more than 50% in all cases (complete rupture in six cases, more than 75% in eight cases and approximately 50% in 17 cases). Mean PA measured 52° pre-operatively and decreased to 40° after PHL. After OHL, the PA averaged 22°. There was a significant difference between the PA value after PHL (M = 40, SD = 11.8) and the PA value after OHL (M = 22, SD = 8.7), p < 0.0001. The gain in PA did not correlate with the extent of semimembranosus muscle divided (p = 0.38) nor with the extent of semitendinosus muscle divided (p = 0.35). No major iatrogenic neurovascular injury was observed.ConclusionsTo the authors’ knowledge, this is the first prospective study concerning the anatomic effects of PHL. Although it is a quick procedure, it is often associated with difficulty by the operating surgeon to identify and evaluate what should be cut percutaneously, leading to abusive injury of the muscle itself rather than the fascia alone. In addition, the gain in PA is statistically less following PHL than following OHL despite undesirable extensive muscle injury following PHL. This may be due to the multiple fascial cuts (fractional lengthening) usually performed in OHL.

Experimental study on high-speed WEDM finishing in steam water mist

In order to further improve the surface quality in high-speed wire electrical discharge machine (HS-WEDM), a new procedure water mist-liquid combined multiple cut (the finishing is in steam water mist) is presented and has been carried out on the contrast experiment to conventional WEDM multi-cutting processing. Experiments were performed under different cutting conditions of pulse duration, peak current, worktable feed, offset, and amount of mist. Based on the single-factor experiment in steam water mist, Cr12MoV was machined with molybdenum wire electrode by adopting face-centered central composite design of response surface methodology (RSM). Analysis of variance (ANOVA) was applied to investigate the influence of process parameters and their interactions. Further, a mathematical model has been formulated in order to estimate the machining characteristics. When first cut was performed in emulsion, second cut was performed in steam water mist, and third cut was done in atmosphere, the surface roughness is improved compared with conventional WEDM.

Lipoinjection and Multiple Internal Cuts for Congenital Constriction Bands: A New Treatment Approach

BackgroundTraditional treatment for a congenital constriction band of the limb involves multiple Z-plasties and W-plasties. We propose an alternative surgical procedure for the treatment of congenital constriction bands that obviates the need for Z-plasties and eliminates the constriction band.MethodsWe present the case of a 36-year-old woman with a congenital constriction band of the leg. Using a minimally invasive approach, the skin segment that included the band was dissected from the deep tissues. Afterwards, multiple slices were performed on the internal surface of the fibrous ring. This and lipoinjection were used to reverse the depression that characterizes the “hourglass sign” and homogenize the skin surface.ResultsResults have remained stable in a follow-up period of 18 months.ConclusionsThis surgical alternative can be considered as an option for the treatment of congenital constriction bands. It is a safe, reproducible procedure that does not cause additional scars and has good functional and aesthetic results.Level of evidence VThis journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266.

Is the percutaneous myofascial lengthening of the hamstrings as effective and simple as open surgery?

Medial hamstring fractional lengthening is commonly performed in children with cerebral palsy (CP). Percutaneous procedures are gaining more and more popularity even in the pediatric population with equivocal results. The purpose was to determine the efficacy and safety of percutaneous medial hamstring myofascial lengthening (PHL). This is a cross-over randomized controlled trial, including 31 consecutive knees from 18 patients with cerebral palsy (CP) scheduled for medial hamstring tenotomy in the setting of multilevel tendon lengthening procedures in a university hospital. Other concomitant lower extremity surgeries were not exclusionary. A first pediatric orthopedic surgeon executes the percutaneous medial hamstrings presumed myofascial lengthening (PHL) at one level as recently described in the literature. Another surgeon opens and extends the wound to explore what had been cut during the PHL, and completes fractional lengthening (OHL) of both semi-membranosus (SM) and semi-tendinosus (ST) when possible. Popliteal angle (PA) was assessed by a third surgeon immediately before PHL, after PHL, and then after OHL, using a goniometer, in a standardized reproducible manner. All 3 surgeons were blinded to the others’ findings. Primary endpoints included easiness to perform PHL, the percentage of tendon-fascia muscle portion sectioned percutaneously, and improvement of PA. Comparison between PA after PHL and OHL was done using a paired t -test with a 95% confidence interval. The first surgeon was at ease in palpating and identifying through the skin both medial hamstrings before PHL in 10 cases only. PHL led to undesirable cut of the semi-membranosus muscle fibers to more than 50% of the muscle section area in 30 cases ( P P = 0.38) nor with the extent of semi-tendinosus muscle divided ( P = 0.35). No major iatrogenic neurovascular injury was observed. This is the first prospective study concerning the anatomic effects of PHL. This quick procedure is often associated with difficulty to identify and evaluate what should be cut percutaneously, leading to abusive injury of the muscle itself. The gain in PA is statistically less following PHL than following OHL despite undesirable extensive muscle injury following PHL. This may be due to the multiple fascial cuts (fractional lengthening) usually performed in OHL.

Optimum Vegetation Conditions for Successful Establishment of Planted Eastern White Pine (Pinus strobus L.)

The 10th-growing season performance of planted eastern white pine (Pinus strobus L.) seedlings was evaluated in response to herbaceous and woody vegetation control treatments within a clearcut and two variants of the uniform shelterwood regeneration system (single vs. multiple future removal cuts). Herbaceous vegetation control involved the suppression of grasses, forbs, ferns and low shrubs for the first 2 or 4 growing seasons after planting. Deciduous woody vegetation control treatments, conducted in combination with the herbaceous treatments within a response-surface design, involved the permanent removal of all tall shrubs and deciduous trees at the time of planting, at the end of the 2nd or 5th growing seasons, or not at all. In general, the average size of planted pine was related positively to the duration of herbaceous vegetation control and negatively to delays in woody control. White pine weevil (Pissodes strobi Peck) altered these trends, reducing the height of pine on plots with little or no overtopping deciduous woody vegetation or mature tree cover. Where natural pine regeneration occurred on these plots, growth was similar but subordinate to the planted pine. Data from the three sites indicate that at least 60% of planted pine may be expected to reach an age-10 height target of 2.5 m when overtopping cover (residual overstory + regenerating deciduous) is managed at approximately 65% ± 10%, and total herbaceous cover is suppressed to levels not exceeding 50% in the first five years. On productive sites, this combination may be difficult to achieve in a clearcut, and requires fairly rigorous vegetation management in shelterwood regeneration systems. Currently, synthetic herbicides offer the only affordable and effective means of achieving such vegetation control.

Origin and distribution of abnormally high pressure in the Mahanadi Basin, east coast of India

Drilling deep wells in the Mahanadi Basin of the east coast of India is highly challenging because of the variations in pore pressure in the Miocene formations. We have observed that the wells drilled in the northern part of the study area have more drilling hazards due to the presence of high pore pressure (modular dynamic test measurements of up to 18.5 ppg) when compared with wells drilled in the southern part of the basin. In the northern part, pore pressure prediction assuming disequilibrium compaction (DC) underpredicts by approximately 2–3.5 ppg when compared with observed pressures; however, in the southern part, pressure prediction matches the observed pressures in the drilled wells. Analysis of sonic velocity-density crossplots suggests that along with DC, some other secondary mechanism also plays an important role in generating excess overpressure in the northern part of the study area; however, the well data do not indicate the presence of an established secondary mechanism, such as fluid expansion, clay conversion, or cementation. The prime difference between the northern and southern areas is the presence of multiple canyon cuts in the northern part and the observation that very high overpressures occur below these canyon cuts. Hence, an attempt was made to ascertain the relationship between the presence of canyon cuts and the observed high pressure with the help of burial history modeling that incorporates the canyon cut features. Pressure estimation based on this approach closely matches the observed pressures in the drilled wells. This very high overpressure observed in the northern part is most likely generated by the combined effect of porosity rebound (due to overburden removal) along with persistence of overpressures that developed prior to erosion. This burial history modeling approach helps in recognizing and understanding the impact of erosional canyon cut events on generation of excess overpressure in the study area. Furthermore, effective stress methods that take secondary pressure generating mechanisms (unloading) into account are used to quantify the difference in pore pressure.

Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty

We study a risk-averse approach to multistage stochastic linear programming, where the conditional value-at-risk is incorporated into the objective function as the risk measure. We consider five decompositions of the resulting risk-averse model to solve it via the nested L-shaped method. We introduce separate approximations of the mean and the risk measure and also investigate the effectiveness of multiple cuts. As an application, we formulate a water allocation problem by risk-averse multistage programming, which has the advantage of controlling high-risk severe water shortage events. We apply the proposed formulation to the southeastern portion of Tucson, AZ to best use the limited water resources available to that region. In numerical experiments we (1) present a comparative computational study of the risk-averse nested L-shaped variants and (2) analyze the risk-averse approach to the water allocation problem.