Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob’ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob’ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

Pulse-front tilt for short-wavelength lasing by means of traveling-wave plasma-excitation

Generation of coherent short-wavelength radiation across a plasma column is dramatically improved under traveling-wave excitation (TWE). The latter is optimized when its propagation is close to the speed of light, which implies small-angle target-irradiation. Yet, short-wavelength lasing needs large irradiation angles in order to increase the optical penetration of the pump into the plasma core. Pulse-front back-tilt is considered to overcome such trade-off. In fact, the TWE speed depends on the pulse-front slope (envelope of amplitude), whereas the optical penetration depth depends on the wave-front slope (envelope of phase). Pulse-front tilt by means of compressor misalignment was found effective only if coupled with a high-magnification front-end imaging/focusing component. It is concluded that speed matching should be accomplished with minimal compressor misalignment and maximal imaging magnification.

Design of nest access grids and perches in front of the nests: Influence on the behavior of laying hens.

In aviary systems for laying hens, it is important to provide suitable nest access platforms in front of the nests, allowing hens to reach and explore each of the nests easily. This access platform is needed to achieve good nest acceptance by the hens and thereby prevent mislaid eggs. In the present experiment, the behavior of hens using 2 different nest access platforms, a plastic grid and 2 wooden perches, was examined. Furthermore, the nests were placed on both sides of the aviary rack (corridor side and outdoor side), either integrated into the aviary rack itself (integrated nest; IN) or placed on the walls of the pens (wall nest; WN), resulting in a 2 × 2 factorial design Four thousand five hundred white laying hens were housed in 20 test pens. The eggs in the nests and mislaid eggs were collected daily, and the behavior of hens on the nest accesses was filmed during wk 25 and 26, using focal observation and scan sampling methods. More balancing, body contact, and agonistic interactions were expected for nests with perches, whereas more walking and nest inspections were expected for nests with grids. There were more mislaid eggs and balancing found in pens equipped with nests with wooden perches. More agonistic interactions and balancing, less standing, and a longer duration of nest inspection were found with the WN compared with the IN. Interactions between platform design and position of the nests were found for duration of nest visits, body contact, and walking, with the highest amount for WN equipped with plastic grids. Nests on the corridor side were favored by the hens. Nest-related behaviors, such as nest inspection, standing, and walking, decreased over time as did the number of hens on the nest accesses, whereas sitting increased. These results indicate that the hens had more difficulties in gripping the perches as designed. The lower number of hens on the nest access platforms in front of IN may be due to a better distribution around nests and tier changes within the aviary rack. Based on these results, grids rather than perches provide for improved nesting behavior.

Redox front geochemistry and weathering: theory with application to the Osamu Utsumi uranium mine, Poços de Caldas, Brazil

Numerical calculations describing weathering of the Poços de Caldas alkaline complex (Minas Gerais, Brazil) by infiltrating groundwater are carried out for time spans up to two million years in the absence of pyrite, and up to 500,000 years with pyrite present. Deposition of uranium resulting from infiltration of oxygenated, uranium bearing groundwater through the hydrothermally altered phonolitic host rock at the Osamu Utsumi uranium mine is also included in the latter calculation. The calculations are based on the quasi-stationary state approximation to mass conservation equations for pure advective transport. This approximation enables the prediction of solute concentrations, mineral abundances and porosity as functions of time and distance over geologic time spans. Mineral reactions are described by kinetic rate laws for both precipitation and dissolution. Homogeneous equilibrium is assumed to be maintained within the aqueous phase. No other constraints are imposed on the calculations other than the initial composition of the unaltered host rock and the composition of the inlet fluid, taken as rainwater modified by percolation through a soil zone. The results are in qualitative agreement with field observations at the Osamu Utsumi uranium mine. They predict a lateritic cover followed by a highly porous saprolitic zone, a zone of oxidized rock with pyrite replaced by iron-hydroxide, a sharp redox front at which uranium is deposited, and the reduced unweathered host rock. Uranium is deposited in a narrow zone located on the reduced side of the redox front in association with pyrite, in agreement with field observations. The calculations predict the formation of a broad dissolution front of primary kaolinite that penetrates deep into the host rock accompanied by the precipitation of secondary illite. Secondary kaolinite occurs in a saprolitic zone near the surface and in the vicinity of the redox front. Gibbsite forms a bi-modal distribution consisting of a maximum near the surface followed by a thin tongue extending downward into the weathered profile in agreement with field observations. The results are found to be insensitive to the kinetic rate constants used to describe mineral reactions.

Outcomes in Advanced Head and Neck Cancer Treated with Up-front Neck Dissection prior to (Chemo)Radiotherapy.

OBJECTIVE Our aim was to compare outcomes with and without up-front neck dissection prior to (chemo)radiotherapy in head and neck squamous cell carcinoma. STUDY DESIGN Case series with chart review. SETTING Tertiary referral center. SUBJECTS AND METHODS Outcomes of oropharyngeal, laryngeal, and hypopharyngeal squamous cell carcinoma cases with neck lymph node metastases treated from January 2001 to March 2012 were analyzed. Due to imbalances in baseline characteristics between groups treated with (n = 129) and without (n = 95) up-front neck dissection, propensity score matching was performed. RESULTS Median follow-up was 48 months (range, 12-148). With up-front neck dissection, the hazard ratio for the primary end point, disease-free survival, was 0.63 (95% confidence interval: 0.37-1.06, P = .08). Up-front neck dissection reduced acute grade ≥3 toxicity significantly when xerostomia was excluded (odds ratio: 0.40, 95% confidence interval: 0.20-0.82, P = .012). CONCLUSION Our results indicate less acute treatment toxicity without any significant difference in terms of oncologic outcome with up-front neck dissection prior to (chemo)radiotherapy as compared with (chemo)radiotherapy alone. Well-designed randomized trials are required to verify this result and further investigate the impact of this strategy on late toxicity and oncologic outcome.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.