Robustness in multi-objective optimization using evolutionary algorithms

This work discusses robustness assessment during multi-objective optimization with a Multi-Objective Evolutionary Algorithm (MOEA) using a combination of two types of robustness measures. Expectation quantifies simultaneously fitness and robustness, while variance assesses the deviation of the original fitness in the neighborhood of the solution. Possible equations for each type are assessed via application to several benchmark problems and the selection of the most adequate is carried out. Diverse combinations of expectation and variance measures are then linked to a specific MOEA proposed by the authors, their selection being done on the basis of the results produced for various multi-objective benchmark problems. Finally, the combination preferred plus the same MOEA are used successfully to obtain the fittest and most robust Pareto optimal frontiers for a few more complex multi-criteria optimization problems.     

Risk Sensitive Filtering with Poisson Process Observations

In this paper we consider risk sensitive filtering for Poisson process observations. Risk sensitive filtering is a type of robust filtering which offers performance benefits in the presence of uncertainties. We derive a risk sensitive filter for a stochastic system where the signal variable has dynamics described by a diffusion equation and determines the rate function for an observation process. The filtering equations are stochastic integral equations. Computer simulations are presented to demonstrate the performance gain for the risk sensitive filter compared with the risk neutral filter. Accepted 23 July 1999     

稳健宽带波束形成器设计的低阶统计量法*

由于传声器阵列通常对阵元失配误差较为敏感,因此稳健波束形成器的设计已成为传声器阵列处理领域的研究热点之一。概率密度法是目前传声器阵列稳健波束形成器设计中的一类重要方法,但该方法所需的阵元失配误差的概率密度信息在实际中较难获取。针对这一问题,本文研究了基于阵元失配误差低阶统计量的稳健波束形成器设计方法,该方法仅利用在实际中较易获取的阵元失配误差的一阶和二阶统计量信息。本文分别研究了基于阵元失配误差低阶统计量的固定权和变加权最小二乘波束形成器设计,给出了两种波束形成器的相关设计理论。理论和仿真分析表明,在小误差条件下,低阶统计量法所设计的波束形成器仍保持与概率密度法相当的性能。     

Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation

In most multi-objective optimization problems we aim at selecting the most preferred among the generated Pareto optimal solutions (a subjective selection among objectively determined solutions). In this paper we consider the robustness of the selected Pareto optimal solution in relation to perturbations within weights of the objective functions. For this task we design an integrated approach that can be used in multi-objective discrete and continuous problems using a combination of Monte Carlo simulation and optimization. In the proposed method we introduce measures of robustness for Pareto optimal solutions. In this way we can compare them according to their robustness, introducing one more characteristic for the Pareto optimal solution quality. In addition, especially in multi-objective discrete problems, we can detect the most robust Pareto optimal solution among neighboring ones. A computational experiment is designed in order to illustrate the method and its advantages. It is noteworthy that the Augmented Weighted Tchebycheff proved to be much more reliable than the conventional weighted sum method in discrete problems, due to the existence of unsupported Pareto optimal solutions.     

Robustness of networks against cascading failures

Inspired by other related works, this paper proposes a non-linear load-capacity model against cascading failures, which is more suitable for real networks. The simulation was executed on the B-A scale-free network, E-R random network, Internet AS level network, and the power grid of the western United States. The results show that the model is feasible and effective. By studying the relationship between network cost and robustness, we find that the model can defend against cascading failures better and requires a lower investment cost when higher robustness is required.     

Glucose biosensor based on the layer-by-layer self-assembling of glucose oxidase and chitosan derivatives on a thiolated gold surface

This work examines in deep the analytical performance of an example of “first-generation” microdevices: capillary electrophoresis microchip (CE) with end-channel electrochemical detection (ED). A hydroquinone and arbutin separation strategically chosen as route involving pharmaceutical-clinical testing, public safety and food control scenes was carried out. The reproducibility of the unpinched electrokinetic protocol was carefully studied and the technical possibility of working indiscriminately and/or sequentially with both simple cross-injectors was also demonstrated using a real sample (R.S.D.'s less than 7%). The robustness of the injection protocol allowed checking the state of the microchip/detector coupling and following the extraction efficiency of the analyte from real sample. Separation variables such as pH, ionic strength and, separation voltage were also carefully assayed and optimized. Analyte screening was performed using borate buffer (pH 9, 60 mM) in less than 180 s in the samples studied improving dramatically the analysis times used for the same analytes on a conventional scale (15 min), with good precision (R.S.D.'s ranging 5-10%), accuracy (recoveries ranging 90-110%) and acceptable resolution (Rs ≥ 1.0).In addition, the excellent analytical performance of the overall analytical method indicated the quality of the whole analytical microsystem and allowed to introduce the definition of robustness for methodologies developed into the “lab-on-a-chip” scene.     

Robustness study of a reversed-phase liquid chromatographic method for the analysis of carboxylic acids in industrial reaction mixtures

The robustness study of the reversed-phase liquid chromatographic method developed for the quantitative analysis of carboxylic acids is a real asset to prepare method transfer because it provides an indication of its reliability during routine use. Indeed, it was possible to predict the consequences of small variations in operating conditions on the responses. The design of experiments approach was applied to model the effects and interactions of a high number of factors varying simultaneously with a limited number of runs. First we identified the factors which potentially affect the chromatographic responses used for carboxylic acids quantitation: detection wavelength (λ), column temperature (T), acetonitrile ratio in mobile phase (Me), duration of the plateau before the gradient (L) and gradient slope (S). Then we estimated the order of magnitude of realistic variations to assign factor levels. Finally a central composite design was carried out around the nominal conditions defined during method optimization. The statistical treatment of responses (retention factors, and concentrations) showed that the column temperature, the acetonitrile ratio in the mobile phase, the duration of the plateau before the gradient and the gradient slope were the most influent factors. The building of the robust domain from response-surfaces allowed us to give tolerance limits for the factors (216 nm < λ < 222 nm, 49.3 °C < T < 51.4 °C, 4.90% < Me < 5.18%, v/v, 4.5 min < L < 5.4 min, 9% < S < 11%) for which the performances of the method were maintained.     

Determination of ibuprofen and tetrazepam in human urine by micellar electrokinetic capillary chromatography

A new micellar electrokinetic capillary chromatography method (MEKC) is proposed for the determination of ibuprofen and tetrazepam in human urine samples over a concentration range of therapeutic interest. A fused silica capillary (60 cm × 75 μm) is used. Ibuprofen and tetrazepam are detected via UV detection at 220 and 228 nm, respectively. Separation is performed at 25 °C and at a separation voltage of 30 kV, with 15 mM borate buffer (pH 10.2) containing 40 mM sodium dodecylsulfate as the electrolyte solution. Under these conditions the analytes were separated in <11 min. Sulfamethazine is used as an internal standard. Prior to determination, the samples are purified and enriched by means of an extraction–preconcentration step with a preconditioned C₁₈ cartridge and by eluting the compounds with methanol. Good linearity, accuracy, precision, robustness and solution stability were achieved for the technique. Detection limits of 200 μg L⁻¹ for ibuprofen and 300 μg L⁻¹ for tetrazepam were obtained. These analytes were then determined in real urine using the technique.     

Robust portfolio modeling with incomplete cost information and project interdependencies

Robust portfolio modeling (RPM) [Liesiö, J., Mild, P., Salo, A., 2007. Preference programming for robust portfolio modeling and project selection. European Journal of Operational Research 181, 1488–1505] supports project portfolio selection in the presence of multiple evaluation criteria and incomplete information. In this paper, we extend RPM to account for project interdependencies, incomplete cost information and variable budget levels. These extensions lead to a multi-objective zero-one linear programming problem with interval-valued objective function coefficients for which all non-dominated solutions are determined by a tailored algorithm. The extended RPM framework permits more comprehensive modeling of portfolio problems and provides support for advanced benefit–cost analyses. It retains the key features of RPM by providing robust project and portfolio recommendations and by identifying projects on which further attention should be focused. The extended framework is illustrated with an example on product release planning.