Scalarizing cost-effective multiobjective optimization algorithms made possible with kriging

The use of kriging in cost-effective single-objective optimization is well established, and a wide variety of different criteria now exist for selecting design vectors to evaluate in the search for the global minimum. Additionly, a large number of methods exist for transforming a multi-objective optimization problem to a single-objective problem. With these two facts in mind, this paper discusses the range of kriging assisted algorithms which are possible (and which remain to be explored) for cost-effective multi-objective optimization

Considerations of Accuracy and Uncertainty with Kriging Surrogate Models in Single-Objective Electromagnetic Design Optimization

The high computational cost of evaluating objective functions in electromagnetic optimal design problems necessitates the use of cost-effective techniques. This paper discusses the use of one popular technique, surrogate modelling, with emphasis placed on the importance of considering both the accuracy of, and uncertainty in, the surrogate model. After briefly reviewing how such considerations have been made in the single-objective optimization of electromagnetic devices, their use with kriging surrogate models is investigated. Traditionally, space-filling experimental designs are used to construct the initial kriging model, with the aim to maximize the accuracy of the initial surrogate model, from which the optimization search will start. Utility functions, which balance the predictions made by this model with its uncertainty, are often used to select the next point to be evaluated. In this paper, the performances of several different utility functions are examined using experimental designs which yield initial kriging models of varying degrees of accuracy. It is found that no advantage is necessarily achieved through searching for optima using utility functions on initial kriging models of higher accuracy, and that a reduction in the total number of objective function evaluations may be achieved by starting the iterative optimization search earlier with utility functions on kriging models of lower accuracy. The implications for electromagnetic optimal design are discussed

A Joint Intensity and Depth Co-Sparse Analysis Model for Depth Map Super-Resolution

High-resolution depth maps can be inferred from low-resolution depth measurements and an additional high-resolution intensity image of the same scene. To that end, we introduce a bimodal co-sparse analysis model, which is able to capture the interdependency of registered intensity and depth information. This model is based on the assumption that the co-supports of corresponding bimodal image structures are aligned when computed by a suitable pair of analysis operators. No analytic form of such operators exist and we propose a method for learning them from a set of registered training signals. This learning process is done offline and returns a bimodal analysis operator that is universally applicable to natural scenes. We use this to exploit the bimodal co-sparse analysis model as a prior for solving inverse problems, which leads to an efficient algorithm for depth map super-resolution.Comment: 13 pages, 4 figure

The consideration of surrogate model accuracy in single-objective electromagnetic design optimization

The computational cost of evaluating the objective function in electromagnetic optimal design problems necessitates the use of cost-effective techniques. This paper describes how one popular technique, surrogate modelling, has been used in the single-objective optimization of electromagnetic devices. Three different types of surrogate model are considered, namely polynomial approximation, artificial neural networks and kriging. The importance of considering surrogate model accuracy is emphasised, and techniques used to improve accuracy for each type of model are discussed. Developments in this area outside the field of electromagnetic design optimization are also mentioned. It is concluded that surrogate model accuracy is an important factor which should be considered during an optimization search, and that developments have been made elsewhere in this area which are yet to be implemented in electromagnetic design optimization

Poor performance of broadleaf plantations and possible remedial silvicultural systems - a review

Peer-reviewedOver the last two decades planting of broadleaves has been part of forest policy. In addition to the provision of a range of ecosystem services, it is intended that this resource will have a direct economic stimulus through the supply of quality hardwood. A number of challenges must be met in order to achieve this objective, particularly as current observations would indicate that many first rotation broadleaf plantations comprise a relatively high proportion of poor quality stems. A literature review has been carried out on the probable causes of poor performance in broadleaf crops. Silvicultural systems to rehabilitate poor quality stands are discussed. Subsequent papers will deal with these silvicultural systems in more detail.COFOR

Probability of improvement methods for constrained multi-objective optimization

This paper shows how the simultaneous consideration of multiple Kriging models can lead to useful metrics for the selection of design vectors in constrained multiobjective optimization. The savings in computational cost with such methods make them particularly useful for optimal electromagnetic design

Balancing Exploration and Exploitation using Kriging Surrogate Models in Electromagnetic Design Optimization

The balance between exploration and exploitation is an important issue when attempting to find the global minimum of an objective function. This paper describes how this balance may be carefully controlled when using Kriging surrogate models to approximate the objective function

Genetic determinants of the response to bezafibrate treatment in the lower extremity arterial disease event reduction (LEADER) trial.

Genetic determinants of baseline levels and the fall in plasma triglyceride and fibrinogen levels in response to bezafibrate treatment were examined in 853 men taking part in the lower extremity arterial disease event reduction (LEADER) trial. Three polymorphisms in the peroxisome proliferator activated receptor alpha (PPARalpha) gene were investigated (L162V, G>A in intron 2 and G>C in intron 7), two in the apolipoprotein CIII (APOC3) gene (-482C>T and -455T>C) and one in the beta-fibrinogen (FIBB) gene (-455G>A). The presence of diabetes (n=158) was associated with 15% higher triglyceride levels at baseline compared to non-diabetics (n=654) (PC substitution. In the non-diabetic patients, the PPARalpha V162 allele was significantly associated with 9% higher baseline triglyceride levels (P<0.03) and a similar, but non-significant trend was seen for the intron 7 polymorphism. Overall, triglyceride levels fell by 26% with 3 months of bezafibrate treatment, and current smokers showed a poorer response compared to ex/non-smokers (23% fall compared to 28% P=0.03), but none of the genotypes examined had a significant influence on the magnitude of response. Carriers of the -455A polymorphism of the FIBB gene had, as expected, marginally higher baseline fibrinogen levels, 3.43 versus 3.36 g/l (P=0.055), but this polymorphism did not affect response to treatment. Overall, fibrinogen levels fell by 12%, with patients with the highest baseline fibrinogen levels showing the greatest decrease in response to bezafibrate. For both the intron 2 and the L162V polymorphisms of the PPARalpha gene there was a significant interaction (both P<0.01) between genotype and baseline levels of fibrinogen on the response of fibrinogen levels to bezafibrate, such that individuals carrying the rare alleles in the lowest tertile showed essentially no overall decrease compared to a 0.18 g/l fall in homozygotes for the common allele. Thus while these genotypes are a minor determinant of baseline triglyceride and fibrinogen levels, there is little evidence from this study that the magnitude of response to bezafibrate treatment in men with peripheral vascular disease is determined by variation at these loci