Statistical bound of genetic solutions to quadratic assignment problems

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

Analysis of response to enteral infusion of levodopa in patients with Parkinson's disease

Objective: We present a new evaluation of levodopa plasma concentrations and clinical effects during duodenal infusion of a levodopa/carbidopa gel (Duodopa ) in 12 patients with advanced Parkinson s disease (PD), from a study reported previously (Nyholm et al, Clin Neuropharmacol 2003; 26(3): 156-163). One objective was to investigate in what state of PD we can see the greatest benefits with infusion compared with corresponding oral treatment (Sinemet CR). Another objective was to identify fluctuating response to levodopa and correlate to variables related to disease progression. Methods: We have computed mean absolute error (MAE) and mean squared error (MSE) for the clinical rating from -3 (severe parkinsonism) to +3 (severe dyskinesia) as measures of the clinical state over the treatment periods of the study. Standard deviation (SD) of the rating was used as a measure of response fluctuations. Linear regression and visual inspection of graphs were used to estimate relationships between these measures and variables related to disease progression such as years on levodopa (YLD) or unified PD rating scale part II (UPDRS II).Results: We found that MAE for infusion had a strong linear correlation to YLD (r2=0.80) while the corresponding relation for oral treatment looked more sigmoid, particularly for the more advanced patients (YLD>18).