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. 

On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Changes in Apoptotic Gene Expression Induced by DNA Cross-Linkers

The Millard Research Laboratory is interested in the cytotoxic mechanisms of the bifunctional alkylators diepoxybutane (DEB), epichlorohydrin (ECH), and (1-chloroethenyl) oxirane (COX). Studies performed in the laboratory examine the dual nature of these DNA cross-linking compounds that can act as carcinogens or anti-cancer agents. The mechanisms through which these compounds induce cell death are explored in this study. Cells either undergo cell death due to necrosis or apoptosis. HL-60 cells were treated with varying concentrations of DEB, ECH, or COX. A caspase 3/7 assay was used to test for induction of apoptosis in the treated cells at varying incubation times. It was concluded that DEB induces apoptosis in HL-60 cells treated with 100 μM for 24 hours. Quantitative reverse transcriptase polymerase chain reaction (qRT-PCR) was then used to explore the changes in gene expression of various genes involved in apoptosis signaling. The results were inconclusive as to specific genes involved in DEB induced apoptosis, but the data does suggest that apoptosis is induced by a mitochondrial-mediated apoptosis signaling pathway.