Sensitivity analysis of the greedy heuristic for binary knapsack problems

Greedy heuristics are a popular choice of heuristics when we have to solve a large variety of NP -hard combinatorial problems. In particular for binary knapsack problems, these heuristics generate good results. If some uncertainty exists beforehand regarding the value of any one element in the problem data, sensitivity analysis procedures can be used to know the tolerance limits within which the value may vary will not cause changes in the output. In this paper we provide a polynomial time characterization of such limits for greedy heuristics on two classes of binary knapsack problems, namely the 0-1 knapsack problem and the subset sum problem. We also study the relation between algorithms to solve knapsack problems and algorithms to solve their sensitivity analysis problems, the conditions under which the sensitivity analysis of the heuristic generates bounds for the toler-ance limits for the optimal solutions, and the empirical behavior of the greedy output when there is a change in the problem data.

Calculation of Stability Radii for Combinatorial Optimization Problems

We present algorithms to calculate the stability radius of optimal or approximate solutions of binary programming problems with a min-sum or min-max objective function. Our algorithms run in polynomial time if the optimization problem itself is polynomially solvable. We also extend our results to the tolerance approach to sensitivity analysis

Calculation of Stability Radii for Combinatorial Optimization Problems

We present algorithms to calculate the stability radius of optimal or approximate solutions of binary programming problems with a min-sum or min-max objective function. Our algorithms run in polynomial time if the optimization problem itself is polynomially solvable. We also extend our results to the tolerance approach to sensitivity analysis.sensitivity analysis;computational complexity;binary programming;postoptimal analysis;stability radius;tolerance approach

Complexity of determining exact tolerances for min-max combinatorial optimization problems

Suppose that we are given an instance of a combinatorial optimization problemwith min-max objective along with an optimal solution for it. Let the cost of asingle element be varied. We refer to the range of values of the element’s costfor which the given optimal solution remains optimal as its exact tolerance. Inthis paper we examine the problem of determining the exact tolerance of eachelement in combinatorial optimization problems with min-max objectives. Weshow that under very weak assumptions, the exact tolerance of each elementcan be determined in polynomial time if and only if the original optimizationproblem can be solved in polynomial time

Association of occupational exposure on semen density in male industrial workers undergoing infertility treatment at tertiary care hospital

Background: Working with particular substances or under certain working situations may cause some workers to experience abnormalities in their sexual or reproductive health. Occupational exposures can lead to infertility, but the workers may not be aware of such problems. The purpose of the study was to determine the association between male infertility and occupation of industrial workers in organized sector.Methods: Prospective case-controlled study that included 136 industrial workers working in organized sector and attending infertility clinic for treatment. This study included male partners aged between 21-46 years with primary or secondary infertility and undertaking same occupation for at least last three months. Complete infertility workup of all male partners attending infertility clinic was done that included detailed history and information related to occupation. Routine semen parameters were evaluated according to the 2010 World Health Organization (WHO) criteria.Results: In the present study, significant semen abnormalities were observed in male partners with age more than 31 years and undertaking arduous jobs for more than 5 years (p <0.05) in study group (n=136) as compared to control group (n=62). The abnormal semen count were observed in 114 (83.2%) workers in the study group that included 43 (31.6%) with total sperm concentration (TSC) less than 10 million/ml and azoospermia in 44 (32.3%). Reduced motility (asthenozoo-spermia) was observed in majority 125 (91.9%) of male partners. The findings were significant (p <0.05) as compared to control group.Conclusions: Preventive measures in the workplace need to be established to reduce the effect of occupational hazards and its influence in the semen parameters ultimately leading to infertility