Solving Vehicle Routing Problems Using Constraint Programming and Lagrangean Relaxation in a Metaheuristics Framework

This paper presents a methodology based on the Variable Neighbourhood Search metaheuristic, applied to the Capacitated Vehicle Routing Problem. The presented approach uses Constraint Programming and Lagrangean Relaxation methods in order to improve algorithm’s efficiency. The complete problem is decomposed into two separated subproblems, to which the mentioned techniques are applied to obtain a complete solution. With this decomposition, the methodology provides a quick initial feasible solution which is rapidly improved by metaheuristics’ iterative process. Constraint Programming and Lagrangean Relaxation are also embedded within this structure to ensure constraints satisfaction and to reduce the calculation burden. By means of the proposed methodology, promising results have been obtained. Remarkable results presented in this paper include a new best-known solution for a rarely solved 200-customers test instance, as well as a better alternative solution for another benchmark problem.

Spermatogenesis in Klinefelter's syndrome

The results of a study of seminal fluid, chromosomal formula and testicular tissue performed on 32 patients with Klinefelter's syndrome are presented. The significance of the microscopic study of seminal fluid in this syndrome is well emphasized. The possible relationship of the histological pattern to spermatogenic function and chromosomal constitution is discussed. Our conclusions are that most patients were azoospermic and the the volume of the ejaculate was low or absent. The decreased density of seminal fluid was the result of the absence of spermatozoa. The seminal pH remained normal during the study. Finally, we consider that cases showing areas of spermatogenesis with spermatozoa might correspond to a gondal mosaicism we have failed to diagnose.