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This paper addresses the Vehicle Routing Problem with Time Windows (VRPTW) and shows that implementing algorithms for solving various instances of VRPs can significantly reduce transportation costs that occur during the delivery process. Two metaheuristic algorithms were developed for solving VRPTW: Simulated Annealing and Iterated Local Search. Both algorithms generate initial feasible solution using constructive heuristics and use operators and various strategies for an iterative improvement. The algorithms were tested on Solomon’s benchmark problems and real world vehicle routing problems with time windows. In total, 44 real world problems were optimized in the case study using described algorithms. Obtained results showed that the same distribution task can be accomplished with savings up to 40% in the total travelled distance and that manually constructed routes are very ineffective.

When applied to a problem which has more than one local optimal solution, most nonlinear programming algorithms will terminate with the first local solution found. Several methods have been suggested for extending the search to find the global optimum of such a nonlinear program. In this report we present the results of some numerical experiments designed to compare the performance of various strategies for finding the global solution.

En este trabajo se presenta una metodología para reducir las pérdidas de energía en redes primarias de distribución, considerando un algoritmo combinado que involucra la reconfiguración óptima del sistema y el balance de fases. El modelo matemático es no lineal entero mixto, el cual tiene en cuenta los costos de inversión y operación de la red, sujeto a un conjunto de restricciones técnicas impuestas por el sistema. Para solucionar el problema de reconfiguración y balance de fases se emplean los algoritmos Simulated Annealing y Colonia de Hormigas, respectivamente. El algoritmo es comprobado usando el sistema IEEE de 37 nodos.

The paper provides a statistical solution to a very general problem in nonlinear programming. Specifically, it does not make any assumptions about the convexity (or, for that matter, quasiconvexity or pseudo-convexity) of any of the functions involved in the problem. On the other hand, it does not provide a guaranteed global optimum of the objective function, but is confined to the computation of a feasible and 'near optimum' solution, and the computation of confidence limits between which the global optimum is guaranteed to lie with a specified statistical confidence coefficient. (Author)