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a b s t r a c tThis paper proposes a variant of the well-known capacitated vehicle routing problem that models the routing of vehicles in the cash-in-transit industry by introducing a risk constraint. In the Risk-constrained Cash-inTransit Vehicle Routing Problem (RCTVRP), the risk of being robbed, which is assumed to be proportional both to the amount of cash being carried and the time or the distance covered by the vehicle carrying the cash, is limited by a risk threshold.A library containing two sets of instances for the RCTVRP, some with known optimal solution, is generated. A mathematical formulation is developed and small instances of the problem are solved by using IBM CPLEX.Four constructive heuristics as well as a local search block composed of six local search operators are developed and combined using two different metaheuristic structures: a multistart heuristic and a perturband-improve structure. In a statistical experiment, the best parameter settings for each component are determined, and the resulting heuristic configurations are compared in their best possible setting. The resulting metaheuristics are able to obtain solutions of excellent quality in very limited computing times.

A systematic, elementary and pedagogical approach to a class of soliton equations, and to their spectral formulation, is presented. This approach, based on the use of exponential polynomials, follows naturally from a comparison of some simple results for two representatives of the class: the KdV-and the Boussinesq-equation.

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