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Abstract:The vehicle routing problem with time windows (VRPTW) is an extension of the well-known vehicle routing problem with a central depot. The objective is to design an optimal set of routes that services all customers and satisfies the given constraints, especially the time window constraints.The objective function considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance minimization (secondary criterion). In this paper, two evolution strategies for solving the VRPTW are proposed. The evolution strategies were tested on 58 problems from the literature with sizes varying from 100 to 417 customers and 2 to 54 vehicles. The generated new best known solutions indicate that evolution strategies are effective in reducing both the number of vehicles and the total travel distance.

This paper presents a parallel tabu search algorithm for the container loading problem with a single container to be loaded. The emphasis is on the case of a weakly heterogeneous load. The distributed-parallel approach is based on the concept of multi-search threads according to Toulouse et al. [Issues in designing parallel and distributed search algorithms for discrete optimization problems, Publication CRT-96-36, Centre de recherche sur les transports, Universit e ede Montr e eal, Canada, 1996] i.e., several search paths are investigated concurrently. The parallel searches are carried out by differently configured instances of a tabu search algorithm, which cooperate by the exchange of (best) solutions at the end of defined search phases. The parallel search processes are executed on a corresponding number of LAN workstations. The efficiency of the parallel tabu search algorithm is demonstrated by an extensive comparative test including well-known reference problems and loading procedures from other authors.

This paper presents a parallel genetic algorithm (PGA) for the container loading problem with a single container to be loaded. The emphasis is on the case of a strongly heterogeneous load. The PGA follows a migration model. Several separate sub-populations are subjected to an evolutionary process independently of each other. At the same time the best individuals are exchanged between the sub-populations. The evolution of the different sub-populations is carried out on a corresponding number of LAN workstations. The quality of the PGA is demonstrated by an extensive comparative test including well-known reference problems and loading procedures from other authors.

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The paper presents a genetic algorithm (GA) for the container loading problem. The main ideas of the approach are first to generate a set of disjunctive box towers and second to arrange the box towers on the floor of the container according to a given optimization criterion. The loading problem may include different practical constraints. The performance of the GA is demonstrated by a numerical test comparing the GA and several other procedures for the container loading problem.

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