In this paper, we address a real problem of packing boxes into a multi-compartment container, in which the boxes must be delivered to customers in a predefined route. This problem arises, for example, in the distribution of beverages (packed in "boxes") by trucks whose container has multiple compartments. The objective is to find a feasible packing plan that minimizes the handling of boxes inside the container along the whole truck route. The following practical constraints must be met: orientation of the boxes, cargo stability, load bearing strength of the boxes and load balancing. To the best of our knowledge, this is the first study focusing on a vehicle packing problem with multi-compartment containers in the context of beverage distribution. To solve this problem, we present a hybrid approach which consists of a heuristic method based on the generation of horizontal layers and on the solution of mixed integer linear programming models. Computational tests were performed with this approach and a large variety of instances based on real data from a soft drink company. The results show that the approach is able to find feasible solutions for all instances considered under all constraints, contrary to what was observed in practice with the manual procedures available in the company. In practice, if a feasible solution is not obtained, it is necessary to change the predefined route plan and/or to consider an additional new delivery route and/or to use a solution that violates some of the constraints involved. In this sense, the proposed solution approach has good potential for being embedded into existing expert and intelligent systems for supporting the decision making process.

This paper deals with the problem of linear gate assignment in two layout styles: one-dimensional logic array and gate matrix layout. The goal is to find the optimal sequencing of gates in order to minimize the required number of tracks, and thus to reduce the overall circuit layout area. This is known to be an NP-hard optimization problem, for which no absolute approximation algorithm exists. Here we report the use of a new optimization heuristic derived from statistical mechanics-the microcanonical optimization algorithm, /spl mu/0-to solve the linear gate assignment problem. Our numerical results show that /spl mu/0 compares favorably with at least five previously employed heuristics: simulated annealing, the unidirectional and the bidirectional Hong construction methods, and the artificial intelligence heuristics GM Plan and GM Learn. We also show how the algorithm is able to outperform microcanonical annealing. Moreover, in a massive set of experiments with circuits whose optimal layout is not known, our algorithm has been able to match and even to improve, by as much as seven tracks, the best solutions known so far.