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In this paper, we propose a logic-based Benders decomposition (LBBD), as well as an LBBD/gossip method to solve the heterogeneous multi-vehicle routing problem (HMVRP). HMVRP is a newly formalized extension of the NP-hard multi-traveling salesman problem (mTSP). First, a hybrid algorithm based on LBBD is formulated that decomposes the HMVRP into an assignment problem and a cluster of sequencing problems...
The behavior of a system can be described by a set of operations — sometimes called activities or tasks. The process to specify these operation seems to be a real challenge in various situations, for example when designing automation systems or keeping track of the work at an emergency department. In practice, operation behavior specification is often quite inflexible because every possible execution...
The numerical sensitivity of Linear Matrix Inequalities (LMIs) arising in the H∞ norm computation in discrete time is analyzed. Rapid sampling scenarios are examined comparing both shift and delta operator formulations of the equations. The shift operator formulation is shown in general to be arbitrarily poorly conditioned as the sampling rate increases. The delta operator formulation includes both...
The numerical sensitivity of linear matrix inequalities (LMIs) arising from discrete-time control with short sampling periods is analyzed using shift and delta operators. The delta operator avoids cancellation problems for short sampling periods, and it includes a system scaling proportional to the inverse of the sampling period. The numerical sensitivity of both these mechanisms is investigated analytically,...
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