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Abstract

Taking into account the multimodality of urban transportation networks for computing the itinerary of an individual passenger introduces a number of additional constraints such as mode restrictions and various objective functions. In this paper, constraints on modes are gathered under the concept of viable path, modeled by a non deterministic finite state automaton (NFA). The goal is to find the nondominated viable shortest paths considering the minimization of the travel time and of the number of modal transfers. We show that the problem, initially considered by Lozano and Storchi (2001), is a polynomially-solvable bi-objective variant of the mono-objective regular language-constrained shortest path problem (Barett et al., 2000, Delling et al., 2009). We propose several label setting algorithms for solving the problem: a topological label-setting algorithm improving on algorithms proposed by Pallottino and Scutella (1998) and Lozano and Storchi (2001), a multi-label algorithm using buckets and its bidirectional variant, as well as dedicated goal oriented techniques. Furthermore, we propose a new NFA state-based dominance rule. The computational experiments, carried-out on a realistic urban network, show that the state-based dominance rule associated with bidirectional search yields significant average speed-ups. On an expanded graph comprising 1 859 350 nodes, we obtain on average 3.5 nondominated shortest paths in less than 180 ms.

Abstract

SDMA (Spatial Division Multiple Access) is a principle of radio resource sharing that relies on the division of the space dimension into separated communication channels. SDMA basically relies on adaptive and dynamic beam-forming associated to a clever algorithm in charge of resource allocation. As satellite communication systems move towards an increasing number of users and a larger throughput for each of them, SDMA is one of the most promising techniques that can reach these two goals. This paper studies static Frequency Assignment Problems (FAP) in a satellite communication system involving a gateway connected to a terrestrial network and some user terminals located in a service area. Two scenarios are considered: one based on SDMA and the other based on usual spot coverage. We propose original integer linear programming formulations and greedy allocation algorithms for the FAP which involves unusual cumulative interference constraints. By considering the link budget of each user, the objective is to maximize the number of users that the system can serve. We show through computational experiments on realistic data that the FAP associated with the SDMA system can be solved efficiently, yielding substantial improvement compared to the traditional system.

Abstract

This paper considers the following basic problem in scheduling under uncertainty: given an activity-on-node network where each activity has an uncertain duration represented by an interval, compute the minimum float of each activity over all duration scenarios. For solving this NP-hard problem, Dubois et al. 2005 and Fortin et al. 2010 have recently proposed an algorithm based on path enumeration. In this paper, we establish structural properties of optimal solutions and a new lower bound allowing us to design an efficient branch-and-bound procedure. We also propose two mixed integer programming formulations. The methods are compared experimentally on a large variety of randomly generated problem instances. The results show that the proposed branch-and-bound procedure is very fast and consistently outperforms the MIP formulations and the path enumeration algorithm.

Abstract

In this paper, we focus on the resource-constrained modulo scheduling problem, a general periodic scheduling problem, abstracted from the problem solved by compilers when optimizing inner loops at instruction level for VLIW parallel processors. Heuristic solving scheme have been proposed since many years to solve this problem, among which the decomposed software pipeling method. In this method, a cyclic scheduling problem ignoring resource constraints is first considered and a so-called legal retiming of the operations is issued. Second, a standard acyclic problem, taking this retiming as input, is solved through list scheduling techniques. In this paper, we propose an hybrid approach, which uses the decomposed software pipeling method to obtain a good retiming. Then the obtained retiming is used to build an Integer Linear Programming formulation of reduced size, which allows to solve it exactly. Experimental results show that a lot more problems are solved with this new approach. The gap to the optimal solution is really small (0 or 1%) on all the tested problem instances.

Abstract

Taking into account the multimodality of urban transportation networks for computing the itinerary of an individual passenger introduces a number of additional constraints such as restriction and/or preferences in using some modes. In this paper, such constraints are gathered under the concept of viable path modeled by a deterministic nite state automaton. Several polynomial algorithms are proposed to solve a bi-objective problem where the goal is to find all the nondominated viable shortest paths under the two objectives travel time and number of modal transfers. Among these algorithms, we consider an improved variant of the topological label-setting algorithm provided by Lozano and Storchi (2001), a new multilabel multi-queue algorithm and its bidirectional variant. The different algorithms are compared on a real network. The results show that, on the considered network, the proposed algorithms outperform the Lozano and Storchi (2001) algorithm, both for the time-independent and time-dependent case. Finally, A* acceleration techniques are discussed.

Abstract

In this paper we make a comparative study of several mixed integer linear programming (MILP) formulations for resource-constrained project scheduling problems (RCPSPs). First, we present three discrete and continuous time MILP formulations issued from the literature. Second, instead of relying on the traditional discretization of the time horizon, we propose two original MILP formulations for the RCPSP based on the concept of event : the Start/End formulation and the On/Off formulation. These formulations present the advantage of involving fewer variables than the formulations indexed by time. Because the variables of this type of formulations are not function of the time horizon, we have a better capacity to deal with instances of very large scheduling horizon. We also illustrate our contribution with a series of tests on various types of instances with the three MILP formulations issued from the literature together with our two new formulations, and we draw some conclusions on their use.

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